IndisputableMonolith.Foundation.OptionAFalsifierRegistry
IndisputableMonolith/Foundation/OptionAFalsifierRegistry.lean · 275 lines · 35 declarations
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1import Mathlib
2
3/-!
4# Option A Falsifier Registry
5
6Finite registry pairing each C1-C9 cross-domain theorem with its empirical
7test class. This does not prove the empirical claims. It keeps the falsifiers
8attached to the Lean theorem bundle so the cross-domain work cannot drift into
9unfalsifiable numerology.
10
11Lean status: 0 sorry, 0 axiom.
12-/
13
14namespace IndisputableMonolith
15namespace Foundation
16namespace OptionAFalsifierRegistry
17
18/-- The implemented Option A combinations. C10 was left as commentary. -/
19inductive CombinationID where
20 | c1CognitiveTensor
21 | c2PlanetStrata
22 | c3OncologyTensor
23 | c4QuantumMolecularDepth
24 | c5AttentionTensor
25 | c6EriksonReverse
26 | c7UniversalResponse
27 | c8MillerSpan
28 | c9RegulatoryCeiling
29 deriving DecidableEq, Repr, Fintype
30
31theorem combinationID_count : Fintype.card CombinationID = 9 := by
32 decide
33
34/-- Coarse empirical test class attached to a combination. -/
35inductive TestClass where
36 | eegDecoder
37 | seismicAtmosphericRatio
38 | tcgaClinicalResponse
39 | quantumCircuitDepth
40 | attentionBlinkPlateaus
41 | adniDementiaProgression
42 | crossFieldEquilibriumResponse
43 | workingMemorySpanReduction
44 | encodeTcgaRegulatoryModule
45 deriving DecidableEq, Repr, Fintype
46
47theorem testClass_count : Fintype.card TestClass = 9 := by
48 decide
49
50/-- Status of the Lean theorem relative to the empirical claim. -/
51inductive EmpiricalStatus where
52 | theoremOnly
53 | theoremPlusHypothesis
54 | scaffoldPlusHypothesis
55 deriving DecidableEq, Repr, Fintype
56
57theorem empiricalStatus_count : Fintype.card EmpiricalStatus = 3 := by
58 decide
59
60/-- Dataset class expected to carry the empirical test. -/
61inductive DatasetClass where
62 | eegMegDecoderCorpus
63 | seismicAtmosphericCatalog
64 | tcgaClinicalTrials
65 | quantumChemistryBenchmarks
66 | attentionBlinkMeg
67 | adniLongitudinal
68 | crossDomainPanel
69 | workingMemoryPerturbation
70 | encodeTcgaRegulatory
71 deriving DecidableEq, Repr, Fintype
72
73theorem datasetClass_count : Fintype.card DatasetClass = 9 := by
74 decide
75
76/-- Observable predicted by the Lean structural theorem plus RS hypothesis. -/
77inductive PredictedObservable where
78 | tensorRank125
79 | strataRatioPhiPower
80 | multiplicativeTherapyResponse
81 | fiveBitAddressBound
82 | fortyStableFiveTransient
83 | reverseEriksonOrder
84 | unitResponseCoefficient
85 | qSpaceSpanSequence
86 | regulatoryCeiling70
87 deriving DecidableEq, Repr, Fintype
88
89theorem predictedObservable_count : Fintype.card PredictedObservable = 9 := by
90 decide
91
92/-- What empirical pattern would count as a failure of the associated claim. -/
93inductive FailureMode where
94 | singleAxisDecoderSuffices
95 | noSmallPhiPowerRatio
96 | additiveTherapyResponse
97 | depthExceedsFiveBits
98 | nonFortyPlateauSpectrum
99 | nonReverseDementiaOrder
100 | nonUnitSharedCoefficient
101 | nonQSpaceSpanCollapse
102 | moduleExceedsCeiling70
103 deriving DecidableEq, Repr, Fintype
104
105theorem failureMode_count : Fintype.card FailureMode = 9 := by
106 decide
107
108/-- The empirical test class for each Option A combination. -/
109def falsifierClass : CombinationID → TestClass
110 | .c1CognitiveTensor => .eegDecoder
111 | .c2PlanetStrata => .seismicAtmosphericRatio
112 | .c3OncologyTensor => .tcgaClinicalResponse
