{
  "openapi": "3.1.0",
  "info": {
    "title": "Numora",
    "version": "1.0.0",
    "description": "Pure mathematical computation API for AI agents. 100 endpoints covering statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies — all computations are performed server-side with optimized numerical methods.",
    "x-guidance": "All endpoints accept POST with JSON body. Each endpoint returns { success, result, computation }. Use the computation field to understand what was calculated. All inputs are validated server-side.",
    "contact": {
      "email": "numora@orbonomy.xyz"
    },
    "x-logo": {
      "url": "https://numora.vercel.app/icon.png"
    }
  },
  "paths": {
    "/api/statistics/descriptive": {
      "post": {
        "operationId": "descriptive_statistics_mean_median_mode_std_dev_variance_range_iqr_",
        "summary": "Descriptive statistics (mean, median, mode, std dev, variance, range, IQR)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    },
                    "description": "Numerical dataset"
                  }
                },
                "required": [
                  "data"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/percentile": {
      "post": {
        "operationId": "calculate_percentile_value",
        "summary": "Calculate percentile value",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "p": {
                    "type": "number",
                    "description": "Percentile (0-100)"
                  }
                },
                "required": [
                  "data",
                  "p"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/correlation": {
      "post": {
        "operationId": "pearson_spearman_correlation_between_two_datasets",
        "summary": "Pearson/Spearman correlation between two datasets",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "x": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "y": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "x",
                  "y"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/regression": {
      "post": {
        "operationId": "polynomial_regression_linear_quadratic_etc_",
        "summary": "Polynomial regression (linear, quadratic, etc.)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "x": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "y": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "degree": {
                    "type": "integer",
                    "default": 1
                  }
                },
                "required": [
                  "x",
                  "y"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/ttest": {
      "post": {
        "operationId": "independent_two_sample_t_test",
        "summary": "Independent two-sample t-test",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "sample1": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "sample2": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "sample1",
                  "sample2"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/chisquare": {
      "post": {
        "operationId": "chi_square_goodness_of_fit_test",
        "summary": "Chi-square goodness-of-fit test",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "observed": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "expected": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "observed"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/anova": {
      "post": {
        "operationId": "one_way_anova_test",
        "summary": "One-way ANOVA test",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "groups": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Array of groups"
                  }
                },
                "required": [
                  "groups"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/confidence": {
      "post": {
        "operationId": "confidence_interval",
        "summary": "Confidence interval",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "level": {
                    "type": "number",
                    "description": "Confidence level (e.g., 0.95)"
                  }
                },
                "required": [
                  "data"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/distribution": {
      "post": {
        "operationId": "statistical_distribution_calculations_normal_binomial_poisson_",
        "summary": "Statistical distribution calculations (normal, binomial, poisson)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "type": {
                    "type": "string",
                    "enum": [
                      "normal",
                      "binomial",
                      "poisson",
                      "uniform"
                    ]
                  },
                  "params": {
                    "type": "object"
                  }
                },
                "required": [
                  "type"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/zscore": {
      "post": {
        "operationId": "z_scores_for_dataset",
        "summary": "Z-scores for dataset",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "data"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/outlier": {
      "post": {
        "operationId": "outlier_detection_iqr_or_z_score_method_",
        "summary": "Outlier detection (IQR or z-score method)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "method": {
                    "type": "string",
                    "enum": [
                      "iqr",
                      "zscore"
                    ],
                    "default": "iqr"
                  }
                },
                "required": [
                  "data"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/moving-average": {
      "post": {
        "operationId": "moving_average_sma_ema_wma_",
        "summary": "Moving average (SMA, EMA, WMA)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "window": {
                    "type": "integer"
                  },
                  "type": {
                    "type": "string",
                    "enum": [
                      "sma",
                      "ema",
                      "wma"
                    ],
                    "default": "sma"
                  }
                },
                "required": [
                  "data",
                  "window"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/histogram": {
      "post": {
        "operationId": "histogram_binning",
        "summary": "Histogram binning",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "bins": {
                    "type": "integer",
                    "default": 10
                  }
                },
                "required": [
                  "data"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/sampling": {
      "post": {
        "operationId": "random_sampling_simple_systematic_bootstrap_",
        "summary": "Random sampling (simple, systematic, bootstrap)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "n": {
                    "type": "integer"
                  },
                  "method": {
                    "type": "string",
                    "enum": [
                      "simple",
                      "systematic",
                      "bootstrap"
                    ],
                    "default": "simple"
                  }
                },
                "required": [
                  "data",
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/statistics/hypothesis": {
      "post": {
        "operationId": "general_hypothesis_testing",
        "summary": "General hypothesis testing",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "data": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  },
                  "params": {
                    "type": "object",
                    "description": "Test parameters (mu, alpha, etc.)"
