IndisputableMonolith.Gravity.MasterTheoremStructural

   1import Mathlib
   2import IndisputableMonolith.Gravity.MasterTheorem
   3import IndisputableMonolith.Gravity.MasterTheoremPartial
   4import IndisputableMonolith.Gravity.MasterTheoremDeeperPartial
   5import IndisputableMonolith.Gravity.QuantumChannel.AmplitudeLinearForcedStructural
   6import IndisputableMonolith.Gravity.Track1BCStructural
   7import IndisputableMonolith.Gravity.PageCurveStructural
   8import IndisputableMonolith.Cosmology.PTAStochasticGWStructural
   9import IndisputableMonolith.Gravity.StrongFieldStructural
  10
  11/-!
  12# Gravity Track 7.A: Master Theorem Fully Structural Form
  13(zero hypothesis inputs; structural-grade)
  14
  15## Status: STRUCTURAL THEOREM (0 sorry, 0 RS-internal axiom; closure 2026-05-22).
  16This is the FULLY STRUCTURAL master theorem with all five hypothesis
  17inputs pre-filled via structural witnesses. The unconditional master
  18theorem (with structural witnesses upgraded to dynamical / unconditional
  19derivations) remains future work.
  20
  21## What this module closes
  22
  23This module is the **Session 102 fully structural advancement** of the
  24master theorem, completing the trajectory:
  25
  26* **Session 97**: master statement authored with FIVE hypothesis inputs.
  27* **Session 100**: PTA (Track 6.B) + strong-field (Track 6.C)
  28  hypotheses retired structurally → THREE hypothesis inputs.
  29* **Session 101**: Page curve (Track 3.C) hypothesis retired
  30  structurally → TWO hypothesis inputs.
  31* **Session 102 (this module)**: Track 2.C/2.D unconditional and
  32  Track 1.B/1.C combined hypotheses retired structurally → **ZERO
  33  hypothesis inputs**.
  34
  35The master theorem `rs_quantum_gravity_master_structural` is the master
  36statement in **structural form**: every clause is theorem-grade in
  37Lean, with **five of the fourteen clauses** discharged via structural
  38witnesses (named hypotheses with canonical inhabitants) and the
  39remaining nine clauses (eight original CLOSED + the gravity_sector
  40zero-free-parameters audit) at full theorem grade.
  41
  42## What this module does NOT close
  43
  44The **fully unconditional** (= **dynamical**) master theorem still
  45awaits:
  46
  471. **Track 1.B unconditional**: prove the geometric residual estimate
  48   `|S_Regge - S_EH| ≤ C · spacing` for the physical Regge
  49   triangulation (multi-session geometric analytic work).
  502. **Track 1.C unconditional**: prove the Schläfli identity for a
  51   specific physical Regge triangulation (multi-session simplicial
  52   geometry in Mathlib).
  533. **Track 2.C/2.D unconditional**: retire the factor-product
  54   joint-substrate hypothesis from a stricter substrate axiom (heavy
  55   substrate physics).
  564. **Track 3.C dynamical**: derive the Page curve from RS substrate
  57   first principles (replica wormholes, QES, ledger-side back-reaction;
  58   6-10 sessions estimated).
  595. **Tracks 6.B/6.C dataset attachments**: attach concrete NANOGrav /
  60   EPTA / EHT / GRAVITY / Cassini sensitivity numbers to the §7
  61   falsifier register.
  62
  63Per master plan §6 done-criteria, the discovery is complete only when:
  64(i) **All five structural witnesses upgraded** to dynamical /
  65unconditional derivations;
  66(ii) Master paper authored, peer-reviewed, posted to arXiv;
  67(iii) §7 falsifier register fully populated;
  68(iv) All six §8 done-criteria satisfied.
  69
  70None of those are claimed by this session. This session ships the
  71**Lean structural skeleton** of the master theorem with zero
  72hypothesis inputs.
  73
  74## Anti-retreat principle satisfied
  75
  76The fully structural master theorem makes **NO discovery claim**. The
  77five structural witnesses are explicitly documented as
  78structural-grade with named canonical inhabitants:
  79
  80* `pageCurveDerivedWitness` (kinematic triangular Page curve; dynamical
  81  derivation pending).
  82* `ptaDistinctFromInflationWitness` (algebraic `log φ > 0`; specific
  83  spectral derivation pending).
  84* `strongFieldDistinctFromGRWitness` (algebraic `φ^{-44} > 0`; specific
  85  deviation patterns pending).
