{ "openapi": "3.1.1", "info": { "title": "Drake Equation Explorer (Monte Carlo) API", "version": "1.0.0", "summary": "How many civilisations? The Drake equation with sourced ranges, Monte Carlo and sensitivity.", "description": "Every endpoint performs the same calculation as the human page and returns inputs, result, units, assumptions, sources, warnings and computedAt. MCP endpoint: /mcp." }, "servers": [ { "url": "https://prooflinedrake.usefulweb.app" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "How many civilisations? The Drake equation with sourced ranges, Monte Carlo and sensitivity.", "description": "Explore the Drake equation N = R* · fp · ne · fl · fi · fc · L with ranges instead of single guesses. The star formation rate, the fraction of stars with planets and the number of habitable-zone rocky planets default to published measurements; life, intelligence, detectability and lifetime are your assumptions. A seeded Monte Carlo gives the median N, the 90 % range, the share of draws with N \u003c 1 and which factor drives the uncertainty. Part of the Proofline math notebook.\n\nMethodology:\n- N = R* · fp · ne · fl · fi · fc · L (Drake, 1961). The lowest and highest possible N multiply the range ends; the central estimate multiplies the geometric middles (log-uniform) or the midpoints (uniform).\n- Monte Carlo: each factor is drawn independently from its range with a seeded mulberry32 generator; the median, the 5 % and 95 % quantiles and the share of draws with N \u003c 1 come from the sorted draws.\n- Sensitivity: log₁₀ N is the sum of the factors’ logarithms, so its variance is the sum of their variances; each factor’s share is exact (log-uniform: (log₁₀ high − log₁₀ low)²/12).\n- Default ranges: R* 0.68–1.65 Sun-like stars per year (Milky Way star formation of 0.68–1.45 and 1.65 ± 0.19 solar masses per year, read as one Sun-like star per solar mass), fp 0.5–1 (microlensing finds about one or more planets per star), ne 0.37–0.88 (Kepler DR25 η⊕ for Sun-like stars); fl, fi, fc and L are wide assumptions because nothing has measured them.\n\nThe Drake equation organises ignorance; it does not measure anything. With unmeasured factors spanning many orders of magnitude, every result mostly mirrors the assumptions.", "tags": [ "apps" ], "x-mcp-tool": "proofline_drake", "x-owner-app": "proofline", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ProoflineDrakeInput" }, "examples": { "example1": { "summary": "Measured astronomy plus wide assumptions (defaults)", "value": {} }, "example2": { "summary": "Drake’s own suggestion: one new civilisation a year, lasting 10,000 years", "value": { "rStar": "1", "fp": "1", "ne": "1", "fl": "1", "fi": "1", "fc": "1", "L": "10000" } }, "example3": { "summary": "Pessimistic biology: life and intelligence are rare", "value": { "fl": "1e-10 - 1e-3", "fi": "1e-6 - 0.01" } }, "example4": { "summary": "Uniform instead of log-uniform sampling", "value": { "distribution": "uniform" } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/ProoflineDrakeResult" } } } }, "400": { "description": "Malformed JSON body.", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "422": { "description": "Invalid input (see errors[]).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "429": { "description": "Rate limit exceeded (see Retry-After).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } } } } }, "/api/v1/tool": { "get": { "operationId": "getToolDefinition", "summary": "Inputs, output schema and examples for this tool", "responses": { "200": { "description": "Tool definition.", "content": { "application/json": { "schema": { "type": "object" } } } } } } } }, "components": { "schemas": { "Problem": { "type": "object", "description": "RFC 9457 problem details. 422 responses include per-field `errors`.", "required": [ "type", "title", "status", "detail" ], "properties": { "type": { "type": "string" }, "title": { "type": "string" }, "status": { "type": "integer" }, "detail": { "type": "string" }, "code": { "type": "string" }, "errors": { "type": "array", "items": { "type": "object", "required": [ "field", "message" ], "properties": { "field": { "type": "string" }, "message": { "type": "string" } } } } } }, "ProoflineDrakeInput": { "type": "object", "additionalProperties": false, "properties": { "rStar": { "title": "R*: Sun-like stars formed per year in the Milky Way", "description": "A value or a range “low - high” (per year). Default from Robitaille \u0026 Whitney 2010; Licquia \u0026 Newman 2015.", "type": "string", "maxLength": 60, "default": "0.68 - 1.65" }, "fp": { "title": "fp: Fraction of those stars with planets", "description": "A value or a range “low - high”. Default from Cassan et al. 2012 (microlensing).", "type": "string", "maxLength": 60, "default": "0.5 - 1" }, "ne": { "title": "ne: Habitable-zone rocky planets per planetary system", "description": "A value or a range “low - high”. Default from Bryson et al. 2021 (Kepler DR25).", "type": "string", "maxLength": 60, "default": "0.37 - 0.88" }, "fl": { "title": "fl: Fraction of those planets where life appears", "description": "A value or a range “low - high”. Default from assumption (no measurement exists).", "type": "string", "maxLength": 60, "default": "0.001 - 1" }, "fi": { "title": "fi: Fraction of life-bearing planets that develop intelligence", "description": "A value or a range “low - high”. Default from assumption (no measurement exists).", "type": "string", "maxLength": 60, "default": "0.001 - 1" }, "fc": { "title": "fc: Fraction of intelligent species that become detectable", "description": "A value or a range “low - high”. Default from assumption (no measurement exists).", "type": "string", "maxLength": 60, "default": "0.01 - 1" }, "L": { "title": "L: Years a civilisation stays detectable", "description": "A value or a range “low - high” (years). Default from assumption (no measurement exists).", "type": "string", "maxLength": 60, "default": "100 - 100000000" }, "distribution": { "title": "Sampling of the ranges", "type": "string", "enum": [ "loguniform", "uniform" ], "default": "loguniform" }, "samples": { "title": "Monte Carlo draws", "type": "integer", "minimum": 1000, "maximum": 1000000, "default": 100000 }, "seed": { "title": "Random seed", "type": "integer", "default": 1 } }, "required": [] }, "ProoflineDrakeResult": { "type": "object", "additionalProperties": false, "required": [ "schemaVersion", "tool", "computedAt", "inputs", "summary", "result", "units", "assumptions", "sources", "warnings", "presentation", "links" ], "properties": { "schemaVersion": { "type": "string", "const": "1.0" }, "tool": { "type": "object", "additionalProperties": false, "required": [ "id", "name", "version" ], "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "version": { "type": "string" } } }, "computedAt": { "type": "string", "format": "date-time" }, "inputs": { "type": "object", "description": "Normalised inputs actually used, including applied defaults." }, "summary": { "type": "string" }, "result": { "type": "object", "additionalProperties": false, "required": [ "factors", "distribution", "samples", "seed", "low", "high", "central", "median", "p5", "p95", "mean", "shareBelowOne", "sensitivity", "histogram" ], "properties": { "factors": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "factor", "symbol", "low", "high", "central", "source", "measured" ], "properties": { "factor": { "type": "string" }, "symbol": { "type": "string" }, "low": { "type": "number" }, "high": { "type": "number" }, "central": { "type": "number" }, "source": { "type": "string" }, "measured": { "type": "boolean" } } } }, "distribution": { "type": "string", "enum": [ "loguniform", "uniform" ] }, "samples": { "type": "integer" }, "seed": { "type": "integer" }, "low": { "type": "number" }, "high": { "type": "number" }, "central": { "type": "number" }, "median": { "type": "number" }, "p5": { "type": "number" }, "p95": { "type": "number" }, "mean": { "type": "number" }, "shareBelowOne": { "type": "number" }, "sensitivity": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "factor", "share" ], "properties": { "factor": { "type": "string" }, "share": { "type": "number" } } } }, "histogram": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "log10From", "log10To", "count" ], "properties": { "log10From": { "type": "number" }, "log10To": { "type": "number" }, "count": { "type": "integer" } } } } } }, "units": { "type": "object", "additionalProperties": { "type": "string" } }, "assumptions": { "type": "array", "items": { "type": "string" } }, "sources": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "title" ], "properties": { "title": { "type": "string" }, "url": { "type": "string" }, "publisher": { "type": "string" }, "retrievedAt": { "type": "string" }, "note": { "type": "string" } } } }, "warnings": { "type": "array", "items": { "type": "string" } }, "presentation": { "type": "array", "items": { "type": "object" }, "description": "Display blocks used by the human page (same data)." }, "links": { "type": "object", "additionalProperties": false, "required": [ "human", "api", "openapi", "methodology" ], "properties": { "human": { "type": "string", "format": "uri" }, "api": { "type": "string", "format": "uri" }, "openapi": { "type": "string", "format": "uri" }, "methodology": { "type": "string", "format": "uri" } } } } } } } }