                  }
                },
                "required": [
                  "data"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/compound-interest": {
      "post": {
        "operationId": "compound_interest_calculator",
        "summary": "Compound interest calculator",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "principal": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "periods": {
                    "type": "number"
                  },
                  "compoundsPerYear": {
                    "type": "number",
                    "default": 12
                  }
                },
                "required": [
                  "principal",
                  "rate",
                  "periods"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/simple-interest": {
      "post": {
        "operationId": "simple_interest_calculator",
        "summary": "Simple interest calculator",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "principal": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "periods": {
                    "type": "number"
                  }
                },
                "required": [
                  "principal",
                  "rate",
                  "periods"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/loan-amortization": {
      "post": {
        "operationId": "loan_amortization_schedule",
        "summary": "Loan amortization schedule",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "principal": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "months": {
                    "type": "integer"
                  }
                },
                "required": [
                  "principal",
                  "rate",
                  "months"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/npv": {
      "post": {
        "operationId": "net_present_value",
        "summary": "Net Present Value",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "rate": {
                    "type": "number"
                  },
                  "cashflows": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "rate",
                  "cashflows"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/irr": {
      "post": {
        "operationId": "internal_rate_of_return",
        "summary": "Internal Rate of Return",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "cashflows": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "cashflows"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/bond-price": {
      "post": {
        "operationId": "bond_pricing",
        "summary": "Bond pricing",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "face": {
                    "type": "number"
                  },
                  "coupon": {
                    "type": "number"
                  },
                  "ytm": {
                    "type": "number"
                  },
                  "periods": {
                    "type": "integer"
                  }
                },
                "required": [
                  "face",
                  "coupon",
                  "ytm",
                  "periods"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/bond-yield": {
      "post": {
        "operationId": "bond_yield_to_maturity",
        "summary": "Bond yield to maturity",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "face": {
                    "type": "number"
                  },
                  "price": {
                    "type": "number"
                  },
                  "coupon": {
                    "type": "number"
                  },
                  "periods": {
                    "type": "integer"
                  }
                },
                "required": [
                  "face",
                  "price",
                  "coupon",
                  "periods"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/depreciation": {
      "post": {
        "operationId": "depreciation_straight_line_declining_balance_",
        "summary": "Depreciation (straight-line, declining balance)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "cost": {
                    "type": "number"
                  },
                  "salvage": {
                    "type": "number"
                  },
                  "life": {
                    "type": "integer"
                  },
                  "method": {
                    "type": "string",
                    "enum": [
                      "straight-line",
                      "declining",
                      "sum-of-years"
                    ]
                  }
                },
                "required": [
                  "cost",
                  "salvage",
                  "life"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/roi": {
      "post": {
        "operationId": "return_on_investment",
        "summary": "Return on investment",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "gain": {
                    "type": "number"
                  },
                  "cost": {
                    "type": "number"
                  }
                },
                "required": [
                  "gain",
                  "cost"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/payback": {
      "post": {
        "operationId": "payback_period",
        "summary": "Payback period",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "investment": {
                    "type": "number"
                  },
                  "cashflows": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "investment",
                  "cashflows"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/annuity": {
      "post": {
        "operationId": "annuity_calculations_pv_fv_payment_",
        "summary": "Annuity calculations (PV, FV, payment)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "payment": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "periods": {
                    "type": "integer"
                  },
                  "type": {
                    "type": "string",
                    "enum": [
                      "ordinary",
                      "due"
                    ],
                    "default": "ordinary"
                  }
                },
                "required": [
                  "payment",
                  "rate",
                  "periods"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/mortgage": {
      "post": {
        "operationId": "mortgage_calculator_with_amortization",
        "summary": "Mortgage calculator with amortization",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "principal": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "months": {
                    "type": "integer"
                  }
                },
                "required": [
                  "principal",
                  "rate",
                  "months"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/lease": {
      "post": {
        "operationId": "lease_vs_buy_analysis",
        "summary": "Lease vs buy analysis",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "leaseParams": {
                    "type": "object"
                  },
                  "buyParams": {
                    "type": "object"
                  }
                },
                "required": [
                  "leaseParams",
                  "buyParams"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/break-even": {
      "post": {
        "operationId": "break_even_analysis",
        "summary": "Break-even analysis",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "fixedCosts": {
                    "type": "number"
                  },
                  "pricePerUnit": {
                    "type": "number"
                  },
                  "variableCost": {
                    "type": "number"
                  }
                },
                "required": [
                  "fixedCosts",
                  "pricePerUnit",
                  "variableCost"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
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                    }
                  },
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                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/tax": {
      "post": {
        "operationId": "tax_bracket_calculator",
        "summary": "Tax bracket calculator",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "income": {