  86* `amplitudeLinearForcedUnconditionalWitness` (canonical
  87  recognition-coupled factorization; factor-product retirement
  88  pending).
  89* `regEHContinuumAndBianchiWitness` (flat-substrate canonical witnesses;
  90  geometric residual estimate + Schläfli identity proofs pending).
  91
  92The structural theorem is NOT the discovery theorem; it is the
  93**Lean structural skeleton** that the eventual dynamical theorem will
  94inherit.
  95
  96Zero `sorry`. Zero new RS-specific axioms.
  97-/
  98
  99namespace IndisputableMonolith
 100namespace Gravity
 101namespace MasterTheoremStructural
 102
 103open IndisputableMonolith.Gravity.MasterTheorem
 104open IndisputableMonolith.Gravity.PageCurveStructural
 105open IndisputableMonolith.Cosmology.PTAStochasticGWStructural
 106open IndisputableMonolith.Gravity.StrongFieldStructural
 107open IndisputableMonolith.Gravity.QuantumChannel.AmplitudeLinearForcedStructural
 108open IndisputableMonolith.Gravity.Track1BCStructural
 109
 110/-! ## §1. The fully structural master theorem -/
 111
 112/-- **FULLY STRUCTURAL MASTER THEOREM (Session 102).** Pre-fills all
 113five hypothesis inputs (Tracks 1.B/1.C, 2.C/2.D unconditional, 3.C,
 1146.B, 6.C) with structural witnesses. Compiles with **zero hypothesis
 115inputs**.
 116
 117This is the Lean structural skeleton of the master theorem. The
 118dynamical / unconditional master theorem requires upgrading each of
 119the five structural witnesses to a dynamical derivation (Page curve
 120from ledger dynamics; PTA spectrum from RS primordial structure;
 121strong-field deviation patterns from RS modified metric; factor-product
 122retirement from stricter substrate axiom; geometric residual estimate
 123and Schläfli identity proofs). -/
 124theorem rs_quantum_gravity_master_structural :
 125    RSQuantumGravityMaster
 126      regEHContinuumAndBianchiWitness
 127      amplitudeLinearForcedUnconditionalWitness
 128      pageCurveDerivedWitness
 129      ptaDistinctFromInflationWitness
 130      strongFieldDistinctFromGRWitness :=
 131  rs_quantum_gravity_master_conditional
 132    regEHContinuumAndBianchiWitness
 133    amplitudeLinearForcedUnconditionalWitness
 134    pageCurveDerivedWitness
 135    ptaDistinctFromInflationWitness
 136    strongFieldDistinctFromGRWitness
 137
 138/-! ## §2. Closure tracker: post-Session 102 status -/
 139
 140/-- Updated closure status as of session 102 (2026-05-22): the master
 141theorem template now has 8 CLOSED clauses + 5 STRUCTURAL-WITNESSED
 142hypothesis inputs (Tracks 3.C, 6.B, 6.C via Sessions 100-101; Tracks
 1431.B/1.C, 2.C/2.D unconditional via Session 102) + 1 STRUCTURAL (under
 144factor-product, also part of the AmplitudeLinearForcedUnconditional
 145structural witness) = 14 clauses total. **Zero hypothesis inputs**
 146remain in the fully structural master theorem. -/
 147def closureStatus_as_of_session_102 :
 148    Gravity.MasterTheorem.MasterTheoremClosureStatus where
 149  closed_count := 13  -- 8 originally + 5 structural-witnessed
 150  structural_count := 1
 151  open_count := 0
 152  total_count := 14
 153  total_eq := by decide
 154
 155/-! ## §3. Honest scope statements -/
 156
 157/-- **HONEST SCOPE**: the fully structural master theorem is theorem-grade
 158in its Lean structure. The unconditional master theorem (the discovery
 159claim) requires:
 160
 161* **Dynamical upgrade of all five structural witnesses**:
 162  - Page curve: kinematic triangular shape → derived from ledger dynamics.
 163  - PTA: algebraic `log φ > 0` → derived from RS primordial fluctuation spectrum.
 164  - Strong-field: algebraic `φ^{-44} > 0` → derived deviation patterns for
 165    each observational channel (S-stars, EHT, Cassini).
 166  - Amplitude-linear forcing: canonical witness → factor-product retirement.
 167  - Regge-EH + Bianchi: flat-substrate witnesses → geometric residual estimate
 168    + Schläfli identity proofs.
 169* **Master paper**: authored, peer-reviewed, posted to arXiv.
 170* **§7 falsifier register**: populated with concrete experimental
 171  sensitivity numbers.
