IndisputableMonolith.Verification.PhiNonDegenerateCert

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# φ Non-Degeneracy Certificate
   6
   7This audit certificate packages two fundamental **non-degeneracy** properties of φ:
   8
   9> φ ≠ 0 and φ ≠ 1
  10
  11## Why this matters
  12
  131. **Division safety**: φ ≠ 0 ensures we can safely divide by φ in expressions
  14   like φ⁻¹, the J-cost function, and ratio computations.
  15
  162. **Non-trivial optimum**: φ ≠ 1 proves that the golden ratio is NOT at the
  17   cost minimum (J(1) = 0). This is crucial because φ appears throughout RS
  18   as a fundamental constant — it's not "accidentally" at the trivial point.
  19
  203. **Algebraic consequence**: Both follow from 1 < φ (already certified as
  21   part of PhiPositivityCert), but it's useful to have explicit ≠ statements.
  22
  23## Proof approach
  24
  25Both are direct consequences of `one_lt_phi` (1 < φ), which was previously proven.
  26-/
  27
  28namespace IndisputableMonolith
  29namespace Verification
  30namespace PhiNonDegenerate
  31
  32open IndisputableMonolith.Constants
  33
  34structure PhiNonDegenerateCert where
  35  deriving Repr
  36
  37/-- Verification predicate: φ is non-degenerate.
  38
  39φ ≠ 0 (division safe) and φ ≠ 1 (not at cost minimum). -/
  40@[simp] def PhiNonDegenerateCert.verified (_c : PhiNonDegenerateCert) : Prop :=
  41  (phi ≠ 0) ∧ (phi ≠ 1)
  42
  43@[simp] theorem PhiNonDegenerateCert.verified_any (c : PhiNonDegenerateCert) :
  44    PhiNonDegenerateCert.verified c := by
  45  constructor
  46  · exact phi_ne_zero
  47  · exact phi_ne_one
  48
  49end PhiNonDegenerate
  50end Verification
  51end IndisputableMonolith
  52