{"slug":"archived-q1059-edf5435c94cf","identifier":"archived-q1059-edf5435c94cf","title":"Seven Cycle Logic Completeness","author":"Maclain Hunter","sourceSha256":"edf5435c94cf8ae9f45ff709cfdbf56a5aa755162443eae3aa84ada56bcea050","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":"2026-10-03T10:41:43.858Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.valid_unit_seven_checks","HunterAuthored.source_identity_rule"],"units":[{"id":"valid_unit_seven_checks","sourceStatement":"{\n  \"name\": \"Seven Cycle Logic Completeness\",\n  \"formal\": \"∀u ∈ ValidMCBUnit: SevenCycle(u).cycleComplete = true\",\n  \"proof\": \"Each step follows from MCB construction invariants\",\n  \"steps\": [\n    \"Identity (A = A)\",\n    \"Non-Contradiction (¬(A ∧ ¬A))\",\n    \"Excluded Middle (A ∨ ¬A)\",\n    \"Logos Alignment\",\n    \"MCB Parity\",\n    \"4P Validation\",\n    \"Halting Proof\"\n  ]\n}","sourceOffset":0,"scope":"The seven displayed mathematical invariants for an admitted typed valid unit. Coherence/lawfulness are explicit admission evidence, not freely assigned flags. Runtime evidence that state matches the computed exponent, and execution of the host gate routine, remain separate.","status":"candidate","variables":[],"premises":[],"conclusion":"See the exact typed Lean theorem","leanStatement":"def cycleSigned (b : Bool) : Int := if b then 1 else -1\nstructure ValidCycleUnit where\n  value : Int\n  state : Bool\n  depth : Nat\n  coherent : Bool\n  lawful : Bool\n  logosCoherence : coherent = true\n  logosLawful : lawful = true\ndef sevenChecks (u : ValidCycleUnit) : Prop :=\n  u.value = u.value ∧\n  ¬(cycleSigned u.state = 1 ∧ cycleSigned u.state = -1) ∧\n  (cycleSigned u.state = 1 ∨ cycleSigned u.state = -1) ∧\n  (u.coherent = true ∧ u.lawful = true) ∧\n  cycleSigned u.state = cycleSigned u.state ∧\n  (cycleSigned u.state = 1 ∨ cycleSigned u.state = -1) ∧\n  0 ≤ u.depth\ntheorem valid_unit_seven_checks (u : ValidCycleUnit) : sevenChecks u := by\n  refine ⟨rfl, ?_, ?_, ⟨u.logosCoherence, u.logosLawful⟩, rfl, ?_, Nat.zero_le u.depth⟩\n  · cases u.state <;> decide\n  · cases u.state\n    · exact Or.inr rfl\n    · exact Or.inl rfl\n  · cases u.state\n    · exact Or.inr rfl\n    · exact Or.inl rfl\n#print axioms valid_unit_seven_checks\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.valid_unit_seven_checks"},{"id":"source_identity_rule","sourceStatement":"A = A","sourceOffset":208,"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":"791b32edebcffd3204a81a56cba0cefb4ed106ed38edfe24a2890e0457646819","bytes":966},"Proof.lean":{"sha256":"9f135799fcf554323d53acc4eba40099e08fcce17d7a91372efd6d1db2292303","bytes":1351},"lean-check.txt":{"sha256":"d44fad022cafaa113056e6cb57b4ec5a7ea60357f9e39dcc8f0883d3237d3148","bytes":195}},"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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