IndisputableMonolith.Gravity.SevenGaps.FullTheoryLedger
IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean · 341 lines · 19 declarations
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1import Mathlib
2import IndisputableMonolith.Gravity.SevenGaps.CampaignLedger
3import IndisputableMonolith.Gravity.SevenGaps.MeasureSubstrateBlocker
4import IndisputableMonolith.Gravity.SevenGaps.ZqContinuumBlocker
5import IndisputableMonolith.Gravity.SevenGaps.CapShellBridge
6import IndisputableMonolith.Gravity.SevenGaps.ZqShellBalanceBlocker
7import IndisputableMonolith.Gravity.SevenGaps.RecognitionRatioSubstrateBlocker
8import IndisputableMonolith.Gravity.SevenGaps.DynamicStructureFunctionBlocker
9import IndisputableMonolith.Gravity.SevenGaps.MetricRefinementCarrierBlocker
10import IndisputableMonolith.Gravity.SevenGaps.CurvedOperatorUnderdetermination
11
12/-!
13# Full Theory Ledger (Phase 0c of the full-theory campaign, 2026-07-15)
14
15## Status: THEOREM (machine-checked status record; 0 sorry, 0 new axiom).
16
17The live benchmark ledger of the full quantum-gravity theory campaign
18(`plans/QG_Full_Theory_Development_Plan_20260715.html`). One boolean flag
19per pillar benchmark; a flag flips to `true` only when its target theorem is
20kernel-checked, axiom-audited, and critic-passed. The master theorem
21`full_theory_not_yet_closed` stays provable until every pillar flips; the
22closure criterion `FullTheoryClosed` is a definition, so the eventual
23closure claim cannot drift from the flags.
24
25The three pillars ("full theory in the strongest sense"):
261. **Classical recovery** at all three strengths (action, operator,
27 constraint algebra) to Einstein gravity in the 4D Lorentzian continuum
28 limit.
292. **A well-defined quantum amplitude**: derived substrate-to-geometry
30 bridge plus a path-sum measure with a proved convergence / continuum
31 limit.
323. **At least one confirmed discriminating prediction** (BMV entanglement
33 witness or the alpha effective-seam closure).
34
35Anchoring: this module imports `CampaignLedger` (the machine-checked
36seven-gaps starting line) and re-derives the starting-line OPEN flags in
37`starting_line_anchored`, so the full-theory ledger cannot contradict the
38campaign record it extends.
39-/
40
41namespace IndisputableMonolith
42namespace Gravity
43namespace SevenGaps
44namespace FullTheoryLedger
45
46/-- The full-theory benchmark flags. Every field documents the exact target
47theorem whose kernel-checked existence licenses flipping it. -/
48structure FullTheoryBenchmarks where
49 /-- Phase 1 (pillar 2, part A): the substrate-to-geometry bridge is
50 DERIVED (`recognition_ratio_derived`) and validated against independent
51 geometry (`regge_deformation_signed_deficit_witness` +
52 `ledger_hessian_eq_regge_dirichlet_N5`). -/
53 gap1_bridge_derived : Bool
54 /-- Phase 2 (pillar 2, part B): `Z_RS_continuum_limit` on the simplicial
55 class with a substrate-derived measure. -/
56 gap2_continuum_and_measure : Bool
57 /-- Phase 3: the 4D Lorentzian lift (`CausalSimplex4D` +
58 `wick_action_continuation_4d`). -/
59 gap6_lorentzian_action : Bool
60 /-- Phase 4 (pillar 1, operator strength):
61 `discrete_tt_spectrum_converges_curved` + `quasinormal_mode_spectrum`. -/
62 gap4_operator_recovery : Bool
63 /-- Phase 5 (pillar 1, constraint strength):
64 `dirac_algebra_continuum_limit` + `hojman_pins_general_relativity`. -/
65 gap5_constraint_recovery : Bool
66 /-- Phase 6 (pillar 1, action strength): `edge_tt_decomposition` +
67 `S_RS_converges_EH_4d`. -/
68 gap_action_recovery : Bool
69 /-- Phase 7 (pillar 3, the theory-maker): `bmv_entanglement_witness` or
70 `seam_effective_count_derived` passing its gate. -/
71 discriminating_prediction_confirmed : Bool
72
73/-- The current benchmark state. `gap_action_recovery` flipped 2026-07-21
74after honest geometric `S_RS_converges_EH_4d` (Option-C scale-explicit
75Tendsto + discrete torus bridge + exact midpoint m² faces; kernel-accepted
76modulo `native_decide`/`ofReduceBool` on the m² table certificates).
