{"slug":"formal-seven-cycle-logic-completeness","identifier":"formal-seven-cycle-logic-completeness","title":"Seven Cycle Logic Completeness","author":"Maclain Hunter","sourceSha256":"654f95901f1705d915a4354df1489a5498c1c8950014548c0ac177e91e874e61","sourceKind":"formal-theorem","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:41:42.846Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.valid_unit_seven_checks","HunterAuthored.source_identity_rule"],"units":[{"id":"valid_unit_seven_checks","sourceStatement":"Formal statement: ∀u ∈ ValidMCBUnit: SevenCycle(u).cycleComplete = true","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":152,"scope":"The explicitly named Identity rule, over every type and element. 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