113 | .c4QuantumMolecularDepth => .quantumCircuitDepth
114 | .c5AttentionTensor => .attentionBlinkPlateaus
115 | .c6EriksonReverse => .adniDementiaProgression
116 | .c7UniversalResponse => .crossFieldEquilibriumResponse
117 | .c8MillerSpan => .workingMemorySpanReduction
118 | .c9RegulatoryCeiling => .encodeTcgaRegulatoryModule
119
120/-- Whether the implemented Lean content is purely structural or paired with an
121empirical hypothesis. -/
122def empiricalStatus : CombinationID → EmpiricalStatus
123 | .c1CognitiveTensor => .theoremPlusHypothesis
124 | .c2PlanetStrata => .theoremPlusHypothesis
125 | .c3OncologyTensor => .theoremPlusHypothesis
126 | .c4QuantumMolecularDepth => .theoremPlusHypothesis
127 | .c5AttentionTensor => .theoremPlusHypothesis
128 | .c6EriksonReverse => .scaffoldPlusHypothesis
129 | .c7UniversalResponse => .theoremPlusHypothesis
130 | .c8MillerSpan => .theoremPlusHypothesis
131 | .c9RegulatoryCeiling => .theoremPlusHypothesis
132
133/-- Dataset class assigned to each implemented combination. -/
134def datasetClass : CombinationID → DatasetClass
135 | .c1CognitiveTensor => .eegMegDecoderCorpus
136 | .c2PlanetStrata => .seismicAtmosphericCatalog
137 | .c3OncologyTensor => .tcgaClinicalTrials
138 | .c4QuantumMolecularDepth => .quantumChemistryBenchmarks
139 | .c5AttentionTensor => .attentionBlinkMeg
140 | .c6EriksonReverse => .adniLongitudinal
141 | .c7UniversalResponse => .crossDomainPanel
142 | .c8MillerSpan => .workingMemoryPerturbation
143 | .c9RegulatoryCeiling => .encodeTcgaRegulatory
144
145/-- Predicted observable assigned to each implemented combination. -/
146def predictedObservable : CombinationID → PredictedObservable
147 | .c1CognitiveTensor => .tensorRank125
148 | .c2PlanetStrata => .strataRatioPhiPower
149 | .c3OncologyTensor => .multiplicativeTherapyResponse
150 | .c4QuantumMolecularDepth => .fiveBitAddressBound
151 | .c5AttentionTensor => .fortyStableFiveTransient
152 | .c6EriksonReverse => .reverseEriksonOrder
153 | .c7UniversalResponse => .unitResponseCoefficient
154 | .c8MillerSpan => .qSpaceSpanSequence
155 | .c9RegulatoryCeiling => .regulatoryCeiling70
156
157/-- Failure mode assigned to each implemented combination. -/
158def failureMode : CombinationID → FailureMode
159 | .c1CognitiveTensor => .singleAxisDecoderSuffices
160 | .c2PlanetStrata => .noSmallPhiPowerRatio
161 | .c3OncologyTensor => .additiveTherapyResponse
162 | .c4QuantumMolecularDepth => .depthExceedsFiveBits
163 | .c5AttentionTensor => .nonFortyPlateauSpectrum
164 | .c6EriksonReverse => .nonReverseDementiaOrder
165 | .c7UniversalResponse => .nonUnitSharedCoefficient
166 | .c8MillerSpan => .nonQSpaceSpanCollapse
167 | .c9RegulatoryCeiling => .moduleExceedsCeiling70
168
169theorem c1_falsifier :
170 falsifierClass .c1CognitiveTensor = .eegDecoder := rfl
171
172theorem c2_falsifier :
173 falsifierClass .c2PlanetStrata = .seismicAtmosphericRatio := rfl
174
175theorem c3_falsifier :
176 falsifierClass .c3OncologyTensor = .tcgaClinicalResponse := rfl
177
178theorem c4_falsifier :
179 falsifierClass .c4QuantumMolecularDepth = .quantumCircuitDepth := rfl
180
181theorem c5_falsifier :
182 falsifierClass .c5AttentionTensor = .attentionBlinkPlateaus := rfl
183
184theorem c6_falsifier :
185 falsifierClass .c6EriksonReverse = .adniDementiaProgression := rfl
186
187theorem c7_falsifier :
188 falsifierClass .c7UniversalResponse = .crossFieldEquilibriumResponse := rfl
189
190theorem c8_falsifier :
191 falsifierClass .c8MillerSpan = .workingMemorySpanReduction := rfl
192
193theorem c9_falsifier :
