80theorem unity_has_no_phi_structure {N : ℕ} (hN : 0 < N) : 81 ¬ has_phi_structure (InitialCondition.unity_config N hN) := by
proof body
Term-mode proof.
82 intro ⟨i, j, n, hn, hratio⟩ 83 simp only [InitialCondition.unity_config] at hratio 84 have h_div : (1 : ℝ) / 1 = PhiForcing.φ ^ n := hratio 85 simp at h_div 86 exact phi_zpow_ne_one hn h_div.symm 87 88/-! ## Part IV: DERIVED — Recognition Forces Non-Trivial Content (Gap A) 89 90T4 (Recognition Forcing): Recognition requires distinguishing states. 91A configuration where all entries are identical contains zero information 92and cannot support any recognition event. This is the RS formalization 93of "nothing cannot recognize itself" (MP/T1) applied to configurations: 94a uniform ledger is informationally equivalent to nothing. 95 96The derivation: 97 T4 (recognition requires substrate) + T1 (nothing has infinite cost) 98 → at least one entry must differ from the ground state 99 → the configuration is non-trivial 100 101This replaces the old T6_Requirement structure with a THEOREM. -/ 102 103/-- A configuration is **non-trivial** if at least one entry differs from 1. 104 Equivalently: the configuration is not the uniform ground state. -/
depends on (35)
Lean names referenced from this declaration's body.