IndisputableMonolith.Gravity.SevenGaps.Gap2TickPhaseSubstrate
IndisputableMonolith/Gravity/SevenGaps/Gap2TickPhaseSubstrate.lean · 446 lines · 35 declarations
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1import IndisputableMonolith.Gravity.SevenGaps.ZqShellBalanceBlocker
2
3/-!
4# Wave C1 R2: exact-shell tick-phase enrichment schema
5
6Banks the schema residual named in
7`plans/QG_WaveC1_Gap2_Residual_DAG_Draft_20260722.txt` R2 (and the CORE 2
8PHASE design in `plans/QG_WaveC1_Gap2_HardCore_Design_20260722.txt`):
9
10* `ExactPathClass n` is already the GlobalEquivalent quotient (sigma over
11 `ShellSig n` of `Quotient (exactSetoid …)`), so a tick assignment
12 `ExactPathClass n → Fin 8` is well-posed on classes by construction.
13* Dead classes `ShellConstant` / `EventuallyZeroPhase` are banked in
14 `ZqShellBalanceBlocker`; escape requires intra-shell tick variance.
15* Eight-tick API (`RRF.Hypotheses.EightTick`) is a Fin-8 *trace*
16 hypothesis only; it supplies no equidistribution theorem. The
17 equidistribution content lives here as an independent Prop.
18
19## What this module proves (THEOREM)
20
21* Schema structure `ExactShellTickPhaseSubstrate` with derived phase
22 `2π · tick / 8`, plus escape fields `not_shellConstant` /
23 `not_eventuallyZero`.
24* Non-circular guard `TickEquidistributedInShell` (equal fiber
25 cardinalities inside each shell; no mention of amplitudes / tails).
26* Bridge: mass-balanced Fin-8 fibers cancel by 8th-root orthogonality,
27 yielding `ShellAmplitudeVanishes` (`tickEquidistribution_implies_shellAmplitudeVanishes`).
28* Concrete witness: signature vertex-count mod 8 escapes both dead
29 classes (THEOREM). Its `OscillatoryTail` stays OPEN (R4).
30* Decoy: raw complexity tick `2π·(n%8)/8` is `ShellConstant`, hence dead.
31
32## What stays OPEN
33
34* `TypedResidual_strengthened_tick_balance`: contiguous late-block
35 `ExactShellTailCancellation` for a tick phase. Per-shell
36 equidistribution / `ShellAmplitudeVanishes` is necessary but not
37 sufficient for uniform block cancellation.
38* Analytic `OscillatoryTail` for the signature-vertex witness (R4).
39
40Does NOT flip `gap2_continuum_and_measure`. No `sorry`, `admit`, new
41axiom, or `native_decide`.
42-/
43
44namespace IndisputableMonolith
45namespace Gravity
46namespace SevenGaps
47namespace Gap2TickPhaseSubstrate
48
49open ExactShellGaugeUV
50open ZqContinuumBlocker
51open ZqShellBalanceBlocker
52
53noncomputable section
54
55/-! ## §1. Derived phase from a Fin-8 tick assignment -/
56
57/-- Phase (radians) attached to a Fin-8 tick: `2π · tick / 8`. -/
58def tickDerivedPhase (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) :
59 ∀ n : ℕ, ExactPathClass n → ℝ :=
60 fun n c => 2 * Real.pi * ((tau n c : ℕ) : ℝ) / 8
61
62/-- Unit 8th-root character of a tick. -/
63def tickRoot (p : Fin 8) : ℂ :=
64 Complex.exp (2 * (Real.pi : ℂ) * Complex.I * ((p : ℕ) : ℂ) / 8)
65
66theorem tickDerivedPhase_exp (tau : ∀ n : ℕ, ExactPathClass n → Fin 8)
67 (n : ℕ) (c : ExactPathClass n) :
68 Complex.exp (Complex.I * (tickDerivedPhase tau n c : ℂ)) =
69 tickRoot (tau n c) := by
70 unfold tickDerivedPhase tickRoot
71 congr 1
72 push_cast
73 ring
74
75/-! ## §2. Schema structure (escape dead classes; no analytic tail field) -/
76
77/-- Tick-phase enrichment substrate on exact complexity shells.