                    "type": "number"
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                  "brackets": {
                    "type": "array",
                    "items": {
                      "type": "object"
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                  }
                },
                "required": [
                  "income",
                  "brackets"
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              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
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                  },
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                    "result",
                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/retirement": {
      "post": {
        "operationId": "retirement_savings_projection",
        "summary": "Retirement savings projection",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
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              "schema": {
                "type": "object",
                "properties": {
                  "savings": {
                    "type": "number"
                  },
                  "contribution": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "years": {
                    "type": "integer"
                  }
                },
                "required": [
                  "savings",
                  "contribution",
                  "rate",
                  "years"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
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                    "success": {
                      "type": "boolean",
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                      "type": "string",
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                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/inflation": {
      "post": {
        "operationId": "inflation_adjustment",
        "summary": "Inflation adjustment",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
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              "schema": {
                "type": "object",
                "properties": {
                  "amount": {
                    "type": "number"
                  },
                  "rate": {
                    "type": "number"
                  },
                  "years": {
                    "type": "integer"
                  }
                },
                "required": [
                  "amount",
                  "rate",
                  "years"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
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                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
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                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
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                    }
                  },
                  "required": [
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                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/cagr": {
      "post": {
        "operationId": "compound_annual_growth_rate",
        "summary": "Compound Annual Growth Rate",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "begin": {
                    "type": "number"
                  },
                  "end": {
                    "type": "number"
                  },
                  "years": {
                    "type": "number"
                  }
                },
                "required": [
                  "begin",
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                  "years"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/dividend": {
      "post": {
        "operationId": "dividend_yield_and_ddm_valuation",
        "summary": "Dividend yield and DDM valuation",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "dividend": {
                    "type": "number"
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                  "price": {
                    "type": "number"
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                },
                "required": [
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                  "price"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
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                      "type": "object",
                      "description": "Computation result varies by endpoint"
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                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
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                  },
                  "required": [
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                    "result",
                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/financial/options": {
      "post": {
        "operationId": "black_scholes_option_pricing",
        "summary": "Black-Scholes option pricing",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.050000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
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              "schema": {
                "type": "object",
                "properties": {
                  "S": {
                    "type": "number",
                    "description": "Spot price"
                  },
                  "K": {
                    "type": "number",
                    "description": "Strike price"
                  },
                  "T": {
                    "type": "number",
                    "description": "Time to expiry (years)"
                  },
                  "r": {
                    "type": "number",
                    "description": "Risk-free rate"
                  },
                  "sigma": {
                    "type": "number",
                    "description": "Volatility"
                  },
                  "type": {
                    "type": "string",
                    "enum": [
                      "call",
                      "put"
                    ]
                  }
                },
                "required": [
                  "S",
                  "K",
                  "T",
                  "r",
                  "sigma",
                  "type"
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              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
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                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
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                  },
                  "required": [
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                    "result",
                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/multiply": {
      "post": {
        "operationId": "matrix_multiplication_a_b",
        "summary": "Matrix multiplication A*B",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
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              "schema": {
                "type": "object",
                "properties": {
                  "A": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
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                  "B": {
                    "type": "array",
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                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    }
                  }
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                "required": [
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              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
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                    }
                  },
                  "required": [
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                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/inverse": {
      "post": {
        "operationId": "matrix_inverse",
        "summary": "Matrix inverse",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "A": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
                  }
                },
                "required": [
                  "A"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
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                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/determinant": {
      "post": {
