{
  "openapi": "3.1.0",
  "info": {
    "title": "F-Keys published data",
    "version": "1.0.0",
    "summary": "Read-only static datasets. Not a hosted API.",
    "description": "F-Keys does not run a hosted API. Nothing here takes a parameter, no request\nis authenticated, there are no write operations, and there is no rate limit\nbecause there is no server of ours in the path - every file below is static\nand served from a CDN.\n\nWhat this document describes is the read-only data surface that already\nexists: the published gonzalgo measurement tables, the Kernel Trust Profile\nschema and the profiles conforming to it, and the daily status snapshot. It\nis here so an agent can find those files and know their shape without\nscraping HTML.\n\nEvery path in this specification is generated from a file that exists in the\nrepository. If a dataset is removed, it leaves this document on the next\nbuild rather than remaining as a promise.\n\nEach measurement table is a single JSON object carrying its own name,\ndescription, version, sha256, license and series DOI alongside its rows, so a\nconsumer can cite it and verify it did not change underneath them.\n\nPages on this site also serve `text/markdown` when the request asks for it\nvia `Accept`, per acceptmarkdown.com.\n",
    "contact": {
      "name": "F-Keys",
      "email": "hello@f-keys.com",
      "url": "https://f-keys.com/contact.html"
    },
    "license": {
      "name": "CC BY 4.0",
      "identifier": "CC-BY-4.0"
    }
  },
  "servers": [
    {
      "url": "https://f-keys.com/v1",
      "description": "Version 1. The same documents as the bare paths, under a prefix that carries a promise: what is served here keeps the shape it has today, and a breaking change appears as /v2 while /v1 is served with Deprecation and Sunset headers for 180 days. Responses carry X-API-Version: v1."
    },
    {
      "url": "https://f-keys.com",
      "description": "The same files without the version prefix. Identical bytes; pin on each document's own sha256 or seriesDoi instead of on a path."
    }
  ],
  "externalDocs": {
    "url": "https://f-keys.com/developers.html",
    "description": "Developer resources"
  },
  "tags": [
    {
      "name": "Measurement tables",
      "description": "Published measurements of what formal mathematical libraries rest on. Each table carries its own version, sha256 and series DOI."
    },
    {
      "name": "Status",
      "description": "The daily snapshot behind the status page: uptime, package installs, paper views and aggregate site traffic."
    }
  ],
  "paths": {
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      "get": {
        "summary": "The Choice Strength Table",
        "description": "The 1,528 theorems in Metamath's set.mm whose proofs reach a choice principle, each labelled with the strongest of the three the database declares separately — full choice, countable choice, dependent choice — together with the raw membership in all three. 1528 rows, version 2026-08-12.",
        "operationId": "gonzalgo_choice_strength_choice_strength",
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          "Measurement tables"
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            "description": "The Choice Strength Table",
            "content": {
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                      "properties": {
                        "software": {
                          "type": "string"
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                          "type": "string"
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                        "paper": {
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                        },
                        "theorems": {
                          "type": "integer"
                        },
                        "principles": {
                          "type": "string"
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                      "required": [
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                        "principles",
                        "theorems"
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                          "label"
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                    "rows": {
                      "type": "array",
                      "items": {
                        "type": "object",
                        "properties": {
                          "theorem": {
                            "type": "string",
                            "title": "theorem"
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                          "strongest": {
                            "type": "string",
                            "title": "strongest principle needed"
                          },
                          "reaches_full_choice": {
                            "type": "boolean"
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                          "reaches_countable_choice": {
                            "type": "boolean"
                          },
                          "reaches_dependent_choice": {
                            "type": "boolean"
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                          "axioms_reached": {
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                            "title": "axioms reached"
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                    "seriesDoi",
                    "sha256",
                    "url",
                    "version"
                  ],
                  "title": "The Choice Strength Table",
                  "description": "The 1,528 theorems in Metamath's set.mm whose proofs reach a choice principle, each labelled with the strongest of the three the database declares separately — full choice, countable choice, dependent choice — together with the raw membership in all three. 1528 rows, version 2026-08-12."
                }
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            }
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          "404": {
            "description": "The path does not exist. Returned as JSON when the request asks for it, so an agent does not have to parse an HTML error page.",
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                          "type": "string",
                          "description": "Stable machine-readable identifier."
