IndisputableMonolith.Gravity.MasterTheoremPartial

   1import Mathlib
   2import IndisputableMonolith.Gravity.MasterTheorem
   3import IndisputableMonolith.Cosmology.PTAStochasticGWStructural
   4import IndisputableMonolith.Gravity.StrongFieldStructural
   5
   6/-!
   7# Gravity Track 7.A (partial): Master Theorem with PTA + Strong-Field
   8Hypotheses Pre-Filled
   9
  10## Status: STRUCTURAL THEOREM (conditional with 3 remaining hypothesis inputs).
  110 sorry, 0 RS-internal axiom. Closure 2026-05-22 session 100.
  12
  13## What this module closes
  14
  15This module is the **Session 100 partial advancement** of the master
  16theorem authored in Session 97 (`Gravity.MasterTheorem.rs_quantum_gravity_master_conditional`).
  17Session 97's conditional theorem took **five** hypothesis inputs
  18corresponding to the five then-open tracks:
  19
  20* `RegEHContinuumAndBianchi` ↔ Track 1.B/1.C (still OPEN)
  21* `AmplitudeLinearForcedUnconditional` ↔ Track 2.C/2.D unconditional (still OPEN)
  22* `PageCurveDerived` ↔ Track 3.C (still OPEN)
  23* `PTAStochasticGWDistinctFromInflation` ↔ Track 6.B (**closed structurally in Session 100**)
  24* `StrongFieldTestsDistinctFromGR` ↔ Track 6.C (**closed structurally in Session 100**)
  25
  26Session 100 (this module) provides Lean witnesses for the last two
  27hypothesis inputs via the new modules
  28`Cosmology.PTAStochasticGWStructural` and `Gravity.StrongFieldStructural`.
  29The remaining conditional master theorem
  30`rs_quantum_gravity_master_partial_conditional` takes only **three**
  31hypothesis inputs.
  32
  33The discovery is **not** claimed: three hypothesis inputs remain, plus
  34the master paper, plus the §7 falsifier register population, plus the
  35six §8 done-criteria. Per master plan §6, all four must be satisfied
  36for "discovery complete".
  37
  38## The partial conditional theorem
  39
  40```
  41theorem rs_quantum_gravity_master_partial_conditional
  42    (H_d2 : RegEHContinuumAndBianchi)
  43    (H_amp : AmplitudeLinearForcedUnconditional)
  44    (H_page : PageCurveDerived) :
  45    RSQuantumGravityMaster H_d2 H_amp H_page
  46      ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness
  47```
  48
  49The eight CLOSED clauses from Session 97 are still discharged inline
  50from existing theorems. The two NEWLY-FILLED clauses are discharged
  51from `ptaDistinctFromInflationWitness` and
  52`strongFieldDistinctFromGRWitness`. The three REMAINING hypothesis
  53inputs are the same as Session 97's `H_d2`, `H_amp`, `H_page`.
  54
  55## Anti-retreat principle satisfied
  56
  57The PTA and strong-field structural discriminators are theorem-grade
  58algebraically (`0 < log φ` and `0 < φ^{-44}`). They are
  59HYPOTHESIS-grade for empirical match against specific datasets
  60(NANOGrav, EPTA for PTA; EHT, GRAVITY, Cassini for strong-field) —
  61those dataset attachments remain separate falsifier-register
  62obligations in master plan §7.
  63
  64The conditional theorem proves the master statement with **three**
  65remaining hypothesis inputs. No discovery claim, no master-statement
  66softening. Per §6 done-criteria, the discovery is complete only when:
  671. The conditional theorem compiles with zero hypothesis inputs (all
  68   three remaining tracks closed).
  692. Master paper authored, peer-reviewed, posted to arXiv.
  703. §7 falsifier register fully populated.
  714. Six §8 done-criteria satisfied.
  72
  73Zero `sorry`. Zero new RS-specific axioms.
  74-/
  75
  76namespace IndisputableMonolith
  77namespace Gravity
  78namespace MasterTheoremPartial
  79
  80open IndisputableMonolith.Gravity.MasterTheorem
  81open IndisputableMonolith.Cosmology.PTAStochasticGWStructural
  82open IndisputableMonolith.Gravity.StrongFieldStructural
  83
  84/-! ## §1. The partial conditional master theorem -/
  85
  86/-- **PARTIAL CONDITIONAL MASTER THEOREM (Session 100).** Pre-fills the
  87two structural witnesses for Tracks 6.B and 6.C, reducing the
  88hypothesis input count from five (Session 97) to three. -/
  89theorem rs_quantum_gravity_master_partial_conditional
  90    (H_d2 : RegEHContinuumAndBianchi)
  91    (H_amp : AmplitudeLinearForcedUnconditional)
  92    (H_page : PageCurveDerived) :
  93    RSQuantumGravityMaster H_d2 H_amp H_page
  94      ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness :=
  95  rs_quantum_gravity_master_conditional
  96    H_d2 H_amp H_page
  97    ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness
  98
  99/-! ## §2. Closure tracker: post-Session 100 status -/
 100
 101/-- Updated closure status as of session 100 (2026-05-22): the master
 102theorem template has 8 CLOSED clauses + 2 NEWLY-FILLED hypothesis
 103inputs (6.B and 6.C via structural witnesses) + 1 STRUCTURAL (under
 104factor-product) + 3 OPEN hypothesis inputs (1.B/1.C, 2.C/2.D
 105unconditional, 3.C). -/
 106def closureStatus_as_of_session_100 :
 107    Gravity.MasterTheorem.MasterTheoremClosureStatus where
 108  closed_count := 10  -- 8 + 2 newly filled
 109  structural_count := 1
 110  open_count := 3
 111  total_count := 14   -- 12 clauses + 2 newly-counted structural witnesses
 112  total_eq := by decide
 113
 114/-! ## §3. ∀-quantified form -/
 115
 116/-- ∀-quantified form of the partial conditional master theorem. -/
 117theorem rs_quantum_gravity_master_partial_one_statement :
 118    ∀ (H_d2 : RegEHContinuumAndBianchi)
 119      (H_amp : AmplitudeLinearForcedUnconditional)
 120      (H_page : PageCurveDerived),
 121    RSQuantumGravityMaster H_d2 H_amp H_page
 122      ptaDistinctFromInflationWitness strongFieldDistinctFromGRWitness :=
 123  rs_quantum_gravity_master_partial_conditional
 124
 125end MasterTheoremPartial
 126end Gravity
 127end IndisputableMonolith
 128