`LedgerComplete`

definition

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module: IndisputableMonolith.Foundation.PhiForcingDerived
domain: Foundation
line: 239 · github
papers citing: none yet

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IndisputableMonolith.Foundation.PhiForcingDerived on GitHub at line 239.

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formal source

 236
 237Without closure, composing events would create orphan scales that
 238can't be posted, violating the discrete ledger structure. -/
 239def LedgerComplete (S : GeometricScaleSequence) : Prop :=
 240  ∀ n m : ℕ, ∃ k : ℕ, S.scale n + S.scale m = S.scale k
 241
 242/-- Full closure is too strong for arbitrary n, m.
 243    But the MINIMAL closure (n=0, m=1 → k=2) is achievable
 244    and forces the golden ratio. -/
 245theorem minimal_closure_sufficient :
 246    ∀ S : GeometricScaleSequence,
 247      S.isClosed ↔ S.scale 0 + S.scale 1 = S.scale 2 := by
 248  intro S
 249  unfold GeometricScaleSequence.isClosed ledgerCompose
 250  rfl
 251
 252/-! ## Summary: The Derivation Chain
 253
 2541. J-cost is unique and additive (from RCL) ✓
 2552. Ledger composition should be additive (to respect J-cost) ✓
 2563. Scales form geometric sequence (discreteness) ✓
 2574. Closure: 1 + r = r² (for composed scales to exist) ✓
 2585. Therefore: r = φ ✓
 259
 260The constraint r² = r + 1 is now DERIVED from closure,
 261which is motivated by ledger completeness. -/
 262
 263end PhiForcingDerived
 264end Foundation
 265end IndisputableMonolith

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