{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T01:57:22Z",
    "providers": [
      "Claude"
    ],
    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 3,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T10:00:00Z",
      "ingestedAt": "2026-10-06T07:05:24+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "revisions": [
      {
        "at": "2026-10-06T22:46:21+00:00",
        "engine": "codex",
        "fields": [
          "agent_conduct",
          "definition",
          "distinguishing_features"
        ],
        "answering_review": "f0cc479f368e129fcc5b8824af4a0178606b80cdd4eb2b571c8e24779a16a251"
      }
    ],
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-07T10:10:29+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q2654835",
    "registryId": "vr.tr.probable-prime",
    "name": "probable prime",
    "version": "0.2.0-wave.3",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QTY"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q2654835/",
  "model": {
    "registry_id": "vr.tr.probable-prime",
    "name": "probable prime",
    "purpose": "Let an agent define probable primes and the tests that produce them, relay their use in cryptography and record searches, and distinguish probable primes from proven primes and pseudoprimes.",
    "definition": "An integer that satisfies a specified necessary condition for primality, such as a condition checked by a Fermat, Miller-Rabin or Baillie-PSW test, without thereby establishing a proof of primality. Composite numbers that satisfy such conditions are called pseudoprimes relative to the condition used. Passing a necessary condition alone does not establish a high likelihood of primality; confidence depends on the test, its assumptions and how candidates are selected. Probable primes, sometimes called industrial-grade primes, are used in cryptography where the required assurance does not demand a primality proof, and large probable primes such as certain Mersenne and repunit candidates are reported before proofs are available.",
    "what_it_is_for": "Efficient primality assurance in practice.",
    "affordances": [
      "define and explain tests",
      "relay use in cryptography",
      "relay record searches",
      "distinguish from proven primes"
    ],
    "distinguishing_features": [
      "A probable prime satisfies a specified necessary condition for primality.",
      "The assurance provided depends on the test and its assumptions.",
      "Probable-prime tests can offer fast screening.",
      "Probable primes have cryptographic uses.",
      "Passing a probable-prime test is distinct from proving primality."
    ],
    "appearance": "Not a visible object; a number with a test result.",
    "visual_identification": [
      "Integer passing probabilistic primality tests",
      "Fermat, Miller-Rabin, Baillie-PSW probable primes",
      "A proven prime has a certificate; a pseudoprime is a composite that passes"
    ],
    "physical_properties": [
      {
        "quantity": "Miller-Rabin error bound",
        "typical_range": "at most 1/4",
        "unit": "per round",
        "note": "for composites"
      }
    ],
    "families_and_kinds": [
      "Fermat probable primes",
      "strong or Miller-Rabin probable primes",
      "Lucas and Baillie-PSW probable primes",
      "industrial-grade primes in cryptography",
      "large probable primes in record lists"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "positive integer",
        "why": "in registry terms"
      },
      {
        "relation": "is produced by",
        "target": "primality test",
        "why": "such as Miller-Rabin"
      },
      {
        "relation": "is contrasted with",
        "target": "pseudoprime",
        "why": "a composite that passes"
      },
      {
        "relation": "is used in",
        "target": "public-key cryptography",
        "why": "for key generation"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "FIPS 186 and other standards specifying probable prime generation",
      "No regulation of the concept"
    ],
    "failure_modes_and_hazards": [
      "Treating probable as proven",
      "Insufficient test rounds",
      "Adversarial composites against weak tests"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Run primality tests and report which tests were used, their assumptions and any applicable error bounds.",
        "Mark a number as probable prime, not proven prime, until a proof is given."
      ],
      "must_not": [
        "Present a probable prime as proven prime.",
        "Use a test known to be fooled by pseudoprimes, such as a single Fermat base, for security keys.",
        "Accept externally supplied primes for cryptography without independent testing.",
        "Infer high confidence in primality merely from passing an arbitrary necessary condition."
      ],
      "requires_human": [
        "A human must approve prime generation methods for production cryptography."
      ]
    },
    "ethics": {
      "considerations": [
        "Weak primality checks have led to breakable cryptographic keys.",
        "Mathematical records rely on honest distinction between probable and proven."
      ],
      "affected_parties": [
        "Users of cryptographic systems",
        "Mathematicians",
        "Software developers"
      ]
    },
    "owners": {
      "steward": "The public: held in common as mathematical knowledge.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q2654835: probable prime",
      "url": "https://www.wikidata.org/wiki/Q2654835",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Probable prime",
      "url": "https://en.wikipedia.org/wiki/Probable_prime",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "define",
        "name": "Define",
        "description": "Definition.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a probable prime, and how does it differ from a proven prime and a pseudoprime?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about probable primes, proven primes or pseudoprimes?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "tests",
            "name": "Tests",
            "description": "Tests.",
            "findings": [
              {
                "id": "tests-finding",
                "name": "Tests",
                "description": "Tests.",
                "questions": [
                  {
                    "text": "How do Fermat, Miller-Rabin and Baillie-PSW tests work, and what are their error bounds?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the specific test?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "use",
        "name": "Use",
        "description": "Use in practice.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "cryptography",
            "name": "Cryptography",
            "description": "Cryptography.",
            "findings": [
              {
                "id": "cryptography-finding",
                "name": "Cryptography",
                "description": "Cryptography.",
                "questions": [
                  {
                    "text": "How are probable primes generated for keys, and what do standards require?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "records",
            "name": "Records",
            "description": "Record searches.",
            "findings": [
              {
                "id": "records-finding",
                "name": "Records",
                "description": "Records.",
                "questions": [
                  {
                    "text": "What are the largest known probable primes, and how are they later proven?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the information current?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Theory.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "pseudoprimes",
            "name": "Pseudoprimes",
            "description": "Pseudoprimes.",
            "findings": [
              {
                "id": "pseudoprimes-finding",
                "name": "Pseudoprimes",
                "description": "Pseudoprimes.",
                "questions": [
                  {
                    "text": "What pseudoprimes and Carmichael numbers defeat simple tests?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits Carmichael number?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "proof",
            "name": "Proof",
            "description": "Proving primality.",
            "findings": [
              {
                "id": "proof-finding",
                "name": "Proof",
                "description": "Proof.",
                "questions": [
                  {
                    "text": "How do deterministic tests such as AKS and ECPP prove primality?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did probabilistic primality testing develop from Fermat to Rabin and beyond?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of computational number theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "terminology",
            "name": "Terminology",
            "description": "Terminology.",
            "findings": [
              {
                "id": "terminology-finding",
                "name": "Terminology",
                "description": "Terminology.",
                "questions": [
                  {
                    "text": "Where does the term industrial-grade prime come from?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits primality test?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should Miller-Rabin and Baillie-PSW be the primary linked entries?",
    "How should cryptographic standards be linked?",
    "How should record probable primes be recorded?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}