IndisputableMonolith.StandardModel.HiggsEFTLowEnergyLimit

   1import Mathlib
   2import IndisputableMonolith.StandardModel.HiggsEFTBridge
   3import IndisputableMonolith.StandardModel.ElectroweakMassBridge
   4import IndisputableMonolith.StandardModel.HiggsYukawaBridge
   5import IndisputableMonolith.StandardModel.HiggsObservableSkeleton
   6import IndisputableMonolith.StandardModel.LongitudinalVectorScattering
   7
   8/-!
   9# Higgs EFT Low-Energy Limit: Master Certificate
  10
  11This module bundles the five Lean modules that, together, formalise the
  12chain Anil asked us to build:
  13
  14    RS cost geometry
  15        → effective scalar coordinate          (HiggsEFTBridge)
  16        → canonical Higgs EFT                  (HiggsEFTBridge)
  17        → Standard-Model gauge masses          (ElectroweakMassBridge)
  18        → Standard-Model Yukawa couplings       (HiggsYukawaBridge)
  19        → SM amplitudes / collider observables (HiggsObservableSkeleton)
  20        + longitudinal-VV unitarity preserved  (LongitudinalVectorScattering)
  21
  22The master certificate `HiggsEFTLowEnergyLimitCert` exposes one named
  23component per module, each carrying its own honest tag.
  24
  25## Tag Legend
  26
  27* `THEOREM`            — fully proved in Lean, no hypothesis.
  28* `CONDITIONAL_THEOREM`— proved in Lean modulo a named hypothesis (e.g.
  29                        `NormalizationHypothesis`, `RSPreservesLongitudinalUnitarity`).
  30* `TREE_LEVEL_ONLY`    — proved at tree level; loop-level corrections
  31                        (`h → γγ`, `h → gg`, etc.) require additional
  32                        amplitude formalisation that is not yet present.
  33* `OPEN_NORMALIZATION` — open subproblem: deriving `Λ(v)` for the canonical
  34                        normalisation map.
  35* `OPEN_RUNG_MAP`      — open subproblem: deriving the Standard-Model
  36                        rung assignments from cube combinatorics.
  37* `LOOP_LEVEL_OPEN`    — open subproblem: loop-induced collider channels.
  38-/
  39
  40namespace IndisputableMonolith
  41namespace StandardModel
  42namespace HiggsEFTLowEnergyLimit
  43
  44open IndisputableMonolith.StandardModel.HiggsEFTBridge
  45open IndisputableMonolith.StandardModel.ElectroweakMassBridge
  46open IndisputableMonolith.StandardModel.HiggsYukawaBridge
  47open IndisputableMonolith.StandardModel.HiggsObservableSkeleton
  48open IndisputableMonolith.StandardModel.LongitudinalVectorScattering
  49
  50/-! ## §1. Master Certificate -/
  51
  52/-- Master certificate for the cost-geometry → SM-EFT bridge.
  53
  54    The certificate is a structural composition: each component is the
  55    master certificate of the underlying module.  No new theorems are
  56    proved here; the goal is to expose one named, auditable surface for
  57    Anil's chain. -/
  58structure HiggsEFTLowEnergyLimitCert where
  59  /-- THEOREM (modulo `NormalizationHypothesis`):
  60      RS cost geometry → effective scalar coordinate → canonical Higgs EFT. -/
  61  bridge       : HiggsEFTBridgeCert
  62  /-- THEOREM:
  63      W/Z mass relations and Weinberg-angle structure on positive
  64      gauge couplings. -/
  65  ew_mass      : ElectroweakMassBridgeCert
  66  /-- THEOREM:
  67      SM-normalised Yukawa couplings on the φ-ladder. -/
  68  yukawa       : HiggsYukawaBridgeCert
  69  /-- TREE_LEVEL_ONLY:
  70      partial widths, branching ratios, signal strengths under
  71      tree-level matching of amplitudes. -/
  72  observable   : HiggsObservableSkeletonCert
  73  /-- CONDITIONAL_THEOREM (modulo `RSPreservesLongitudinalUnitarity`):
  74      longitudinal vector-boson scattering remains bounded as `s → ∞`. -/
  75  longitudinal : LongitudinalVectorScatteringCert
  76
  77/-- The master certificate is theorem-backed at the level of bundling. -/
  78def higgsEFTLowEnergyLimitCert : HiggsEFTLowEnergyLimitCert where
  79  bridge       := higgsEFTBridgeCert
  80  ew_mass      := electroweakMassBridgeCert
  81  yukawa       := higgsYukawaBridgeCert
  82  observable   := higgsObservableSkeletonCert
  83  longitudinal := longitudinalVectorScatteringCert
  84
  85theorem higgsEFTLowEnergyLimitCert_inhabited :
  86    Nonempty HiggsEFTLowEnergyLimitCert :=
  87  ⟨higgsEFTLowEnergyLimitCert⟩
  88
  89/-! ## §2. Audit Status
  90
  91The structural-level audit of each component:
  92
  93| Component                             | Proof level             | Open subproblem                |
  94|---------------------------------------|-------------------------|--------------------------------|
  95| `bridge.cosh_form`                    | THEOREM                 | (none)                         |
  96| `bridge.quartic_remainder`            | THEOREM                 | (none)                         |
  97| `bridge.mass_term_match`              | CONDITIONAL_THEOREM     | `NormalizationHypothesis`      |
  98| `bridge.quartic_match`                | CONDITIONAL_THEOREM     | `NormalizationHypothesis`      |
  99| `ew_mass.mW_le_mZ`                    | THEOREM                 | (none)                         |
 100| `ew_mass.ratio_eq_cos_sq`             | THEOREM                 | (none)                         |
 101| `yukawa.yukawa_phi_step`              | THEOREM                 | (none, given rung map)         |
 102| `yukawa.yukawa_phi_pow`               | THEOREM                 | (none, given rung map)         |
 103| `observable.tree_pw_match`            | CONDITIONAL_THEOREM     | tree-level coupling match      |
 104| `longitudinal.cancels_under_cond`     | THEOREM                 | (none)                         |
 105| `longitudinal.rs_implies_bounded`     | CONDITIONAL_THEOREM     | `RSPreservesLongitudinalUnitarity` |
 106| Numerical Λ(v)                        | OPEN_NORMALIZATION      | (under construction)           |
 107| Standard-Model rung map               | OPEN_RUNG_MAP           | (under construction)           |
 108| Loop-induced channels (γγ, gg, Zγ)    | LOOP_LEVEL_OPEN         | (under construction)           |
 109-/
 110
 111end HiggsEFTLowEnergyLimit
 112end StandardModel
 113end IndisputableMonolith
 114