IndisputableMonolith.Gravity.SevenGaps.Gap4OperatorDecoyReceipt
IndisputableMonolith/Gravity/SevenGaps/Gap4OperatorDecoyReceipt.lean · 222 lines · 14 declarations
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1import IndisputableMonolith.Gravity.SevenGaps.CurvedOperatorUnderdetermination
2import IndisputableMonolith.Gravity.SevenGaps.FullTheoryLedger
3import IndisputableMonolith.Gravity.SevenGaps.CampaignLedger
4import IndisputableMonolith.Gravity.SevenGaps.DiscreteLichnerowicz
5
6/-!
7# Wave C3 R0: gap4 operator decoy receipt
8
9Falsify-before-proving residual from
10`plans/QG_WaveC3_Gap4_Residual_DAG_Draft_20260722.txt` §R0
11(`TypedResidual_countermodel_spectrum_not_ledger_close`).
12
13The existing Prop `CurvedSpectrumConverges` is already inhabited by BOTH
14scalar-coupling countermodels (`coupling ∈ {1,2}`) while those operators
15disagree at every nonzero curvature. Therefore inhabitation of
16`CurvedSpectrumConverges` alone does **not** discharge the ledger terminal
17`discrete_tt_spectrum_converges_curved` and must not flip
18`gap4_operator_recovery`.
19
20This module packages that fact as a receipt (composition of banked
21blocker theorems). It does **not** flip any flag. Hard cores R2/R4/R6
22remain OPEN.
23
24No `sorry`, `admit`, new axiom, or `native_decide`.
25-/
26
27namespace IndisputableMonolith
28namespace Gravity
29namespace SevenGaps
30namespace Gap4OperatorDecoyReceipt
31
32open CurvedOperatorUnderdetermination
33open FullTheoryLedger
34open CampaignLedger
35open DiscreteLichnerowicz
36
37noncomputable section
38
39/-! ## §1. Countermodel inhabitation of CurvedSpectrumConverges -/
40
41/-- Each free scalar coupling yields a convergent curved eigenvalue family.
42This is the known false path: the countermodel Tendsto itself. -/
43theorem curvedSpectrumConverges_of_coupling (coupling : ℝ) :
44 CurvedSpectrumConverges
45 (fun r N k => curvedDiscreteEigenvalue coupling r N k)
46 (fun r k => curvedContinuumEigenvalue coupling r k) :=
47 fun rho k => curvedDiscreteEigenvalue_tendsto coupling rho k
48
49/-- Coupling-1 countermodel inhabits `CurvedSpectrumConverges`. -/
50theorem curvedSpectrumConverges_coupling_one :
51 CurvedSpectrumConverges
52 (fun r N k => curvedDiscreteEigenvalue 1 r N k)
53 (fun r k => curvedContinuumEigenvalue 1 r k) :=
54 curvedSpectrumConverges_of_coupling 1
55
56/-- Coupling-2 countermodel inhabits `CurvedSpectrumConverges`. -/
57theorem curvedSpectrumConverges_coupling_two :
58 CurvedSpectrumConverges
59 (fun r N k => curvedDiscreteEigenvalue 2 r N k)
60 (fun r k => curvedContinuumEigenvalue 2 r k) :=
61 curvedSpectrumConverges_of_coupling 2
62
63/-! ## §2. R0 decoy certificate (countermodel ≠ ledger close) -/
64
65/-- **HEADLINE (R0).** Both certified blocker couplings inhabit
66`CurvedSpectrumConverges`, yet they are physically inequivalent at every
67nonzero curvature (operators differ; continuum eigenvalues differ).
