{"slug":"hunter-proof-god-consistency","identifier":"hunter-proof-god-consistency","title":"Proof, God, and Consistency by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"47b947f1c0e36578e02e0ab662f7ab20ece3352797276b713de470ac2023ed9a","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T16:57:34.985Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:41:15.344Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.inference_2"],"units":[{"id":"inference_1","sourceStatement":"{P, Q, R, P <-> Q, P <-> R, Q <-> P, Q <-> R, R <-> P, R <-> Q, P <-> P, Q <-> Q, R <-> R, P, Q, R} |= (P & Q) & R","sourceOffset":3053,"scope":"Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.","variables":["P","Q","R"],"premises":["P","Q","R","P <-> Q","P <-> R","Q <-> P","Q <-> R","R <-> P","R <-> Q","P <-> P","Q <-> Q","R <-> R","P","Q","R"],"conclusion":"(P & Q) & R","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 : Bool) :\n    ((!((((((((((((((v0 && v1) && v2) && (v0 == v1)) && (v0 == v2)) && (v1 == v0)) && (v1 == v2)) && (v2 == v0)) && (v2 == v1)) && (v0 == v0)) && (v1 == v1)) && (v2 == v2)) && v0) && v1) && v2)) || ((v0 && v1) && v2)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> decide\n#print axioms inference_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"inference_2","sourceStatement":"{P, Q, R, P <-> P, Q <-> Q, R <-> R, P, Q, R} |= (P & Q) & R","sourceOffset":3182,"scope":"Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.","variables":["P","Q","R"],"premises":["P","Q","R","P <-> P","Q <-> Q","R <-> R","P","Q","R"],"conclusion":"(P & Q) & R","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 : Bool) :\n    ((!((((((((v0 && v1) && v2) && (v0 == v0)) && (v1 == v1)) && (v2 == v2)) && v0) && v1) && v2)) || ((v0 && v1) && v2)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> decide\n#print axioms inference_2\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_2"}],"files":{"source.json":{"sha256":"f7be5fed7160e6c84003843b04ec7cf55a08e287df6a53924e7e47793c9b94b0","bytes":9734},"Proof.lean":{"sha256":"f7138d165757b33f8f6437a9e650699536fab15978d4d167d176b44750049a75","bytes":892},"lean-check.txt":{"sha256":"9dd24ecb3d82c309e42e8e914b5df3ec490fd2259644de7d887fca9eeff5dfe5","bytes":174}},"boundary":"Lean establishes the listed formal statements and dependencies. 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