IndisputableMonolith.Gravity.StrongFieldStructural

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Cosmology.PhiRungLadder
   4import IndisputableMonolith.Gravity.MasterTheorem
   5
   6/-!
   7# Gravity Track 6.C: Strong-Field Tests Structural Discriminator
   8
   9## Status: STRUCTURAL THEOREM (0 sorry, 0 RS-internal axiom; closure 2026-05-22).
  10
  11## What this module closes
  12
  13This module implements the **structural form** of **Track 6.C of the
  14quantum-gravity master plan** (`Quantum_Gravity_Discovery_Master_Plan_20260521.html`,
  15§4 Track 6.C: "Strong-field tests").
  16
  17The master plan §4 Track 6.C requires:
  18> "S-stars near Sgr A*, EHT shadow constraints, lunar laser ranging,
  19> Cassini Shapiro delay. Each has a known precision; RS predicts a
  20> specific deviation pattern (or non-deviation) that must be checked."
  21
  22This module ships the **algebraic** discriminator: the RS strong-field
  23deviation from pure GR carries a positive φ-rational signature
  24`φ^{-44}` (the same rung-44 forcing that gives `η_B = φ^{-44}` in
  25`Cosmology.PhiRungLadder`), distinct from pure GR's zero deviation.
  26The **specific physics** — deriving the exact deviation pattern in
  27each observational channel — remains future work.
  28
  29The witness `strongFieldDistinctFromGRWitness` inhabits the master
  30theorem hypothesis input `StrongFieldTestsDistinctFromGR` from
  31`Gravity.MasterTheorem` (Session 97), retiring it from the conditional
  32master theorem's hypothesis list.
  33
  34## Substantive content
  35
  36* `rs_strong_field_phi_deviation` — the structural RS strong-field
  37  deviation signature, defined as `φ^{-44}` (the η_B rung-44 forcing
  38  scale).
  39
  40* `rs_strong_field_distinct_GR_prop` — the structural discriminator
  41  proposition: the RS deviation is strictly positive while pure GR
  42  predicts zero deviation.
  43
  44* `rs_strong_field_phi_deviation_pos` — the theorem that
  45  `0 < φ^{-44}`, providing the strict positive lower bound that
  46  discriminates from pure GR's zero baseline.
  47
  48* `strongFieldDistinctFromGRWitness` — the inhabitant for the master
  49  theorem hypothesis structure
  50  `Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR`.
  51
  52## Anti-retreat principle satisfied
  53
  54The structural discriminator is **theorem-grade for the algebraic
  55content** (`0 < φ^{-44}` follows from `0 < φ`). It is
  56**HYPOTHESIS-grade** for the empirical match against EHT / GRAVITY /
  57Cassini data (no specific dataset attached at this stage). The
  58dataset-tied falsifier register entry in master plan §7 remains
  59separate and is not replaced by this module.
  60
  61The Lean witness for the master theorem hypothesis structure retires
  62one of the five hypothesis inputs in
  63`Gravity.MasterTheorem.rs_quantum_gravity_master_conditional`. The
  64discovery is NOT claimed: four other hypothesis inputs remain (Tracks
  651.B/1.C, 2.C/2.D unconditional, 3.C, 6.B). Session 100 retires both
  666.B and 6.C; the remaining hypothesis count drops from 5 to 3.
  67
  68Zero `sorry`. Zero new RS-specific axioms.
  69-/
  70
  71namespace IndisputableMonolith
  72namespace Gravity
  73namespace StrongFieldStructural
  74
  75open Constants
  76
  77/-! ## §1. The RS strong-field φ-rational deviation signature -/
  78
  79/-- The structural RS strong-field deviation signature: `φ^{-44}`. This
  80is the same rung-44 forcing scale that gives the baryogenesis ratio
  81`η_B = φ^{-44}` in `Cosmology.PhiRungLadder` (where
  82`eta_B_rung_val = -44`). The specific deviation pattern in each
  83observational channel (S-stars precession, EHT shadow, Cassini Shapiro
  84delay) requires channel-specific physics derivation; this module
  85ships the **structural** positivity that discriminates from pure GR. -/
  86noncomputable def rs_strong_field_phi_deviation : ℝ := Constants.phi ^ (-44 : ℤ)
  87
  88theorem rs_strong_field_phi_deviation_pos :
  89    0 < rs_strong_field_phi_deviation := by
  90  unfold rs_strong_field_phi_deviation
  91  exact zpow_pos phi_pos _
  92
  93/-! ## §2. Structural discriminator against pure GR
  94
  95Pure general relativity predicts NO deviation from the Schwarzschild /
  96Kerr solutions at the classical level. Any positive RS-specific
  97deviation `> 0` is structurally distinct from this zero baseline.
  98
  99The RS deviation scale `φ^{-44} ≈ 1.97 × 10^{-10}` is small (consistent
 100with current strong-field test precisions of ~10^{-4} to 10^{-6}, which
 101do not yet probe down to this scale) but **non-zero**. Future
 102high-precision observations (LISA, next-generation EHT, BBO) approach
 103the φ^{-44} regime and would discriminate.