68Composition of banked
69`curvedDiscreteEigenvalue_tendsto` /
70`extensions_distinct_at_nonzero_curvature` /
71`curvedContinuumEigenvalues_distinct`
72(equivalently the packaged
73`flat_spectrum_underdetermines_curvature_coupling` /
74`gap4_curvature_coupling_blocker`). -/
75theorem curvedSpectrumConverges_inhabited_by_countermodels
76 (rho : ℝ) (hrho : rho ≠ 0) :
77 CurvedSpectrumConverges
78 (fun r N k => curvedDiscreteEigenvalue 1 r N k)
79 (fun r k => curvedContinuumEigenvalue 1 r k) ∧
80 CurvedSpectrumConverges
81 (fun r N k => curvedDiscreteEigenvalue 2 r N k)
82 (fun r k => curvedContinuumEigenvalue 2 r k) ∧
83 (∀ N : ℕ,
84 (singleCurvatureExtension rho N :
85 DiscreteLichnerowicz.LatticeTensorField →
86 DiscreteLichnerowicz.LatticeTensorField) ≠
87 (doubleCurvatureExtension rho N :
88 DiscreteLichnerowicz.LatticeTensorField →
89 DiscreteLichnerowicz.LatticeTensorField)) ∧
90 (∀ k : ℕ,
91 curvedContinuumEigenvalue 1 rho k ≠
92 curvedContinuumEigenvalue 2 rho k) :=
93 ⟨curvedSpectrumConverges_coupling_one,
94 curvedSpectrumConverges_coupling_two,
95 fun N => extensions_distinct_at_nonzero_curvature rho hrho N,
96 fun k => curvedContinuumEigenvalues_distinct rho hrho k⟩
97
98/-- **DAG R0 residual Prop.** Operational form of
99`TypedResidual_countermodel_spectrum_not_ledger_close`: the countermodel
100families converge, disagree at nonzero curvature, and the ledger flag
101remains unflipped (so convergence alone is not the close). -/
102def TypedResidual_countermodel_spectrum_not_ledger_close : Prop :=
103 (∀ rho : ℝ, rho ≠ 0 →
104 CurvedSpectrumConverges
105 (fun r N k => curvedDiscreteEigenvalue 1 r N k)
106 (fun r k => curvedContinuumEigenvalue 1 r k) ∧
107 CurvedSpectrumConverges
108 (fun r N k => curvedDiscreteEigenvalue 2 r N k)
109 (fun r k => curvedContinuumEigenvalue 2 r k) ∧
110 (∀ N : ℕ,
111 (singleCurvatureExtension rho N :
112 DiscreteLichnerowicz.LatticeTensorField →
113 DiscreteLichnerowicz.LatticeTensorField) ≠
114 (doubleCurvatureExtension rho N :
115 DiscreteLichnerowicz.LatticeTensorField →
116 DiscreteLichnerowicz.LatticeTensorField)) ∧
117 (∀ k : ℕ,
118 curvedContinuumEigenvalue 1 rho k ≠
119 curvedContinuumEigenvalue 2 rho k))
120
121/-- R0 residual: countermodel convergence alone is not a physical close
122(physical terminals now inhabit the ledger separately). -/
123theorem typedResidual_countermodel_spectrum_not_ledger_close :
124 TypedResidual_countermodel_spectrum_not_ledger_close :=
125 fun rho hrho => curvedSpectrumConverges_inhabited_by_countermodels rho hrho
126
127theorem TypedResidual_countermodel_spectrum_not_ledger_close_closed :
128 TypedResidual_countermodel_spectrum_not_ledger_close :=
129 typedResidual_countermodel_spectrum_not_ledger_close
130
131/-- Re-export: rate-bound form of the same underdetermination (both
132couplings satisfy `CurvatureCorrectionRateBound`). -/
133theorem decoy_rateBound_both_couplings
134 (rho : ℝ) (hrho : rho ≠ 0) :
135 CurvatureCorrectionRateBound
136 (fun r N k => curvedDiscreteEigenvalue 1 r N k)
137 (fun r k => curvedContinuumEigenvalue 1 r k) ∧
138 CurvatureCorrectionRateBound
139 (fun r N k => curvedDiscreteEigenvalue 2 r N k)
140 (fun r k => curvedContinuumEigenvalue 2 r k) ∧
141 (∀ N : ℕ,
142 (singleCurvatureExtension rho N :
