{"slug":"hunter-pythagorean-proofs","identifier":"hunter-pythagorean-proofs","title":"Pythagorean Proofs by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"d6182166b343de6bd6f63d9927dc20d086c6c877b0337f9a90a9cea8e08a1bed","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T16:41:48.740Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:41:18.338Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.inference_2","HunterAuthored.inference_3","HunterAuthored.inference_4","HunterAuthored.inference_5"],"units":[{"id":"inference_1","sourceStatement":"{P, P <-> Q, Q <-> R} |= (P & Q) & R","sourceOffset":1395,"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_1 (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_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"inference_2","sourceStatement":"{a, a <-> b, b <-> c, c <-> d} |= (d -> c) -> (b -> a)","sourceOffset":2218,"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","a <-> b","b <-> c","c <-> d"],"conclusion":"(d -> c) -> (b -> a)","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 v3 : Bool) :\n    ((!(((v0 && (v0 == v1)) && (v1 == v2)) && (v2 == v3))) || ((!((!v3) || v2)) || ((!v1) || v0))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_2\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_2"},{"id":"inference_3","sourceStatement":"{A, A <-> B, B <-> C} |= (C -> B) -> A","sourceOffset":4676,"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"],"premises":["A","A <-> B","B <-> C"],"conclusion":"(C -> B) -> A","status":"candidate","leanStatement":"theorem inference_3 (v0 v1 v2 : Bool) :\n    ((!((v0 && (v0 == v1)) && (v1 == v2))) || ((!((!v2) || v1)) || v0)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> decide\n#print axioms inference_3\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_3"},{"id":"inference_4","sourceStatement":"{P, P <-> Q, Q <-> R, R <-> S} |= (P & Q) & (R & S)","sourceOffset":6080,"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"],"premises":["P","P <-> Q","Q <-> R","R <-> S"],"conclusion":"(P & Q) & (R & S)","status":"candidate","leanStatement":"theorem inference_4 (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_4\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_4"},{"id":"inference_5","sourceStatement":"{P1, P1 <-> P2, P2 <-> P3} |= (P1 & P2) & P3","sourceOffset":7187,"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"],"premises":["P1","P1 <-> P2","P2 <-> P3"],"conclusion":"(P1 & P2) & P3","status":"candidate","leanStatement":"theorem inference_5 (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_5\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_5"}],"files":{"source.json":{"sha256":"a5e7ed9b77e01637267eaa395a5c5115023c5bd5a2419906eed6f405adab6a68","bytes":8527},"Proof.lean":{"sha256":"db4962b81737ebc10fa472343a567db1bfe1202950ae011731bf614faf0d3978","bytes":1352},"lean-check.txt":{"sha256":"8bd83cac7b1813498b5b471d23e0c629fc6d126b59a48b827d19f768223491b4","bytes":351}},"boundary":"Lean establishes the listed formal statements and dependencies. 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