{"slug":"archived-q1046-6c1c2f61cdb5","identifier":"archived-q1046-6c1c2f61cdb5","title":"The Law of Grounded Identity (LGI)","author":"Maclain Hunter","sourceSha256":"6c1c2f61cdb5aa6d34fa1310071618f42c09e4a5b5987e18d8f3337dc3426210","sourceKind":"archived-authored-source","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:42:12.339Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{(A -> A) -> L, L -> T} |= ((((A -> A) -> L) -> T) & (((A -> A) -> ~L) -> ~T))","sourceOffset":816,"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","L","T"],"premises":["(A -> A) -> L","L -> T"],"conclusion":"((((A -> A) -> L) -> T) & (((A -> A) -> ~L) -> ~T))","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 : Bool) :\n    ((!(((!((!v0) || v0)) || v1) && ((!v1) || v2))) || (((!((!((!v0) || v0)) || v1)) || v2) && ((!((!((!v0) || 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":"source_identity_rule","sourceStatement":"A is A","sourceOffset":84,"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":"d5ca16b3b89738184622bf5c8df3ed57f6a5944faab473e995095947d083f000","bytes":1948},"Proof.lean":{"sha256":"4482c7d24c1005964d977be5a291ef36e0f519b05fb35201e1fef5ecac184782","bytes":653},"lean-check.txt":{"sha256":"c984470b7e70c1b533a43d5274fb204be8ef76a0e5c9aaacde641a6b4b8b74fd","bytes":183}},"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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