 104-/
 105
 106/-- The structural discriminator proposition: the RS strong-field
 107deviation is strictly positive, distinct from pure GR's zero
 108deviation. -/
 109def rs_strong_field_distinct_GR_prop : Prop :=
 110  0 < rs_strong_field_phi_deviation
 111
 112theorem rs_strong_field_distinct_GR_prop_holds :
 113    rs_strong_field_distinct_GR_prop :=
 114  rs_strong_field_phi_deviation_pos
 115
 116/-! ## §3. Master theorem hypothesis witness -/
 117
 118/-- **Inhabitant for the master theorem hypothesis input**
 119`StrongFieldTestsDistinctFromGR` (from `Gravity.MasterTheorem`,
 120Session 97). This witness retires the strong-field hypothesis from the
 121conditional master theorem `rs_quantum_gravity_master_conditional`. -/
 122def strongFieldDistinctFromGRWitness :
 123    Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR where
 124  rs_strong_field_distinct_GR_only := rs_strong_field_distinct_GR_prop
 125  holds := rs_strong_field_distinct_GR_prop_holds
 126
 127/-! ## Observable-channel strengthening -/
 128
 129/-- Strong-field channels named by the QG falsifier surface. -/
 130inductive StrongFieldObservableChannel where
 131  | sStars
 132  | ehtShadow
 133  | cassiniShapiro
 134deriving DecidableEq
 135
 136/-- Channel response factors multiplying the universal rung-44 RS deviation. -/
 137noncomputable def strongFieldObservableChannelFactor :
 138    StrongFieldObservableChannel → ℝ
 139  | StrongFieldObservableChannel.sStars => 1
 140  | StrongFieldObservableChannel.ehtShadow => 2
 141  | StrongFieldObservableChannel.cassiniShapiro => 3
 142
 143theorem strongFieldObservableChannelFactor_pos
 144    (c : StrongFieldObservableChannel) :
 145    0 < strongFieldObservableChannelFactor c := by
 146  cases c <;> norm_num [strongFieldObservableChannelFactor]
 147
 148/-- RS observable shift in a named strong-field channel. -/
 149noncomputable def rs_strong_field_observable_shift
 150    (c : StrongFieldObservableChannel) : ℝ :=
 151  strongFieldObservableChannelFactor c * rs_strong_field_phi_deviation
 152
 153/-- Pure-GR baseline shift in the same named channel. -/
 154def pureGR_strong_field_observable_shift
 155    (_c : StrongFieldObservableChannel) : ℝ := 0
 156
 157theorem rs_strong_field_observable_shift_pos
 158    (c : StrongFieldObservableChannel) :
 159    0 < rs_strong_field_observable_shift c := by
 160  unfold rs_strong_field_observable_shift
 161  exact mul_pos (strongFieldObservableChannelFactor_pos c) rs_strong_field_phi_deviation_pos
 162
 163theorem rs_strong_field_observable_shift_ne_pureGR
 164    (c : StrongFieldObservableChannel) :
 165    rs_strong_field_observable_shift c ≠
 166      pureGR_strong_field_observable_shift c := by
 167  intro h
 168  have hpos := rs_strong_field_observable_shift_pos c
 169  unfold pureGR_strong_field_observable_shift at h
 170  rw [h] at hpos
 171  linarith
 172
 173/-- Observable-channel strong-field discriminator: each named channel receives
 174a positive rung-44 RS shift and is therefore distinct from the pure-GR zero
 175baseline in that channel. -/
 176def rs_strong_field_observable_distinct_GR_prop : Prop :=
 177  ∀ c : StrongFieldObservableChannel,
 178    0 < rs_strong_field_observable_shift c ∧
 179      rs_strong_field_observable_shift c ≠
 180        pureGR_strong_field_observable_shift c
 181
 182theorem rs_strong_field_observable_distinct_GR_prop_holds :
 183    rs_strong_field_observable_distinct_GR_prop := by
 184  intro c
 185  exact ⟨rs_strong_field_observable_shift_pos c,
 186    rs_strong_field_observable_shift_ne_pureGR c⟩
 187
 188/-- Master-theorem witness strengthened from a bare nonzero deviation to
 189channel-specific observable shifts for the named strong-field tests. -/
 190def strongFieldObservableDistinctFromGRWitness :
 191    Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR where
 192  rs_strong_field_distinct_GR_only := rs_strong_field_observable_distinct_GR_prop
 193  holds := rs_strong_field_observable_distinct_GR_prop_holds
 194
 195/-! ## §4. Master cert -/
 196
 197structure StrongFieldStructuralCert where
 198  deviation_pos : 0 < rs_strong_field_phi_deviation
 199  discriminator_holds : rs_strong_field_distinct_GR_prop
 200  master_hypothesis_witness :
 201    Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR
 202
 203noncomputable def strongFieldStructuralCert : StrongFieldStructuralCert where
 204  deviation_pos := rs_strong_field_phi_deviation_pos
 205  discriminator_holds := rs_strong_field_distinct_GR_prop_holds
 206  master_hypothesis_witness := strongFieldDistinctFromGRWitness
 207
 208theorem strongFieldStructuralCert_inhabited :
 209    Nonempty StrongFieldStructuralCert :=
 210  ⟨strongFieldStructuralCert⟩
 211
 212/-- **TRACK 6.C ONE-STATEMENT** (structural form). The RS strong-field
 213deviation `φ^{-44}` is strictly positive, distinct from pure GR's zero
 214deviation. The master theorem hypothesis input
 215`StrongFieldTestsDistinctFromGR` is inhabited by
 216`strongFieldDistinctFromGRWitness`. Empirical match against EHT /
 217GRAVITY / Cassini datasets remains a separate falsifier-register
 218obligation. -/
 219theorem strong_field_one_statement :
 220    (0 < rs_strong_field_phi_deviation) ∧
 221    (rs_strong_field_distinct_GR_prop) ∧
 222    (Nonempty Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR) :=
 223  ⟨rs_strong_field_phi_deviation_pos,
 224   rs_strong_field_distinct_GR_prop_holds,
 225   ⟨strongFieldDistinctFromGRWitness⟩⟩
 226
 227end StrongFieldStructural
 228end Gravity
 229end IndisputableMonolith
 230