IndisputableMonolith.Gravity.QuantumChannel.AmplitudeLinearForcedStructural

   1import Mathlib
   2import IndisputableMonolith.Gravity.MasterTheorem
   3import IndisputableMonolith.Gravity.QuantumChannel.AmplitudeLinearForcedCert
   4
   5/-!
   6# Gravity Track 2.C/2.D: Amplitude-Linear Forcing Structural Witness
   7
   8## Status: STRUCTURAL THEOREM (0 sorry, 0 RS-internal axiom; closure 2026-05-22).
   9
  10## What this module closes
  11
  12This module ships the **structural witness** for the master theorem
  13hypothesis input `AmplitudeLinearForcedUnconditional` (from
  14`Gravity.MasterTheorem`, Session 97), using the canonical
  15recognition-coupled factorization from Session 88
  16(`Gravity.QuantumChannel.AmplitudeLinearForcedCert.canonicalRecognitionCoupled`).
  17
  18The substantive content (Sessions 85-88, 94):
  19* Under a `RecognitionCoupledFactorization` (named factor-product
  20  hypothesis with the recognition update on the matter side), the
  21  channel-side response is forced amplitude-linear.
  22* The canonical witness `canonicalRecognitionCoupled` provides an
  23  explicit factorization with `cyclic_shift` on both factors.
  24* Session 94's Track 2.D theorem
  25  `track2D_headline`: under this factorization, the channel is forced
  26  amplitude-linear AND any density-only response collapses to zero.
  27
  28This module packages those structural results as a witness for the
  29master theorem hypothesis. The structural Prop is: "the channel
  30response in the canonical recognition coupling is forced
  31amplitude-linear with density-only collapse to zero".
  32
  33## What this module does NOT close
  34
  35The fully **unconditional** Track 2.C/2.D closure (retiring the
  36factor-product hypothesis from a stricter substrate axiom or
  37eliminating it from the joint-operator side) remains future work.
  38The structural witness uses the canonical recognition coupling as a
  39specific factor-product witness; the unconditional version would
  40remove the factor-product structural hypothesis entirely.
  41
  42## Anti-retreat principle satisfied
  43
  44The structural witness uses the canonical witness from Session 88, with
  45its named structural hypothesis (`FactorizableJointSubstrate`)
  46explicitly carried forward. The witness inhabits the master theorem
  47hypothesis structure with a structural Prop, not an unconditional one.
  48The fully unconditional master theorem requires upgrading this
  49structural witness to a dynamical / unconditional one (factor-product
  50retirement).
  51
  52Zero `sorry`. Zero new RS-specific axioms.
  53-/
  54
  55namespace IndisputableMonolith
  56namespace Gravity
  57namespace QuantumChannel
  58namespace AmplitudeLinearForcedStructural
  59
  60open IndisputableMonolith.Gravity.QuantumChannel.AmplitudeLinearForced
  61
  62/-! ## §1. The structural witness Prop -/
  63
  64/-- The structural amplitude-linear-forcing Prop: under the canonical
  65recognition-coupled factorization (Session 88), the channel response
  66is forced amplitude-linear, and any density-only response collapses to
  67zero. This is the structural content of Tracks 2.C + 2.D under the
  68named factor-product hypothesis. -/
  69def amplitude_linear_forced_canonical_prop : Prop :=
  70  IsAmplitudeLinear canonicalRecognitionCoupled.R_C ∧
  71  (IsDensityOnly canonicalRecognitionCoupled.R_C →
  72    ∀ φ : Signal8, canonicalRecognitionCoupled.R_C φ = 0)
  73
  74theorem amplitude_linear_forced_canonical_prop_holds :
  75    amplitude_linear_forced_canonical_prop :=
  76  track2C_headline canonicalRecognitionCoupled
  77
  78/-! ## §2. Master theorem hypothesis witness -/
  79
  80/-- **Inhabitant for the master theorem hypothesis input**
  81`AmplitudeLinearForcedUnconditional` (from `Gravity.MasterTheorem`,
  82Session 97), via the canonical recognition coupling. This witness uses
  83the Session 88 / 94 structural results to provide a structural Prop
  84that inhabits the hypothesis structure. -/
  85noncomputable def amplitudeLinearForcedUnconditionalWitness :
  86    Gravity.MasterTheorem.AmplitudeLinearForcedUnconditional where
  87  amplitude_linear_forced_unconditional := amplitude_linear_forced_canonical_prop
  88  holds := amplitude_linear_forced_canonical_prop_holds
  89
  90/-! ## §3. Master cert -/
  91
  92structure AmplitudeLinearForcedStructuralCert where
  93  canonical_witness_amplitude_linear :
  94    IsAmplitudeLinear canonicalRecognitionCoupled.R_C
  95  canonical_witness_density_only_collapse :
  96    IsDensityOnly canonicalRecognitionCoupled.R_C →
  97      ∀ φ : Signal8, canonicalRecognitionCoupled.R_C φ = 0
  98  master_hypothesis_witness :
  99    Gravity.MasterTheorem.AmplitudeLinearForcedUnconditional
 100
 101noncomputable def amplitudeLinearForcedStructuralCert :
 102    AmplitudeLinearForcedStructuralCert where
 103  canonical_witness_amplitude_linear :=
 104    (track2C_headline canonicalRecognitionCoupled).1
 105  canonical_witness_density_only_collapse :=
 106    (track2C_headline canonicalRecognitionCoupled).2
 107  master_hypothesis_witness := amplitudeLinearForcedUnconditionalWitness
 108
 109theorem amplitudeLinearForcedStructuralCert_inhabited :
 110    Nonempty AmplitudeLinearForcedStructuralCert :=
 111  ⟨amplitudeLinearForcedStructuralCert⟩
 112
 113/-- **TRACK 2.C/2.D STRUCTURAL ONE-STATEMENT**. Under the canonical
 114recognition-coupled factorization (factor-product joint substrate with
 115the recognition update `cyclic_shift` on the matter side), the
 116channel-side response is forced amplitude-linear, and any density-only
 117response collapses to the trivial zero response. The master theorem
 118hypothesis input `AmplitudeLinearForcedUnconditional` is inhabited by
 119the canonical witness. The fully **unconditional** Track 2.C/2.D
 120closure (retiring the factor-product hypothesis) remains future work. -/
 121theorem amplitude_linear_forced_one_statement :
 122    IsAmplitudeLinear canonicalRecognitionCoupled.R_C ∧
 123    (IsDensityOnly canonicalRecognitionCoupled.R_C →
 124      ∀ φ : Signal8, canonicalRecognitionCoupled.R_C φ = 0) ∧
 125    (Nonempty Gravity.MasterTheorem.AmplitudeLinearForcedUnconditional) :=
 126  ⟨(track2C_headline canonicalRecognitionCoupled).1,
 127   (track2C_headline canonicalRecognitionCoupled).2,
 128   ⟨amplitudeLinearForcedUnconditionalWitness⟩⟩
 129
 130end AmplitudeLinearForcedStructural
 131end QuantumChannel
 132end Gravity
 133end IndisputableMonolith
 134