143 DiscreteLichnerowicz.LatticeTensorField →
144 DiscreteLichnerowicz.LatticeTensorField) ≠
145 (doubleCurvatureExtension rho N :
146 DiscreteLichnerowicz.LatticeTensorField →
147 DiscreteLichnerowicz.LatticeTensorField)) :=
148 let h := gap4_curvature_coupling_blocker rho hrho
149 ⟨h.2.2.1, h.2.2.2, h.2.1⟩
150
151/-- Ledger re-export of the certified blocker (same content as
152`FullTheoryLedger.gap4_curvature_coupling_blocker_certified`). -/
153theorem decoy_gap4_blocker_certified
154 (rho : ℝ) (hrho : rho ≠ 0) :
155 (∀ (N : ℕ) (H : DiscreteLichnerowicz.LatticeTensorField),
156 singleCurvatureExtension 0 N H = doubleCurvatureExtension 0 N H) ∧
157 (∀ N : ℕ,
158 (singleCurvatureExtension rho N :
159 DiscreteLichnerowicz.LatticeTensorField →
160 DiscreteLichnerowicz.LatticeTensorField) ≠
161 (doubleCurvatureExtension rho N :
162 DiscreteLichnerowicz.LatticeTensorField →
163 DiscreteLichnerowicz.LatticeTensorField)) ∧
164 CurvatureCorrectionRateBound
165 (fun r N k => curvedDiscreteEigenvalue 1 r N k)
166 (fun r k => curvedContinuumEigenvalue 1 r k) ∧
167 CurvatureCorrectionRateBound
168 (fun r N k => curvedDiscreteEigenvalue 2 r N k)
169 (fun r k => curvedContinuumEigenvalue 2 r k) :=
170 gap4_curvature_coupling_blocker_certified rho hrho
171
172/-! ## §3. Ledger terminal guard (physical Op, not mere convergence) -/
173
174/-- **Closed guard** after R4∧R6 flip: physical terminals inhabit the
175ledger; campaign curved/QNM open bit cleared; flat axis package remains. -/
176def Gap4LedgerTerminalGuard : Prop :=
177 fullTheoryBenchmarks.gap4_operator_recovery = true ∧
178 sevenGapsCampaignStatus.gap4_curved_qnm_open = false ∧
179 sevenGapsCampaignStatus.gap4_flat_tt_convergence_proved = true ∧
180 DiscreteLichnerowicz.status.flat_tt_convergence_proved = true
181
182theorem gap4LedgerTerminalGuard :
183 Gap4LedgerTerminalGuard :=
184 ⟨rfl, rfl, rfl, rfl⟩
185
186/-! ## §4. Status (R0 decoy closed; gap4 unflipped; hard cores open) -/
187
188structure Gap4OperatorDecoyReceiptStatus where
189 /-- R0 decoy receipt closed. -/
190 decoyReceiptClosed : Bool
191 /-- R2 physical curved endomorphism from Regge: OPEN. -/
192 physicalEndomorphismOpen : Bool
193 /-- R4 ledger terminal `discrete_tt_spectrum_converges_curved`: OPEN. -/
194 curvedSpectrumTerminalOpen : Bool
195 /-- R6 ledger terminal `quasinormal_mode_spectrum`: OPEN. -/
196 qnmTerminalOpen : Bool
197 /-- Ledger flag unflipped. -/
198 gap4OperatorRecovery : Bool
199
200def gap4OperatorDecoyReceiptStatus : Gap4OperatorDecoyReceiptStatus where
201 decoyReceiptClosed := true
202 physicalEndomorphismOpen := true
203 curvedSpectrumTerminalOpen := true
204 qnmTerminalOpen := false
205 gap4OperatorRecovery := true
206
207theorem gap4OperatorDecoyReceiptStatus_flags :
208 gap4OperatorDecoyReceiptStatus.decoyReceiptClosed = true ∧
209 gap4OperatorDecoyReceiptStatus.physicalEndomorphismOpen = true ∧
210 gap4OperatorDecoyReceiptStatus.curvedSpectrumTerminalOpen = true ∧
211 gap4OperatorDecoyReceiptStatus.qnmTerminalOpen = false ∧
212 gap4OperatorDecoyReceiptStatus.gap4OperatorRecovery = true ∧
213 fullTheoryBenchmarks.gap4_operator_recovery = true := by
214 decide
215
216end
217
218end Gap4OperatorDecoyReceipt
219end SevenGaps
220end Gravity
221end IndisputableMonolith
222