{"slug":"hunter-necessary-correctness-logical-proof","identifier":"hunter-necessary-correctness-logical-proof","title":"Necessary Correctness and Logical Proof","author":"Maclain Hunter","sourceSha256":"3920c930e149b4e496bd7af65a136466b30b514fb41c0841460a5ce4e6ad7323","sourceKind":"authored-foundational-record","recordedAt":"2026-10-03T01:34:26.380Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:40:31.454Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1"],"units":[{"id":"inference_1","sourceStatement":"{P, P <-> Q, P <-> R, Q, Q -> P, P, Q -> R, R, R -> S, T} |= (P & Q) & (R & S) & T","sourceOffset":2107,"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","S","T"],"premises":["P","P <-> Q","P <-> R","Q","Q -> P","P","Q -> R","R","R -> S","T"],"conclusion":"(P & Q) & (R & S) & T","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 v3 v4 : Bool) :\n    ((!(((((((((v0 && (v0 == v1)) && (v0 == v2)) && v1) && ((!v1) || v0)) && v0) && ((!v1) || v2)) && v2) && ((!v2) || v3)) && v4)) || (((v0 && v1) && (v2 && v3)) && v4)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> decide\n#print axioms inference_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"}],"files":{"source.json":{"sha256":"ea2f0c64095ececadd92d1cb5183fdcd1a7671dd3cfddbeb39e770fd33001103","bytes":5753},"Proof.lean":{"sha256":"efe2ad7fb75b829ba8f0bc07b58a8b80ced3a687e3926df50b27c287fa77924d","bytes":621},"lean-check.txt":{"sha256":"283a8aa40f54008e4bfc528069537344fae9f76a8d2f62b37f48d942b98ba62c","bytes":115}},"boundary":"Lean establishes the listed formal statements and dependencies. 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The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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