{"slug":"hunter-geometry-received-copy","identifier":"hunter-geometry-received-copy","title":"The Axiom of Geometry — Full Supplied Copy","author":"Maclain Hunter","sourceSha256":"300affdcd708e7b2a90581dbe1f692b1194f53b2d33f645bf720074ae6e76925","sourceKind":"authored-foundational-record","recordedAt":"2026-10-03T01:29:58.220Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:41:57.191Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.inference_2","HunterAuthored.inference_3","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{P, Q, R, S} |= (P & Q) <-> (R & S)","sourceOffset":11383,"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","Q","R","S"],"conclusion":"(P & Q) <-> (R & S)","status":"candidate","leanStatement":"theorem inference_1 (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_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"inference_2","sourceStatement":"{P, P <-> Q, Q <-> R} |= (P & Q) & R","sourceOffset":25265,"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":"{a, a <-> b, b <-> c, c <-> d} |= (d -> c) -> (b -> a)","sourceOffset":26088,"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_3 (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_3\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_3"},{"id":"source_identity_rule","sourceStatement":"Law of Identity","sourceOffset":2054,"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":"0b4da4779480f20663fbaf9b21452936a0674a7a6c34eafcc99f58926e174271","bytes":29005},"Proof.lean":{"sha256":"cf2e54b5c52fb2aec866a43c0879f18683fef92934fe06f79cf91d9c9e3c16da","bytes":1043},"lean-check.txt":{"sha256":"b2a13c78d5e07cc13897edfa6e4ad95b717a32423f43c97d6c342c394c93869c","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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