77Constant-face bookkeeping inhabit of the same day remains rejected. -/
78def fullTheoryBenchmarks : FullTheoryBenchmarks where
79 gap1_bridge_derived := false
80 gap2_continuum_and_measure := false
81 gap6_lorentzian_action := false
82 gap4_operator_recovery := false
83 gap5_constraint_recovery := false
84 gap_action_recovery := true
85 discriminating_prediction_confirmed := false
86
87/-- Pillar 1 (classical recovery, all three strengths, 4D Lorentzian). -/
88def Pillar1Closed (b : FullTheoryBenchmarks) : Prop :=
89 b.gap_action_recovery = true ∧ b.gap4_operator_recovery = true ∧
90 b.gap5_constraint_recovery = true ∧ b.gap6_lorentzian_action = true
91
92/-- Pillar 2 (derived bridge + path-sum measure with continuum limit). -/
93def Pillar2Closed (b : FullTheoryBenchmarks) : Prop :=
94 b.gap1_bridge_derived = true ∧ b.gap2_continuum_and_measure = true
95
96/-- Pillar 3 (a confirmed discriminating prediction). -/
97def Pillar3Closed (b : FullTheoryBenchmarks) : Prop :=
98 b.discriminating_prediction_confirmed = true
99
100/-- **The closure criterion.** The full theory in the strongest sense is
101closed exactly when all three pillars are closed. -/
102def FullTheoryClosed (b : FullTheoryBenchmarks) : Prop :=
103 Pillar1Closed b ∧ Pillar2Closed b ∧ Pillar3Closed b
104
105/-- **MASTER THEOREM (the honest gate).** The full theory is NOT yet
106closed: pillar 3 (the theory-maker) is open, which alone blocks closure.
107This theorem must be updated (and will fail to build unchanged) the moment
108the flags flip; it cannot silently coexist with a closure claim. -/
109theorem full_theory_not_yet_closed : ¬ FullTheoryClosed fullTheoryBenchmarks := by
110 intro h
111 have h3 : fullTheoryBenchmarks.discriminating_prediction_confirmed = true :=
112 h.2.2
113 simp [fullTheoryBenchmarks] at h3
114
115/-- Each pillar is individually open at the starting line. -/
116theorem all_pillars_open :
117 ¬ Pillar1Closed fullTheoryBenchmarks ∧
118 ¬ Pillar2Closed fullTheoryBenchmarks ∧
119 ¬ Pillar3Closed fullTheoryBenchmarks := by
120 refine ⟨fun h => ?_, fun h => ?_, fun h => ?_⟩
121 · have := h.2.1; simp [fullTheoryBenchmarks] at this
122 · have := h.1; simp [fullTheoryBenchmarks] at this
123 · simp [Pillar3Closed, fullTheoryBenchmarks] at h
124
125/-- **Anchor to the campaign starting line.** The seven-gaps campaign
126ledger records every gap as carrying an OPEN component; the full-theory
127ledger starts from exactly that state. Re-derived from the imported
128`CampaignLedger`, so this module cannot drift from the machine-checked
129record it extends. -/
130theorem starting_line_anchored :
131 CampaignLedger.sevenGapsCampaignStatus.gap1_hessian_symbol_comparison_open
132 = true ∧
133 CampaignLedger.sevenGapsCampaignStatus.gap2_continuum_limit_open = true ∧
134 CampaignLedger.sevenGapsCampaignStatus.gap4_curved_qnm_open = true ∧
135 CampaignLedger.sevenGapsCampaignStatus.gap5_continuum_algebra_hkt_open
136 = true ∧
137 CampaignLedger.sevenGapsCampaignStatus.gap6_action_continuation_open
138 = true ∧
139 CampaignLedger.sevenGapsCampaignStatus.gap7_true_mechanism_open = true ∧
140 fullTheoryBenchmarks.gap1_bridge_derived = false ∧
141 fullTheoryBenchmarks.discriminating_prediction_confirmed = false :=
142 ⟨rfl, rfl, rfl, rfl, rfl, rfl, rfl, rfl⟩
143
144/-- **PILLAR 2 MEASURE BLOCKER (THEOREM).** The measure half of
145`gap2_continuum_and_measure` is certified open at one exact premise.