78
79`tickPhase` is well-posed on the GlobalEquivalent quotient because
80`ExactPathClass` is already that quotient type (no separate descent
81proof). The analytic cancellation field is *not* packed here: it is the
82separate OPEN residual `TypedResidual_strengthened_tick_balance`. -/
83structure ExactShellTickPhaseSubstrate where
84 tickPhase : ∀ n : ℕ, ExactPathClass n → Fin 8
85 not_shellConstant :
86 ¬ ShellConstant (tickDerivedPhase tickPhase)
87 not_eventuallyZero :
88 ¬ EventuallyZeroPhase (tickDerivedPhase tickPhase)
89
90/-- Extracted real phase of a substrate. -/
91def ExactShellTickPhaseSubstrate.phase (S : ExactShellTickPhaseSubstrate) :
92 ∀ n : ℕ, ExactPathClass n → ℝ :=
93 tickDerivedPhase S.tickPhase
94
95/-! ## §3. Non-circular equidistribution guard (cardinal) -/
96
97/-- Fiber of tick value `p` inside shell `n`. -/
98def tickFiber (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) (n : ℕ) (p : Fin 8) :
99 Finset (ExactPathClass n) :=
100 Finset.univ.filter (fun c => tau n c = p)
101
102/-- **Non-circular guard.** Equal cardinalities of tick fibers inside each
103exact shell. Mentions only `tau` and Finset cardinality; never
104`exactShellAmplitude`, `OscillatoryTail`, or limits. -/
105def TickEquidistributedInShell (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) :
106 Prop :=
107 ∀ n : ℕ, ∀ p q : Fin 8, (tickFiber tau n p).card = (tickFiber tau n q).card
108
109/-- Mass of a tick fiber (uses `classMu` only; still free of amplitude /
110tail / limit language). -/
111def tickFiberMass (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) (n : ℕ)
112 (p : Fin 8) : ℝ :=
113 ∑ c ∈ tickFiber tau n p, classMu c
114
115/-- Equal `classMu`-mass across the eight tick fibers of each shell.
116This is the load-bearing hypothesis of the root-of-unity bridge: cardinal
117equidistribution alone cannot cancel unequal class masses. -/
118def TickFiberMassBalanced (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) : Prop :=
119 ∀ n : ℕ, ∀ p q : Fin 8, tickFiberMass tau n p = tickFiberMass tau n q
120
121/-- Cardinal equidistribution + shellwise-constant `classMu` yields mass
122balance (transport between the combinatorial guard and the bridge hyp). -/
123theorem tickCardEquidistribution_constantMu_implies_massBalanced
124 (tau : ∀ n : ℕ, ExactPathClass n → Fin 8)
125 (hcard : TickEquidistributedInShell tau)
126 (hmu : ∀ n : ℕ, ∀ c d : ExactPathClass n, classMu c = classMu d) :
127 TickFiberMassBalanced tau := by
128 intro n p q
129 unfold tickFiberMass
130 obtain ⟨c0⟩ := (inferInstance : Nonempty (ExactPathClass n))
131 have hcard_eq := hcard n p q
132 have hmu_p : ∀ c ∈ tickFiber tau n p, classMu c = classMu c0 :=
133 fun c _ => hmu n c c0
134 have hmu_q : ∀ c ∈ tickFiber tau n q, classMu c = classMu c0 :=
135 fun c _ => hmu n c c0
136 simp only [Finset.sum_congr rfl hmu_p, Finset.sum_congr rfl hmu_q,
137 Finset.sum_const, nsmul_eq_mul]
138 rw [hcard_eq]
139
140/-! ## §4. Eighth-root orthogonality and the amplitude bridge -/
141
142private lemma eighth_root_ne_one :
143 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ≠ 1 := by
144 intro h
145 have hpow :
146 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ 4 =
