{"slug":"hunter-four-proofs-authored-compilation","identifier":"hunter-four-proofs-authored-compilation","title":"Four Proofs (4P)","author":"Maclain Hunter","sourceSha256":"81c9017e1f76d7211ebd691bf5fddf67038d86d994d408a64b382cf885b26449","sourceKind":"authored-foundational-record","recordedAt":"2026-10-03T01:33:02.748Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:38:30.694Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_2","HunterAuthored.inference_4","HunterAuthored.inference_5","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{P <-> Q} |= P & Q","sourceOffset":650,"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"],"premises":["P <-> Q"],"conclusion":"P & Q","status":"countermodel","countermodel":{"P":false,"Q":false},"reason":"The written sequent alone has a countermodel. No authored wording or unstated premise was changed.","kernelStatus":"not_checked"},{"id":"inference_2","sourceStatement":"{P, P -> Q, Q -> R} |= (P & Q) & R","sourceOffset":2540,"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","P -> Q","Q -> R"],"conclusion":"(P & Q) & R","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 : Bool) :\n    ((!((v0 && ((!v0) || v1)) && ((!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"},{"id":"inference_3","sourceStatement":"{P <-> Q} |= P & Q","sourceOffset":3663,"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"],"premises":["P <-> Q"],"conclusion":"P & Q","status":"countermodel","countermodel":{"P":false,"Q":false},"reason":"The written sequent alone has a countermodel. No authored wording or unstated premise was changed.","kernelStatus":"not_checked"},{"id":"inference_4","sourceStatement":"{A, B, C, D} |= (A & B) <-> (C & D)","sourceOffset":4247,"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","B","C","D"],"premises":["A","B","C","D"],"conclusion":"(A & B) <-> (C & D)","status":"candidate","leanStatement":"theorem inference_4 (v0 v1 v2 v3 : Bool) :\n    ((!(((v0 && v1) && v2) && v3)) || ((v0 && v1) == (v2 && v3))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_4\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_4"},{"id":"inference_5","sourceStatement":"{P1, P1 -> P2, P2 -> P3, P3 -> P4} |= (P1 & P2) & (P3 & P4)","sourceOffset":4819,"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":["P1","P2","P3","P4"],"premises":["P1","P1 -> P2","P2 -> P3","P3 -> P4"],"conclusion":"(P1 & P2) & (P3 & P4)","status":"candidate","leanStatement":"theorem inference_5 (v0 v1 v2 v3 : Bool) :\n    ((!(((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3))) || ((v0 && v1) && (v2 && v3))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_5\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_5"},{"id":"source_identity_rule","sourceStatement":"A = A","sourceOffset":4112,"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":"2e145670dc37874cf6e510c823ecf5285d1c11e8d38d421d04dd761ede1b8bce","bytes":6645},"Proof.lean":{"sha256":"3051a3a260a60ea15a4da24bc15dcb5c8ebd0526615dada16202c5ab4c91029d","bytes":1021},"lean-check.txt":{"sha256":"2bd205af14174a8f5ef46f66d5324ded0e4f36cefdfc7baacf3370492b00ebe5","bytes":301}},"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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The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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