194 falsifierClass .c9RegulatoryCeiling = .encodeTcgaRegulatoryModule := rfl
195
196theorem c3_observable :
197 predictedObservable .c3OncologyTensor = .multiplicativeTherapyResponse := rfl
198
199theorem c5_failure :
200 failureMode .c5AttentionTensor = .nonFortyPlateauSpectrum := rfl
201
202theorem c8_dataset :
203 datasetClass .c8MillerSpan = .workingMemoryPerturbation := rfl
204
205theorem falsifierClass_injective : Function.Injective falsifierClass := by
206 intro a b h
207 cases a <;> cases b <;> simp [falsifierClass] at h ⊢
208
209theorem datasetClass_injective : Function.Injective datasetClass := by
210 intro a b h
211 cases a <;> cases b <;> simp [datasetClass] at h ⊢
212
213theorem predictedObservable_injective : Function.Injective predictedObservable := by
214 intro a b h
215 cases a <;> cases b <;> simp [predictedObservable] at h ⊢
216
217theorem failureMode_injective : Function.Injective failureMode := by
218 intro a b h
219 cases a <;> cases b <;> simp [failureMode] at h ⊢
220
221structure FalsifierRegistryCert where
222 nine_combinations : Fintype.card CombinationID = 9
223 nine_test_classes : Fintype.card TestClass = 9
224 three_statuses : Fintype.card EmpiricalStatus = 3
225 nine_dataset_classes : Fintype.card DatasetClass = 9
226 nine_observables : Fintype.card PredictedObservable = 9
227 nine_failure_modes : Fintype.card FailureMode = 9
228 c1_test : falsifierClass .c1CognitiveTensor = .eegDecoder
229 c2_test : falsifierClass .c2PlanetStrata = .seismicAtmosphericRatio
230 c3_test : falsifierClass .c3OncologyTensor = .tcgaClinicalResponse
231 c4_test : falsifierClass .c4QuantumMolecularDepth = .quantumCircuitDepth
232 c5_test : falsifierClass .c5AttentionTensor = .attentionBlinkPlateaus
233 c6_test : falsifierClass .c6EriksonReverse = .adniDementiaProgression
234 c7_test : falsifierClass .c7UniversalResponse = .crossFieldEquilibriumResponse
235 c8_test : falsifierClass .c8MillerSpan = .workingMemorySpanReduction
236 c9_test : falsifierClass .c9RegulatoryCeiling = .encodeTcgaRegulatoryModule
237 c3_predicted_observable :
238 predictedObservable .c3OncologyTensor = .multiplicativeTherapyResponse
239 c5_failure_mode :
240 failureMode .c5AttentionTensor = .nonFortyPlateauSpectrum
241 c8_dataset_class :
242 datasetClass .c8MillerSpan = .workingMemoryPerturbation
243 test_class_injective : Function.Injective falsifierClass
244 dataset_class_injective : Function.Injective datasetClass
245 observable_injective : Function.Injective predictedObservable
246 failure_mode_injective : Function.Injective failureMode
247
248def falsifierRegistryCert : FalsifierRegistryCert where
249 nine_combinations := combinationID_count
250 nine_test_classes := testClass_count
251 three_statuses := empiricalStatus_count
252 nine_dataset_classes := datasetClass_count
253 nine_observables := predictedObservable_count
254 nine_failure_modes := failureMode_count
255 c1_test := c1_falsifier
256 c2_test := c2_falsifier
257 c3_test := c3_falsifier
258 c4_test := c4_falsifier
259 c5_test := c5_falsifier
260 c6_test := c6_falsifier
261 c7_test := c7_falsifier
262 c8_test := c8_falsifier
263 c9_test := c9_falsifier
264 c3_predicted_observable := c3_observable
265 c5_failure_mode := c5_failure
266 c8_dataset_class := c8_dataset
267 test_class_injective := falsifierClass_injective
268 dataset_class_injective := datasetClass_injective
269 observable_injective := predictedObservable_injective
270 failure_mode_injective := failureMode_injective
271
272end OptionAFalsifierRegistry
273end Foundation
274end IndisputableMonolith
275