147 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8 * 4) := by
148 rw [← Complex.exp_nat_mul]
149 congr 1
150 ring
151 have hπ :
152 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8 * 4) =
153 Complex.exp ((Real.pi : ℂ) * Complex.I) := by
154 congr 1
155 ring
156 have hneg : Complex.exp ((Real.pi : ℂ) * Complex.I) = -1 :=
157 Complex.exp_pi_mul_I
158 have : (1 : ℂ) = -1 := by
159 calc (1 : ℂ)
160 = (1 : ℂ) ^ 4 := by norm_num
161 _ = Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ 4 := by rw [h]
162 _ = Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8 * 4) := hpow
163 _ = Complex.exp ((Real.pi : ℂ) * Complex.I) := hπ
164 _ = -1 := hneg
165 exact absurd this (by norm_num)
166
167private lemma eighth_root_pow_eight :
168 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ 8 = 1 := by
169 rw [← Complex.exp_nat_mul]
170 have harg : (8 : ℕ) * (2 * (Real.pi : ℂ) * Complex.I / 8) =
171 2 * (Real.pi : ℂ) * Complex.I := by
172 ring
173 rw [harg, Complex.exp_two_pi_mul_I]
174
175/-- Sum of the eight 8th roots of unity vanishes. -/
176theorem sum_tickRoots_eq_zero : ∑ p : Fin 8, tickRoot p = 0 := by
177 unfold tickRoot
178 have hterm : ∀ p : Fin 8,
179 Complex.exp (2 * (Real.pi : ℂ) * Complex.I * ((p : ℕ) : ℂ) / 8) =
180 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ (p : ℕ) := by
181 intro p
182 rw [← Complex.exp_nat_mul]
183 congr 1
184 ring
185 calc ∑ p : Fin 8,
186 Complex.exp (2 * (Real.pi : ℂ) * Complex.I * ((p : ℕ) : ℂ) / 8)
187 = ∑ p : Fin 8,
188 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ (p : ℕ) :=
189 Finset.sum_congr rfl fun p _ => hterm p
190 _ = ∑ k ∈ Finset.range 8,
191 Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ k :=
192 Fin.sum_univ_eq_sum_range
193 (fun k => Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ k) 8
194 _ = (Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) ^ 8 - 1) /
195 (Complex.exp (2 * (Real.pi : ℂ) * Complex.I / 8) - 1) :=
196 geom_sum_eq eighth_root_ne_one 8
197 _ = 0 := by
198 rw [eighth_root_pow_eight, sub_self, zero_div]
199
200/-- Group the weighted shell amplitude by tick fiber. -/
201theorem exactShellAmplitude_tick_fiberwise
202 (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) (n : ℕ) :
203 exactShellAmplitude (tickDerivedPhase tau) n =
204 ∑ p : Fin 8, (tickFiberMass tau n p : ℂ) * tickRoot p := by
205 unfold exactShellAmplitude tickFiberMass tickFiber
206 have hsplit :
207 (∑ c : ExactPathClass n,
208 (classMu c : ℂ) *
209 Complex.exp (Complex.I * (tickDerivedPhase tau n c : ℂ))) =
210 ∑ p : Fin 8,
211 ∑ c ∈ Finset.univ.filter (fun c => tau n c = p),
212 (classMu c : ℂ) *
213 Complex.exp (Complex.I * (tickDerivedPhase tau n c : ℂ)) := by
214 exact (Finset.sum_fiberwise_of_maps_to
215 (t := Finset.univ) (g := fun c : ExactPathClass n => tau n c)
216 (fun _ _ => Finset.mem_univ _) _).symm
217 rw [hsplit]
218 refine Finset.sum_congr rfl fun p _ => ?_
219 have hmul :
220 ∑ c ∈ Finset.univ.filter (fun c => tau n c = p),
221 (classMu c : ℂ) *
222 Complex.exp (Complex.I * (tickDerivedPhase tau n c : ℂ)) =
223 ∑ c ∈ Finset.univ.filter (fun c => tau n c = p),
224 (classMu c : ℂ) * tickRoot p := by
225 refine Finset.sum_congr rfl fun c hc => ?_
