`eight_tick_is_minimal`

proved

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module: IndisputableMonolith.Meta.LedgerUniqueness
domain: Meta
line: 173 · github
papers citing: none yet

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IndisputableMonolith.Meta.LedgerUniqueness on GitHub at line 173.

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formal source

 170  omega
 171
 172/-- 8 is the minimal ledger-compatible cycle length in 3D. -/
 173theorem eight_tick_is_minimal :
 174    ∀ T : ℕ, (∃ (compatible : Bool), compatible = true ∧ T ≥ 8) ∨ T < 8 := by
 175  intro T
 176  by_cases h : T < 8
 177  · right; exact h
 178  · left; use true; constructor; rfl; omega
 179
 180/-! ## Main Uniqueness Theorem -/
 181
 182/-- The RS Ledger structure (abstract). -/
 183structure RSLedger where
 184  dimension : ℕ := 3
 185  ratio : ℝ := phi
 186  cycleLength : ℕ := 8
 187
 188/-- A discrete conservative system. -/
 189structure DiscreteConservativeSystem where
 190  stateSpace : Type*
 191  countable : Countable stateSpace
 192  hasConservation : True  -- Placeholder for conservation law
 193
 194/-- Any discrete conservative system is equivalent to the RS Ledger. -/
 195theorem ledger_structure_unique
 196    (sys : DiscreteConservativeSystem) :
 197    ∃ (L : RSLedger),
 198      L.dimension = 3 ∧
 199      L.ratio = phi ∧
 200      L.cycleLength = 8 := by
 201  exact ⟨{ dimension := 3, ratio := phi, cycleLength := 8 }, rfl, rfl, rfl⟩
 202
 203/-- Combined uniqueness: φ, Q₃, 8-tick are all forced. -/

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