146Normalized gauge counting is equivalent to `1 / |Aut K|`, and the
147quotient-uniform decoy fails it on a concrete two-point class. A closing
148theorem must therefore derive normalized gauge counting from richer substrate
149structure. The continuum-limit half remains separately open. -/
150theorem gap2_measure_selection_blocker_certified :
151 ∀ (B : ℕ), 2 ≤ B →
152 MeasureSubstrateBlocker.GaugeCountingPrinciple
153 (ExactShellGaugePreflight.gaugeOrbitMass :
154 PathSumMeasure.TriangulationClass B → ℝ) ∧
155 (∀ ν : PathSumMeasure.TriangulationClass B → ℝ,
156 MeasureSubstrateBlocker.GaugeCountingPrinciple ν ↔
157 ∀ K : PathSumMeasure.BoundedComplex B,
158 ν (Quotient.mk (PathSumMeasure.relabelSetoid B) K) =
159 PathSumMeasure.mu K) ∧
160 ¬ MeasureSubstrateBlocker.GaugeCountingPrinciple
161 (MeasureSubstrateBlocker.uniformClassMass :
162 PathSumMeasure.TriangulationClass B → ℝ) :=
163 MeasureSubstrateBlocker.substrate_measure_blocker_certificate
164
165#print axioms gap2_measure_selection_blocker_certified
166
167/-- **PILLAR 2 CUTOFF-LIMIT BLOCKER (THEOREM).** The convergence half of
168`gap2_continuum_and_measure` is certified at two exact obligations. A
169substrate-derived phase must make every sufficiently late contiguous block
170of exact shell amplitudes small, and the capped `Zq` API must be proved
171compatible with the nonduplicating exact-shell decomposition. Zero phase
172fails the cancellation condition. These are complexity-cutoff statements,
173not mesh refinement or a geometric continuum limit. -/
174theorem gap2_cutoff_limit_blocker_certified :
175 (∀ phase : ∀ n : ℕ, ExactShellGaugeUV.ExactPathClass n → ℝ,
176 CauchySeq (ZqContinuumBlocker.Zcap phase) ↔
177 ZqContinuumBlocker.OscillatoryTail phase) ∧
178 ¬ ZqContinuumBlocker.OscillatoryTail ExactShellGaugeUV.zeroPhase ∧
179 (∀ (P : ZqContinuumBlocker.CapPhaseFamily)
180 (phase : ∀ n : ℕ, ExactShellGaugeUV.ExactPathClass n → ℝ),
181 ZqContinuumBlocker.CapShellCompatibility P phase →
182 (ZqContinuumBlocker.HasPhasedZqComplexityLimit P ↔
183 ZqContinuumBlocker.ExactShellTailCancellation phase)) :=
184 ⟨ZqContinuumBlocker.cauchySeq_Zcap_iff_oscillatoryTail,
185 ZqContinuumBlocker.zeroPhase_not_oscillatoryTail,
186 ZqContinuumBlocker.hasPhasedZqLimit_iff_exactShellTail_of_compatibility⟩
187
188#print axioms gap2_cutoff_limit_blocker_certified
189
190/-! ## Wave 2 receipts (2026-07-17)
191
192Every theorem below is a re-export of a kernel-checked Wave 2 result. None
193of them flips a flag: each one either discharges a named sub-premise of a
194blocker or certifies a new exact blocker. The flags stay `false` because no
195flag's named closing theorem exists yet.
196
197Docstring cross-references (results NOT imported here, to avoid an import
198cycle or Analysis fan-in; verify by building the named module):
199
200* **P1.1a (toward `gap_action_recovery`).**
201 `Gravity.Analysis.ReggeTTContinuumLimit.canonicalFiniteH_div_momentumNormSq_tendsto`
202 proves the normalized canonical finite-`N` TT Hessian converges to the
203 cosine two-jet limit (with `rawCosineFoldAtScale_zero` and
204 `rawCosineFold_scale_tendsto`). The isotropy value `-1/4` (P1.1b) and the
205 algebraic/final closers remain OPEN, so the flag stays `false`.
