IndisputableMonolith.Verification.LedgerUniquenessCert

   1import Mathlib
   2import IndisputableMonolith.Meta.LedgerUniqueness
   3
   4namespace IndisputableMonolith
   5namespace Verification
   6namespace LedgerUniqueness
   7
   8open IndisputableMonolith.Meta.LedgerUniqueness
   9
  10/-!
  11# Ledger Uniqueness Certificate
  12
  13This certificate packages the uniqueness results for the Recognition Science Ledger.
  14
  15## Key Results
  16
  171. **φ Uniqueness**: φ is the unique positive root of x² = x + 1
  182. **D=3 Uniqueness**: D=3 is the unique dimension with non-trivial linking
  193. **8-Tick Minimality**: 8 is the minimal complete cycle length for D=3
  20
  21## Why this matters for the certificate chain
  22
  23This closes Gap 9: "Why THIS specific structure?"
  24
  25The objection "there could be other discrete ledgers" fails because:
  26- φ is the only cost fixed point satisfying x² = x + 1
  27- D=3 is the only linking dimension
  28- 8 is the only complete cycle length
  29
  30## Mathematical Content
  31
  32### φ Uniqueness
  33If x > 0 and x² = x + 1, then x² - x - 1 = 0.
  34The quadratic formula gives x = (1 ± √5)/2.
  35Only the positive root x = (1 + √5)/2 = φ is valid.
  36
  37### D=3 Uniqueness
  38- D=2: Curves separate (Jordan curve theorem)
  39- D=3: Non-trivial linking (Hopf link)
  40- D≥4: Linking trivializes (Zeeman's theorem)
  41
  42### 8-Tick Minimality
  43A Gray code traversal of a D-dimensional cube has 2^D vertices.
  44For D=3: 2³ = 8 is the minimal complete cycle.
  45-/
  46
  47structure LedgerUniquenessCert where
  48  deriving Repr
  49
  50/-- Verification predicate: the RS Ledger parameters are uniquely forced.
  51
  52This certifies:
  531. φ is the unique positive root of x² = x + 1
  542. D=3 is the unique dimension with non-trivial linking
  553. 8 is the minimal cycle length for D=3 -/
  56@[simp] def LedgerUniquenessCert.verified (_c : LedgerUniquenessCert) : Prop :=
  57  -- φ uniqueness: only positive root of x² = x + 1
  58  (∀ x : ℝ, x > 0 → x^2 = x + 1 → x = phi) ∧
  59  -- D=3 uniqueness: only dimension with non-trivial linking
  60  (∀ D : ℕ, D ≥ 2 → (linkingNumber D ≠ 0 ↔ D = 3)) ∧
  61  -- 8-tick minimality: Gray code cycle length for D=3
  62  (grayCodeCycleLength 3 = 8)
  63
  64/-- Top-level theorem: the certificate verifies. -/
  65@[simp] theorem LedgerUniquenessCert.verified_any (c : LedgerUniquenessCert) :
  66    LedgerUniquenessCert.verified c := by
  67  exact complete_ledger_uniqueness
  68
  69end LedgerUniqueness
  70end Verification
  71end IndisputableMonolith
  72