226 have htau : tau n c = p := (Finset.mem_filter.mp hc).2
227 rw [tickDerivedPhase_exp, htau]
228 rw [hmul, ← Finset.sum_mul, Complex.ofReal_sum]
229
230/-- Under equal fiber masses, every shell amplitude is identically zero
231(8th-root cancellation). -/
232theorem exactShellAmplitude_eq_zero_of_massBalanced
233 (tau : ∀ n : ℕ, ExactPathClass n → Fin 8)
234 (hbal : TickFiberMassBalanced tau) (n : ℕ) :
235 exactShellAmplitude (tickDerivedPhase tau) n = 0 := by
236 rw [exactShellAmplitude_tick_fiberwise]
237 have hconst : ∀ p : Fin 8, tickFiberMass tau n p = tickFiberMass tau n 0 :=
238 fun p => hbal n p 0
239 calc ∑ p : Fin 8, (tickFiberMass tau n p : ℂ) * tickRoot p
240 = ∑ p : Fin 8, (tickFiberMass tau n 0 : ℂ) * tickRoot p := by
241 refine Finset.sum_congr rfl fun p _ => ?_
242 rw [hconst p]
243 _ = (tickFiberMass tau n 0 : ℂ) * ∑ p : Fin 8, tickRoot p := by
244 rw [Finset.mul_sum]
245 _ = (tickFiberMass tau n 0 : ℂ) * 0 := by rw [sum_tickRoots_eq_zero]
246 _ = 0 := by ring
247
248/-- **BRIDGE THEOREM.** Mass-balanced Fin-8 tick equidistribution forces
249the shell-local necessary condition `ShellAmplitudeVanishes`.
250
251Honesty: the named design bridge is realized by equal fiber *mass*
252(`TickFiberMassBalanced`). The cardinal guard
253`TickEquidistributedInShell` is non-circular and independent; with
254shellwise-constant `classMu` it implies mass balance via
255`tickCardEquidistribution_constantMu_implies_massBalanced`. -/
256theorem tickEquidistribution_implies_shellAmplitudeVanishes
257 (tau : ∀ n : ℕ, ExactPathClass n → Fin 8)
258 (hbal : TickFiberMassBalanced tau) :
259 ShellAmplitudeVanishes (tickDerivedPhase tau) := by
260 intro ε hε
261 refine ⟨0, fun n _ => ?_⟩
262 rw [exactShellAmplitude_eq_zero_of_massBalanced tau hbal n, norm_zero]
263 exact hε
264
265/-! ## §5. Strengthened contiguous-block residual (OPEN) -/
266
267/-- **OPEN typed residual** (R3→R4 analytic half). Contiguous late-block
268cancellation for a tick-derived phase:
269`ExactShellTailCancellation (tickDerivedPhase tau)`.
270
271Why per-shell equidistribution is insufficient: `TickFiberMassBalanced`
272(and even the consequence `ShellAmplitudeVanishes`) only forces each
273individual late shell amplitude to vanish. `ExactShellTailCancellation`
274(equivalently `OscillatoryTail`) demands uniform smallness of every
275contiguous late block `∑_{k ∈ Ico (m+1) (n+1)} amp_k`. Vanishing of
276summands does not automatically control coherent accumulation across many
277shells; the banked implication
278`oscillatoryTail_implies_shellAmplitudeVanishes` is one-directional.
279
280This Prop is uninhabited in this module on purpose. -/
281def TypedResidual_strengthened_tick_balance
282 (tau : ∀ n : ℕ, ExactPathClass n → Fin 8) : Prop :=
283 ExactShellTailCancellation (tickDerivedPhase tau)
284
285/-- Schema package Prop matching DAG R2 (existence of an escaping
286tick-phase enrichment; analytic tail NOT required). -/
287def TypedResidual_shell_phase_enrichment_schema : Prop :=
288 Nonempty ExactShellTickPhaseSubstrate
289
290/-! ## §6. Concrete escaping witness: signature vertex-count mod 8 -/
291
292/-- Intra-shell tick from the shell-signature vertex count mod 8.
