IndisputableMonolith.Physics.AnchorPolicyCertified

   1import Mathlib
   2import IndisputableMonolith.Recognition.Certification
   3import IndisputableMonolith.RSBridge.Anchor
   4
   5/-!
   6# AnchorPolicy Certified Interface (no RG-in-Lean required)
   7
   8This module provides a **remedy** for the fact that `Physics/AnchorPolicy.lean` treats the
   9Standard-Model RG residue as an axiom/interface.
  10
  11Instead of asserting a global axiom
  12
  13  `|f_residue f μ⋆ - gap(ZOf f)| < 1e-6`
  14
  15we express the dependency as a *certificate*: an externally produced table of residue intervals
  16(`Ires`) plus charge-wise gap intervals (`Igap`) with a validity proof. Lean can then derive:
  17
  18  - per-species closeness to `gap(Z)` (inequality form),
  19  - equal-Z degeneracy bounds,
  20
  21without assuming an equality axiom.
  22
  23What this does **not** do: it does not implement the SM RG kernels/integration in Lean. It only
  24makes the dependency explicit and machine-checkable once you provide certified bounds from an
  25external computation (e.g. a Python audit).
  26-/
  27
  28namespace IndisputableMonolith.Physics
  29namespace AnchorPolicyCertified
  30
  31noncomputable section
  32open Classical
  33
  34open IndisputableMonolith.Recognition.Certification
  35open IndisputableMonolith.RSBridge
  36
  37/-! ## Specialize the generic certification schema to RSBridge fermions -/
  38
  39abbrev Species : Type := Fermion
  40
  41abbrev Z (f : Species) : Int := ZOf f
  42
  43abbrev Fgap (z : Int) : ℝ := gap z
  44
  45/-! ## Main certified consequences -/
  46
  47/-- If an external certificate bounds the per-species residues at the anchor, then every species'
  48residue is close to the closed-form display `gap(Z)` (inequality form). -/
  49theorem anchor_identity_from_cert
  50    (C : AnchorCert Species)
  51    (hC : Valid Z Fgap C)
  52    (resAtAnchor : Species → ℝ)
  53    (hres : ∀ f, memI (C.Ires f) (resAtAnchor f)) :
  54    ∀ f : Species, |resAtAnchor f - Fgap (Z f)| ≤ 2 * C.eps (Z f) := by
  55  -- Directly reuse the generic lemma.
  56  simpa [Species, Z, Fgap] using
  57    (anchorIdentity_cert (Z := Z) (Fgap := Fgap) (C := C) hC resAtAnchor hres)
  58
  59/-- Equal-Z degeneracy bound from a certificate: if two species share the same Z, their residues
  60must lie within the certified band. -/
  61theorem equalZ_residue_from_cert
  62    (C : AnchorCert Species)
  63    (hC : Valid Z Fgap C)
  64    (resAtAnchor : Species → ℝ)
  65    (hres : ∀ f, memI (C.Ires f) (resAtAnchor f))
  66    {f g : Species} (hZ : Z f = Z g) :
  67    |resAtAnchor f - resAtAnchor g| ≤ 2 * C.eps (Z f) := by
  68  simpa [Species, Z, Fgap] using
  69    (equalZ_residue_of_cert (Z := Z) (Fgap := Fgap) (C := C) hC resAtAnchor hres hZ)
  70
  71end
  72
  73end AnchorPolicyCertified
  74end IndisputableMonolith.Physics
  75