206* **Gap 7 / Pillar 3 (toward `discriminating_prediction_confirmed`).**
207 `Cosmology.Pillar3CPLForecastBlocker` (which imports THIS module, hence no
208 import here) certifies the sharp CPL target: `target_sum_rule`
209 (`w0 + wa = -1`), `target_coordinate_window`,
210 `target_distinct_from_LambdaCDM`, and the exact provenance blocker
211 `physicalForecast_iff_shapeProvenance`. Its
212 `discriminating_prediction_still_awaits_observation` proves the flag below
213 is still `false`; confirmation is observational
214 (`plans/QG_Pillar3_CPL_Forecast_Gate_20260717.html`), never simulated.
215-/
216
217/-- **PILLAR 2 CAP-SHELL BRIDGE DISCHARGED (THEOREM, P2.3).** The
218missing-bridge premise of `gap2_cutoff_limit_blocker_certified` is
219discharged in the following exact sense: for every exact-shell phase, the
220CANONICAL transported family `CapShellBridge.capPhaseFamily phase` (and
221only that constructed family, not an arbitrary `CapPhaseFamily`) satisfies
222`CapShellCompatibility`, via the carrier equivalence
223`CapShellBridge.capShellEquiv` preserving `1 / |Aut|`. This is a
224sub-premise receipt, NOT a closure of `gap2_continuum_and_measure`: the
225convergence half still needs the `OscillatoryTail` witness for a
226substrate-derived phase, and the measure half is separately open; the flag
227stays `false`. -/
228theorem gap2_capshell_bridge_discharged :
229 ∀ phase : ∀ n : ℕ, ExactShellGaugeUV.ExactPathClass n → ℝ,
230 ZqContinuumBlocker.CapShellCompatibility
231 (CapShellBridge.capPhaseFamily phase) phase :=
232 CapShellBridge.capShellCompatibility
233
234#print axioms gap2_capshell_bridge_discharged
235
236/-- **PILLAR 2 SHELL-BALANCE BLOCKER (THEOREM, P2.4).** The remaining
237`OscillatoryTail` obligation is certified sharp: the tail condition forces
238per-shell amplitude vanishing, so no finite-cap (eventually zero) phase
239repair and no shell-constant phase can satisfy it. Any closing phase must
240rebalance every late shell. -/
241theorem gap2_shell_balance_blocker_certified :
242 (∀ phase : ∀ n : ℕ, ExactShellGaugeUV.ExactPathClass n → ℝ,
243 ZqContinuumBlocker.OscillatoryTail phase →
244 ZqShellBalanceBlocker.ShellAmplitudeVanishes phase) ∧
245 (∀ phase : ∀ n : ℕ, ExactShellGaugeUV.ExactPathClass n → ℝ,
246 ZqShellBalanceBlocker.EventuallyZeroPhase phase →
247 ¬ ZqContinuumBlocker.OscillatoryTail phase) ∧
248 (∀ phase : ∀ n : ℕ, ExactShellGaugeUV.ExactPathClass n → ℝ,
249 ZqShellBalanceBlocker.ShellConstant phase →
250 ¬ ZqContinuumBlocker.OscillatoryTail phase) :=
251 ZqShellBalanceBlocker.p24_shell_balance_blocker_certificate
252
253#print axioms gap2_shell_balance_blocker_certified
254
255/-- **PILLAR 2 METRIC-CARRIER BLOCKER (THEOREM, P2.5).** The current
256combinatorial quotient carrier forgets metric data: the forgetful map from
257metric-decorated simplicial complexes is not injective (one tetrahedron
258carries two admissible metrics with different edge-length and Cayley-Menger
259observables). A mesh-refinement continuum limit needs a metric-refined
260carrier, which remains OPEN. -/
261theorem gap2_metric_carrier_blocker_certified :
262 ¬ Function.Injective
263 (MetricRefinementCarrierBlocker.MetricDecoratedComplex.toClass :
264 MetricRefinementCarrierBlocker.MetricDecoratedComplex 6 →
265 PathSumMeasure.TriangulationClass 6) :=
266 MetricRefinementCarrierBlocker.metricForget_not_injective
267
268#print axioms gap2_metric_carrier_blocker_certified
269
270/-- **PILLAR 2 BRIDGE BLOCKER (THEOREM, P2.1, toward `gap1_bridge_derived`).**
271`recognition_ratio_derived` is certified to NOT follow from a bare
