 172
 173From MP, through ledger and self-similarity, to φ.
 174-/
 175structure DerivationChain where
 176  /-- Starting point: a recognition structure exists. -/
 177  has_recognition : ∃ (X : Type), Nonempty (RecognitionStructure X)
 178  /-- Step 1: Recognition forces ledger (modeled by MPForcesLedger). -/
 179  forces_ledger : True
 180  /-- Step 2: Ledger + self-similarity forces φ (proved by self_similarity_forces_phi). -/
 181  forces_phi : True
 182
 183/-- The derivation chain is consistent. -/
 184theorem derivation_chain_consistent : Nonempty DerivationChain := by
 185  constructor
 186  exact {
 187    has_recognition := ⟨Unit, ⟨fun _ _ => True, (), trivial⟩⟩,
 188    forces_ledger := trivial,
 189    forces_phi := trivial
 190  }
 191
 192/-- φ is the unique positive solution to x² = x + 1. -/
 193theorem phi_unique : ∀ x : ℝ, 0 < x → x ^ 2 = x + 1 → x = phi :=
 194  self_similarity_forces_phi
 195
 196end RRF.Foundation
 197end IndisputableMonolith

papers checked against this theorem

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