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                        "status": {
                          "type": "integer"
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                        "path": {
                          "type": "string"
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                        "hints": {
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                      "The full site map is at https://f-keys.com/sitemap.xml",
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    },
    "/gonzalgo/cleanable/cleanable.json": {
      "get": {
        "summary": "The Cleanable Table",
        "description": "Declarations in Lean 4 core, Std, Batteries, Mathlib and Plausible where a rewrite removing a classical dependence was attempted, with the module, the compiler-generated proof term carrying the dependence, the outcome, and the kernel's reason where it refused. 280 rows, version 2026-08-12.",
        "operationId": "gonzalgo_cleanable_cleanable",
        "tags": [
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            "description": "The Cleanable Table",
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                        "acceptance": {
                          "type": "string"
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                          "label"
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                        "properties": {
                          "library": {
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                            "title": "library"
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                          "module": {
                            "type": "string",
                            "title": "module"
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                          "declaration": {
                            "type": "string",
                            "title": "declaration"
                          },
                          "generated_term": {
                            "type": "string"
                          },
                          "occurrences": {
                            "type": "integer",
                            "title": "occurrences"
                          },
                          "outcome": {
                            "type": "string",
                            "title": "outcome"
                          }
                        },
                        "required": [
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                          "generated_term",
                          "library",
                          "module",
                          "occurrences",
                          "outcome"
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                      }
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                    "license",
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                    "name",
                    "producedBy",
                    "rows",
                    "seriesDoi",
                    "sha256",
                    "url",
                    "version"
                  ],
                  "title": "The Cleanable Table",
                  "description": "Declarations in Lean 4 core, Std, Batteries, Mathlib and Plausible where a rewrite removing a classical dependence was attempted, with the module, the compiler-generated proof term carrying the dependence, the outcome, and the kernel's reason where it refused. 280 rows, version 2026-08-12."
                }
              }
            }
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          "404": {
            "description": "The path does not exist. Returned as JSON when the request asks for it, so an agent does not have to parse an HTML error page.",
            "content": {
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                    ]
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              }
            }
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        }
      }
    },
    "/gonzalgo/controlled-tactics/controlled-tactics.json": {
      "get": {
        "summary": "The Controlled Tactic Table",
        "description": "A controlled experiment over Lean tactics. 27 arithmetic goals over Nat and Int, each put to ten tactics, with the axiom set recorded for every cell. Holding the goal fixed and varying only the tactic separates a classical dependence introduced by the proof from one required by the statement. 270 rows, version 2026-08-12.",
        "operationId": "gonzalgo_controlled_tactics_controlled_tactics",
        "tags": [
          "Measurement tables"
        ],
        "responses": {
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            "description": "The Controlled Tactic Table",
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                          "type": "string"
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                            "type": "integer"
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                          "closed": {
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                          "classical": {
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                            "title": "classical"
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                          "axioms": {
                            "type": "string",
                            "title": "axioms"
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                          "closed",
                          "family",
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                    "rows",
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                    "url",
                    "version"
                  ],
                  "title": "The Controlled Tactic Table",
                  "description": "A controlled experiment over Lean tactics. 27 arithmetic goals over Nat and Int, each put to ten tactics, with the axiom set recorded for every cell. Holding the goal fixed and varying only the tactic separates a classical dependence introduced by the proof from one required by the statement. 270 rows, version 2026-08-12."
                }
              }
            }
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          "404": {
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                    "message": "No resource exists at /gonzalgo/nope.json",
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                      "The full site map is at https://f-keys.com/sitemap.xml",
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                    ]
                  }
                }
              }
            }
          }
        }
      }
    },
    "/gonzalgo/dominator-table/dominator-table.json": {
      "get": {
        "summary": "The Dominator Table",
        "description": "Sites of classical dependence in Mathlib ranked by how many theorems each is uniquely responsible for — the number that would stop depending on the axiom of choice if that site alone were rebuilt. Computed as a dominator tree over the reversed dependency graph rooted at the axiom, with chains of constants that free the same theorems collapsed to a single site. 1500 rows, version 2026-08-12.",
        "operationId": "gonzalgo_dominator_table_dominator_table",
        "tags": [
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            "description": "The Dominator Table",
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                          "type": "string"
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                          "site": {
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                          "kind": {
                            "type": "string",
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                          "theorems_dominated": {
                            "type": "integer",
                            "title": "theorems dominated"
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                          "area": {
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                          "eligible": {
                            "type": "boolean",
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                          "chain_length": {
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                            "type": "string"
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                            "type": "integer"
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                  "title": "The Dominator Table",
                  "description": "Sites of classical dependence in Mathlib ranked by how many theorems each is uniquely responsible for — the number that would stop depending on the axiom of choice if that site alone were rebuilt. Computed as a dominator tree over the reversed dependency graph rooted at the axiom, with chains of constants that free the same theorems collapsed to a single site. 1500 rows, version 2026-08-12."
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    "/gonzalgo/entry-points/entry-points.json": {
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        "description": "The 20 largest sites of classical dependence in Mathlib, each with the number of declarations in its dominator subtree that cite a choice primitive directly. Separates sites where the axiom is spent from sites that dominate theorems while inheriting the axiom from further up. 20 rows, version 2026-08-12.",
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        "description": "Kernel-verified substitution attempted against the 20 largest sites of classical dependence in Mathlib. For each declaration: occurrences of Classical.propDecidable in its proof term, how many the harness could reach, how many had a Decidable instance synthesised, and how many produced a term the kernel accepted. 20 rows, version 2026-08-12.",
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