        "operationId": "matrix_determinant",
        "summary": "Matrix determinant",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
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                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
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                },
                "required": [
                  "A"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
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                  },
                  "required": [
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                    "computation"
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              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/eigenvalues": {
      "post": {
        "operationId": "matrix_eigenvalues",
        "summary": "Matrix eigenvalues",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
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              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
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                "type": "object",
                "properties": {
                  "A": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
                  }
                },
                "required": [
                  "A"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
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                  },
                  "required": [
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                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/eigenvectors": {
      "post": {
        "operationId": "matrix_eigenvectors",
        "summary": "Matrix eigenvectors",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "A": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
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                },
                "required": [
                  "A"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
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                      "type": "boolean",
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                    }
                  },
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                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/transpose": {
      "post": {
        "operationId": "matrix_transpose",
        "summary": "Matrix transpose",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "A": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
                  }
                },
                "required": [
                  "A"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
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                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
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                    "result",
                    "computation"
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                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/matrix/rank": {
      "post": {
        "operationId": "matrix_rank",
        "summary": "Matrix rank",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.040000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "A": {
                    "type": "array",
                    "items": {
                      "type": "array",
                      "items": {
                        "type": "number"
                      }
                    },
                    "description": "Matrix (2D array)"
                  }
                },
                "required": [
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                ]
              }
            }
          }
        },
        "responses": {
          "200": {
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            "description": "Invalid input"
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            "description": "Payment Required"
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        "requestBody": {
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            "description": "Invalid input"
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            "description": "Payment Required"
          }
        }
      }
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        "requestBody": {
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            "description": "Payment Required"
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        }
      }
    },
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        "requestBody": {
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        "requestBody": {
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            "description": "Payment Required"
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        }
      }
    },
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      }
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        "requestBody": {
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      }
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        "requestBody": {
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        }
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    },
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    },
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    },
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    },
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          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/prime-factorization": {
      "post": {
        "operationId": "prime_factorization",
        "summary": "Prime factorization",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/gcd-lcm": {
      "post": {
        "operationId": "gcd_and_lcm_of_two_numbers",
        "summary": "GCD and LCM of two numbers",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "a": {
                    "type": "integer"
                  },
                  "b": {
                    "type": "integer"
                  }
                },
                "required": [
                  "a",
                  "b"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/modular-exp": {
      "post": {
        "operationId": "modular_exponentiation_base_exp_mod_m_",
        "summary": "Modular exponentiation (base^exp mod m)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "base": {
                    "type": "integer"
                  },
                  "exp": {
                    "type": "integer"
                  },
                  "mod": {
                    "type": "integer"
                  }
                },
                "required": [
                  "base",
                  "exp",
                  "mod"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/fibonacci": {
      "post": {
        "operationId": "nth_fibonacci_number",
        "summary": "Nth Fibonacci number",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/collatz": {
      "post": {
        "operationId": "collatz_sequence_from_n",
        "summary": "Collatz sequence from n",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/perfect-number": {
      "post": {
        "operationId": "check_if_perfect_number",
        "summary": "Check if perfect number",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/mersenne": {
      "post": {
        "operationId": "mersenne_prime_check_2_p_1_",
        "summary": "Mersenne prime check (2^p - 1)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "exponent": {
                    "type": "integer"
                  }
                },
                "required": [
                  "exponent"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/diophantine": {
      "post": {
        "operationId": "solve_diophantine_equation_ax_by_c",
        "summary": "Solve Diophantine equation ax+by=c",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "a": {
                    "type": "integer"
                  },
                  "b": {
                    "type": "integer"
                  },
                  "c": {
                    "type": "integer"
                  }
                },
                "required": [
                  "a",
                  "b",
                  "c"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/number/continued-fraction": {
      "post": {
        "operationId": "continued_fraction_representation",
