{"slug":"universal-logic-implication-cycle","identifier":"universal-logic-implication-cycle","title":"Universal Logic Implication Cycle by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"232de602289f0b875b23dab7618f969bde1fbbeaeae9cffbcd09042c27b8e7ec","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T14:16:31.768Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:42:47.937Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1"],"units":[{"id":"inference_1","sourceStatement":"{P, P → Q, Q → R, R → S, S → T, T → U, U → P, ~(~P & ~Q & ~R & ~S & ~T & ~U)} |= ((P & Q) & (R & S) & T) & U","sourceOffset":0,"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","P → Q","Q → R","R → S","S → T","T → U","U → P","~(~P & ~Q & ~R & ~S & ~T & ~U)"],"conclusion":"((P & Q) & (R & S) & T) & U","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 v3 v4 v5 : Bool) :\n    ((!(((((((v0 && ((!v0) || v1)) && ((!v1) || v2)) && ((!v2) || v3)) && ((!v3) || v4)) && ((!v4) || v5)) && ((!v5) || v0)) && (!((((((!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_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"}],"files":{"source.json":{"sha256":"c14bb01cb687189e776ba339445e97474902c63cc0ba93b26addd9befc9e070c","bytes":2556},"Proof.lean":{"sha256":"299dd566b323b91000b06bbfce2f3734c8dd628691572ee228d8217282d31820","bytes":719},"lean-check.txt":{"sha256":"283a8aa40f54008e4bfc528069537344fae9f76a8d2f62b37f48d942b98ba62c","bytes":115}},"boundary":"Lean establishes the listed formal statements and dependencies. 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The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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