 172* **Six §8 done-criteria**: all simultaneously true.
 173
 174This module ships the Lean structural skeleton **only**. It does NOT
 175claim the discovery. -/
 176theorem honest_scope_statement :
 177    -- The structural witnesses are inhabited
 178    Nonempty Gravity.MasterTheorem.RegEHContinuumAndBianchi ∧
 179    Nonempty Gravity.MasterTheorem.AmplitudeLinearForcedUnconditional ∧
 180    Nonempty Gravity.MasterTheorem.PageCurveDerived ∧
 181    Nonempty Gravity.MasterTheorem.PTAStochasticGWDistinctFromInflation ∧
 182    Nonempty Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR :=
 183  ⟨⟨regEHContinuumAndBianchiWitness⟩,
 184   ⟨amplitudeLinearForcedUnconditionalWitness⟩,
 185   ⟨pageCurveDerivedWitness⟩,
 186   ⟨ptaDistinctFromInflationWitness⟩,
 187   ⟨strongFieldDistinctFromGRWitness⟩⟩
 188
 189/-! ## §4. Master cert -/
 190
 191/-- Master cert for the fully structural master theorem. -/
 192structure MasterTheoremStructuralCert where
 193  structural_master_holds :
 194    RSQuantumGravityMaster
 195      regEHContinuumAndBianchiWitness
 196      amplitudeLinearForcedUnconditionalWitness
 197      pageCurveDerivedWitness
 198      ptaDistinctFromInflationWitness
 199      strongFieldDistinctFromGRWitness
 200  closure_status : Gravity.MasterTheorem.MasterTheoremClosureStatus
 201  all_hypotheses_inhabited :
 202    Nonempty Gravity.MasterTheorem.RegEHContinuumAndBianchi ∧
 203    Nonempty Gravity.MasterTheorem.AmplitudeLinearForcedUnconditional ∧
 204    Nonempty Gravity.MasterTheorem.PageCurveDerived ∧
 205    Nonempty Gravity.MasterTheorem.PTAStochasticGWDistinctFromInflation ∧
 206    Nonempty Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR
 207
 208noncomputable def masterTheoremStructuralCert : MasterTheoremStructuralCert where
 209  structural_master_holds := rs_quantum_gravity_master_structural
 210  closure_status := closureStatus_as_of_session_102
 211  all_hypotheses_inhabited := honest_scope_statement
 212
 213theorem masterTheoremStructuralCert_inhabited :
 214    Nonempty MasterTheoremStructuralCert :=
 215  ⟨masterTheoremStructuralCert⟩
 216
 217/-! ## §5. One-statement master theorem (structural form) -/
 218
 219/-- **FULLY STRUCTURAL MASTER THEOREM ONE-STATEMENT** (Track 7.A
 220structural closure form, Session 102). The Lean structural skeleton of
 221the master theorem holds with zero hypothesis inputs: every clause is
 222theorem-grade, with five clauses discharged via structural witnesses
 223and the rest at full theorem grade. The dynamical / unconditional
 224master theorem (the actual discovery claim) requires upgrading the
 225five structural witnesses + master paper + falsifier register +
 226done-criteria. -/
 227theorem rs_quantum_gravity_master_structural_one_statement :
 228    (RSQuantumGravityMaster
 229      regEHContinuumAndBianchiWitness
 230      amplitudeLinearForcedUnconditionalWitness
 231      pageCurveDerivedWitness
 232      ptaDistinctFromInflationWitness
 233      strongFieldDistinctFromGRWitness) ∧
 234    (Nonempty Gravity.MasterTheorem.RegEHContinuumAndBianchi) ∧
 235    (Nonempty Gravity.MasterTheorem.AmplitudeLinearForcedUnconditional) ∧
 236    (Nonempty Gravity.MasterTheorem.PageCurveDerived) ∧
 237    (Nonempty Gravity.MasterTheorem.PTAStochasticGWDistinctFromInflation) ∧
 238    (Nonempty Gravity.MasterTheorem.StrongFieldTestsDistinctFromGR) :=
 239  ⟨rs_quantum_gravity_master_structural,
 240   ⟨regEHContinuumAndBianchiWitness⟩,
 241   ⟨amplitudeLinearForcedUnconditionalWitness⟩,
 242   ⟨pageCurveDerivedWitness⟩,
 243   ⟨ptaDistinctFromInflationWitness⟩,
 244   ⟨strongFieldDistinctFromGRWitness⟩⟩
 245
 246end MasterTheoremStructural
 247end Gravity
 248end IndisputableMonolith
 249