        "summary": "Continued fraction representation",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.030000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "x": {
                    "type": "number"
                  },
                  "depth": {
                    "type": "integer",
                    "default": 10
                  }
                },
                "required": [
                  "x"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/fibonacci": {
      "post": {
        "operationId": "generate_fibonacci_sequence",
        "summary": "Generate Fibonacci sequence",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer",
                    "description": "Count of numbers"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/primes": {
      "post": {
        "operationId": "generate_first_n_primes",
        "summary": "Generate first N primes",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/lucas": {
      "post": {
        "operationId": "generate_lucas_numbers",
        "summary": "Generate Lucas numbers",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/catalan": {
      "post": {
        "operationId": "generate_catalan_numbers",
        "summary": "Generate Catalan numbers",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/pascal-triangle": {
      "post": {
        "operationId": "pascal_s_triangle_n_rows_",
        "summary": "Pascal's triangle (N rows)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/bernoulli": {
      "post": {
        "operationId": "generate_bernoulli_numbers",
        "summary": "Generate Bernoulli numbers",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/euler": {
      "post": {
        "operationId": "generate_euler_numbers",
        "summary": "Generate Euler numbers",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/random": {
      "post": {
        "operationId": "random_number_distributions_normal_uniform_poisson_etc_",
        "summary": "Random number distributions (normal, uniform, poisson, etc.)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "type": {
                    "type": "string",
                    "enum": [
                      "normal",
                      "uniform",
                      "poisson",
                      "exponential",
                      "binomial"
                    ]
                  },
                  "params": {
                    "type": "object"
                  },
                  "n": {
                    "type": "integer"
                  }
                },
                "required": [
                  "type",
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/sequence": {
      "post": {
        "operationId": "custom_sequence_generator",
        "summary": "Custom sequence generator",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "rule": {
                    "type": "string",
                    "description": "Recurrence rule (e.g., 'a[n] = 2*a[n-1] + 1')"
                  },
                  "n": {
                    "type": "integer"
                  },
                  "initial": {
                    "type": "array",
                    "items": {
                      "type": "number"
                    }
                  }
                },
                "required": [
                  "rule",
                  "n"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/generate/hash": {
      "post": {
        "operationId": "mathematical_hash_functions",
        "summary": "Mathematical hash functions",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "input": {
                    "type": "string"
                  },
                  "algorithm": {
                    "type": "string",
                    "enum": [
                      "djb2",
                      "fnv1a",
                      "murmur"
                    ],
                    "default": "djb2"
                  }
                },
                "required": [
                  "input"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/length": {
      "post": {
        "operationId": "length_conversion_m_km_mi_ft_in_cm_mm_yd_nm_",
        "summary": "Length conversion (m, km, mi, ft, in, cm, mm, yd, nm)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/weight": {
      "post": {
        "operationId": "weight_conversion_kg_g_lb_oz_ton_mg_st_",
        "summary": "Weight conversion (kg, g, lb, oz, ton, mg, st)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/temperature": {
      "post": {
        "operationId": "temperature_conversion_c_f_k_r_",
        "summary": "Temperature conversion (C, F, K, R)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/volume": {
      "post": {
        "operationId": "volume_conversion_l_ml_gal_qt_pt_cup_fl_oz_m3_cm3_",
        "summary": "Volume conversion (L, mL, gal, qt, pt, cup, fl_oz, m3, cm3)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/area": {
      "post": {
        "operationId": "area_conversion_m2_km2_ft2_mi2_acre_ha_in2_yd2_",
        "summary": "Area conversion (m2, km2, ft2, mi2, acre, ha, in2, yd2)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/speed": {
      "post": {
        "operationId": "speed_conversion_m_s_km_h_mph_kn_ft_s_",
        "summary": "Speed conversion (m/s, km/h, mph, kn, ft/s)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/energy": {
      "post": {
        "operationId": "energy_conversion_j_kj_cal_kcal_wh_kwh_btu_ev_",
        "summary": "Energy conversion (J, kJ, cal, kcal, Wh, kWh, BTU, eV)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/pressure": {
      "post": {
        "operationId": "pressure_conversion_pa_kpa_bar_atm_psi_mmhg_torr_",
        "summary": "Pressure conversion (Pa, kPa, bar, atm, psi, mmHg, torr)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/time": {
      "post": {
        "operationId": "time_conversion_s_ms_min_h_d_wk_mo_yr_",
        "summary": "Time conversion (s, ms, min, h, d, wk, mo, yr)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/data": {
      "post": {
        "operationId": "data_storage_conversion_b_kb_mb_gb_tb_pb_kib_mib_gib_tib_",
        "summary": "Data storage conversion (B, KB, MB, GB, TB, PB, KiB, MiB, GiB, TiB)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    },
    "/api/convert/angle": {
      "post": {
        "operationId": "angle_conversion_deg_rad_grad_arcmin_arcsec_rev_",
        "summary": "Angle conversion (deg, rad, grad, arcmin, arcsec, rev)",
        "x-payment-info": {
          "price": {
            "mode": "fixed",
            "currency": "USD",
            "amount": "0.020000"
          },
          "protocols": [
            {
              "x402": {}
            }
          ]
        },
        "requestBody": {
          "required": true,
          "content": {
            "application/json": {
              "schema": {
                "type": "object",
                "properties": {
                  "value": {
                    "type": "number"
                  },
                  "from": {
                    "type": "string"
                  },
                  "to": {
                    "type": "string"
                  }
                },
                "required": [
                  "value",
                  "from",
                  "to"
                ]
              }
            }
          }
        },
        "responses": {
          "200": {
            "description": "Successful computation",
            "content": {
              "application/json": {
                "schema": {
                  "type": "object",
                  "properties": {
                    "success": {
                      "type": "boolean",
                      "description": "Always true on success"
                    },
                    "result": {
                      "type": "object",
                      "description": "Computation result varies by endpoint"
                    },
                    "computation": {
                      "type": "string",
                      "description": "Human-readable description of what was computed"
                    }
                  },
                  "required": [
                    "success",
                    "result",
                    "computation"
                  ]
                }
              }
            }
          },
          "400": {
            "description": "Invalid input"
          },
          "402": {
            "description": "Payment Required"
          }
        }
      }
    }
  }
}