{"slug":"hunter-consistency-completeness","identifier":"hunter-consistency-completeness","title":"Consistency and Completeness by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"53d97c616c1c1e3268b8200c603e7bdee76d092ce2327c43e3f353043b8859a1","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T21:22:42.854Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:37:56.012Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1"],"units":[{"id":"inference_1","sourceStatement":"{P, P -> Q, Q -> R, R -> S, S -> T} |= (((P & Q) & R) <-> S) -> T","sourceOffset":1916,"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","Q -> R","R -> S","S -> T"],"conclusion":"(((P & Q) & R) <-> S) -> T","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 v3 v4 : Bool) :\n    ((!((((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3)) && ((!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"},{"id":"inference_2","sourceStatement":"{GIT, ~R} |= GIT -> ~P","sourceOffset":5097,"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":["GIT","P","R"],"premises":["GIT","~R"],"conclusion":"GIT -> ~P","status":"countermodel","countermodel":{"GIT":true,"P":true,"R":false},"reason":"The written sequent alone has a countermodel. No authored wording or unstated premise was changed.","kernelStatus":"not_checked"}],"files":{"source.json":{"sha256":"9899e310226f6edb8b2974fe8a6c32824f4964b364b69771d00a5f582e331288","bytes":7323},"Proof.lean":{"sha256":"d3e1951253fc27e214d9e9c670bc6b84fa67002bd5fc496db00e6266df260b86","bytes":586},"lean-check.txt":{"sha256":"283a8aa40f54008e4bfc528069537344fae9f76a8d2f62b37f48d942b98ba62c","bytes":115}},"boundary":"Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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