{"slug":"negation-identity-logos-proof","identifier":"negation-identity-logos-proof","title":"Negation, Identity, and Logos by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"5df940f97f0269418a4c17f0c1de664ac22380fa19f0adc70470d110e22d84fd","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T14:05:43.168Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:40:35.292Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.inference_2","HunterAuthored.inference_3","HunterAuthored.inference_4","HunterAuthored.inference_5","HunterAuthored.inference_6","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{A} |= A","sourceOffset":58,"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":["A"],"premises":["A"],"conclusion":"A","status":"candidate","leanStatement":"theorem inference_1 (v0 : Bool) :\n    ((!v0) || v0) = true := by\n  cases v0 <;> decide\n#print axioms inference_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"inference_2","sourceStatement":"{P, D1, D2} |= (P <-> D1) & D2","sourceOffset":1098,"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":["D1","D2","P"],"premises":["P","D1","D2"],"conclusion":"(P <-> D1) & D2","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 : Bool) :\n    ((!((v2 && v0) && v1)) || ((v2 == v0) && v1)) = 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"},{"id":"inference_3","sourceStatement":"{P, D1, D2, A1} |= (P <-> D1) <-> (D1 <-> A1)","sourceOffset":2100,"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":["A1","D1","D2","P"],"premises":["P","D1","D2","A1"],"conclusion":"(P <-> D1) <-> (D1 <-> A1)","status":"candidate","leanStatement":"theorem inference_3 (v0 v1 v2 v3 : Bool) :\n    ((!(((v3 && v1) && v2) && v0)) || ((v3 == v1) == (v1 == v0))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_3\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_3"},{"id":"inference_4","sourceStatement":"{A2 <-> PC} |= (A2 <-> PC)","sourceOffset":2379,"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":["A2","PC"],"premises":["A2 <-> PC"],"conclusion":"(A2 <-> PC)","status":"candidate","leanStatement":"theorem inference_4 (v0 v1 : Bool) :\n    ((!(v0 == v1)) || (v0 == v1)) = true := by\n  cases v0 <;> cases v1 <;> decide\n#print axioms inference_4\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_4"},{"id":"inference_5","sourceStatement":"{P, Q, R, S, T, U} |= ((((P & Q) & R) & S) & T) & U","sourceOffset":6315,"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","U"],"premises":["P","Q","R","S","T","U"],"conclusion":"((((P & Q) & R) & S) & T) & U","status":"candidate","leanStatement":"theorem inference_5 (v0 v1 v2 v3 v4 v5 : Bool) :\n    ((!(((((v0 && v1) && v2) && v3) && v4) && v5)) || (((((v0 && v1) && v2) && v3) && v4) && v5)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> decide\n#print axioms inference_5\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_5"},{"id":"inference_6","sourceStatement":"{MP, MP -> RA} |= MP <-> RA","sourceOffset":6599,"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":["MP","RA"],"premises":["MP","MP -> RA"],"conclusion":"MP <-> RA","status":"candidate","leanStatement":"theorem inference_6 (v0 v1 : Bool) :\n    ((!(v0 && ((!v0) || v1))) || (v0 == v1)) = true := by\n  cases v0 <;> cases v1 <;> decide\n#print axioms inference_6\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_6"},{"id":"source_identity_rule","sourceStatement":"A is A","sourceOffset":76,"scope":"The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.","status":"candidate","variables":[],"premises":[],"conclusion":"∀ (α : Type) (a : α), a = a","leanStatement":"theorem source_identity_rule (α : Type) (a : α) : a = a := rfl\n#print axioms source_identity_rule\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.source_identity_rule"}],"files":{"source.json":{"sha256":"ea553364f3fbee841c5222cbafdc6e21997dbed8600976ef7eec4a4a3245f61b","bytes":7363},"Proof.lean":{"sha256":"a897a0d79ba2d9ef792cbd3a233c1e9101842bd30e7f20657e8f1feb68012544","bytes":1478},"lean-check.txt":{"sha256":"8d10e8ef59cd84923d19a15a272cf84d14408167f8321716e8c2796044caf886","bytes":478}},"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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