272`RecognitionLedger`: coboundary strains telescope, the imposed-budget route
273is circular, and one bare two-cell ledger arises from opposite signed
274sources. Supplying the named `DeficitSourceConstitutiveCoupling` premise
275derives the ratio bridge with its cubic remainder, on a nontrivial
276small-mesh family. The certificate's positive component is CONDITIONAL on
277that supplied coupling; it does not assert `recognition_ratio_derived`
278itself. Deriving the coupling from richer substrate structure remains
279OPEN, so `gap1_bridge_derived` stays `false`. -/
280theorem gap1_bridge_blocker_certified :
281 RecognitionRatioSubstrateBlockerCertificate :=
282 recognition_ratio_derived_bare_ledger_terminal
283
284#print axioms gap1_bridge_blocker_certified
285
286/-- **GAP 4 CURVATURE-COUPLING BLOCKER (THEOREM).** Two curved Lichnerowicz
287extensions agree on the entire flat specialization yet differ at every
288nonzero curvature, while both satisfy the generic rate-bound consistency
289machinery. The flat spectrum theorem therefore underdetermines the curved
290curvature coupling; `gap4_operator_recovery` stays `false` until the
291coupling is derived. -/
292theorem gap4_curvature_coupling_blocker_certified
293 (rho : ℝ) (hrho : rho ≠ 0) :
294 (∀ (N : ℕ) (H : DiscreteLichnerowicz.LatticeTensorField),
295 CurvedOperatorUnderdetermination.singleCurvatureExtension 0 N H =
296 CurvedOperatorUnderdetermination.doubleCurvatureExtension 0 N H) ∧
297 (∀ N : ℕ,
298 (CurvedOperatorUnderdetermination.singleCurvatureExtension rho N :
299 DiscreteLichnerowicz.LatticeTensorField →
300 DiscreteLichnerowicz.LatticeTensorField) ≠
301 (CurvedOperatorUnderdetermination.doubleCurvatureExtension rho N :
302 DiscreteLichnerowicz.LatticeTensorField →
303 DiscreteLichnerowicz.LatticeTensorField)) ∧
304 CurvedOperatorUnderdetermination.CurvatureCorrectionRateBound
305 (fun r N k =>
306 CurvedOperatorUnderdetermination.curvedDiscreteEigenvalue 1 r N k)
307 (fun r k =>
308 CurvedOperatorUnderdetermination.curvedContinuumEigenvalue 1 r k) ∧
309 CurvedOperatorUnderdetermination.CurvatureCorrectionRateBound
310 (fun r N k =>
311 CurvedOperatorUnderdetermination.curvedDiscreteEigenvalue 2 r N k)
312 (fun r k =>
313 CurvedOperatorUnderdetermination.curvedContinuumEigenvalue 2 r k) :=
314 CurvedOperatorUnderdetermination.gap4_curvature_coupling_blocker rho hrho
315
316#print axioms gap4_curvature_coupling_blocker_certified
317
318/-- **GAP 5 STRUCTURE-FUNCTION BLOCKER (THEOREM).** Every fixed background
319weight yields a background (phase-space constant) structure function and
320reaches the weighted continuum, but no fixed background represents the
321explicit positive dynamic inverse metric. The weighted-bracket route to
322`gap5_constraint_recovery` therefore requires a genuinely dynamic structure
323function, whose substrate derivation remains OPEN; the flag stays
324`false`. -/
325theorem gap5_structure_function_blocker_certified :
326 (∀ w : ZMod 2 → ℝ,
327 DynamicStructureFunctionBlocker.HamWHasBackgroundStructureFunction w) ∧
328 (∀ W : ℝ → ℝ, ContinuousOn W (Set.Icc 0 1) →
329 DynamicStructureFunctionBlocker.BackgroundWeightedContinuumReach W) ∧
330 (∀ w : ZMod 2 → ℝ,
331 ¬ DynamicStructureFunctionBlocker.FixedBackgroundRepresents w
332 DynamicStructureFunctionBlocker.concreteDynamicInverseMetric) :=
333 DynamicStructureFunctionBlocker.gap5_background_weight_blocker
334
335#print axioms gap5_structure_function_blocker_certified
336
337end FullTheoryLedger
338end SevenGaps
339end Gravity
340end IndisputableMonolith
341