293
294`ExactPathClass n = Σ s : ShellSig n, Quotient …` exposes the signature
295`(v,e,t)` outside the GlobalEquivalent quotient. Vertex count `sigV`
296therefore descends automatically and varies inside a shell (e.g. isolated
297`(n,0,0)` vs edge-heavy `(1,n,0)`). Quotient-internal incidence data is
298*not* used here; R4 feasibility for true oscillatory cancellation may
299still need richer class invariants than signature counts alone. -/
300def signatureVertexTick (n : ℕ) (c : ExactPathClass n) : Fin 8 :=
301 ⟨sigV c.1 % 8, Nat.mod_lt _ (by norm_num : (0 : ℕ) < 8)⟩
302
303/-- Edge-heavy labeled complex at signature `(1, n, 0)`. -/
304def edgeHeavyComplex (n : ℕ) : ExactComplex 1 n 0 where
305 edgeVerts := fun _ => (0, 0)
306 tetVerts := fun i => i.elim0
307
308/-- Shell signature `(1, n, 0)` at level `n ≥ 1`. -/
309def edgeHeavySig (n : ℕ) (hn : 1 ≤ n) : ShellSig n :=
310 ⟨(⟨1, by omega⟩, ⟨n, Nat.lt_succ_self n⟩, ⟨0, Nat.succ_pos n⟩), by
311 change max (1 : ℕ) (max n 0) = n
312 rw [Nat.max_zero]
313 exact Nat.max_eq_right hn⟩
314
315/-- Class of the edge-heavy complex inside shell `n`. -/
316def edgeHeavyClass (n : ℕ) (hn : 1 ≤ n) : ExactPathClass n :=
317 ⟨edgeHeavySig n hn, Quotient.mk _ (edgeHeavyComplex n)⟩
318
319theorem signatureVertexTick_edgeHeavy (n : ℕ) (hn : 1 ≤ n) :
320 signatureVertexTick n (edgeHeavyClass n hn) =
321 ⟨1 % 8, Nat.mod_lt _ (by norm_num : (0 : ℕ) < 8)⟩ := by
322 rfl
323
324theorem signatureVertexTick_isolated (n : ℕ) :
325 signatureVertexTick n (isolatedClass n) =
326 ⟨n % 8, Nat.mod_lt _ (by norm_num : (0 : ℕ) < 8)⟩ := by
327 rfl
328
329theorem signatureVertexTickPhase_not_shellConstant :
330 ¬ ShellConstant (tickDerivedPhase signatureVertexTick) := by
331 intro hconst
332 have h := hconst 2 (edgeHeavyClass 2 (by norm_num))
333 -- LHS tick = 1, RHS tick = 2
334 have hL : tickDerivedPhase signatureVertexTick 2 (edgeHeavyClass 2 (by norm_num)) =
335 2 * Real.pi * (1 : ℝ) / 8 := by
336 simp only [tickDerivedPhase, signatureVertexTick_edgeHeavy]
337 norm_num
338 have hR : tickDerivedPhase signatureVertexTick 2 (isolatedClass 2) =
339 2 * Real.pi * (2 : ℝ) / 8 := by
340 simp only [tickDerivedPhase, signatureVertexTick_isolated]
341 norm_num
342 have hEq : (2 * Real.pi * (1 : ℝ) / 8) = 2 * Real.pi * (2 : ℝ) / 8 := by
343 calc 2 * Real.pi * (1 : ℝ) / 8
344 = tickDerivedPhase signatureVertexTick 2 (edgeHeavyClass 2 (by norm_num)) :=
345 hL.symm
346 _ = tickDerivedPhase signatureVertexTick 2 (isolatedClass 2) := h
347 _ = 2 * Real.pi * (2 : ℝ) / 8 := hR
348 have hπ : (0 : ℝ) < Real.pi := Real.pi_pos
349 have : (1 : ℝ) = 2 := by
350 have := congrArg (fun x : ℝ => x * 8 / (2 * Real.pi)) hEq
351 field_simp [hπ.ne'] at this
352 linarith
353 norm_num at this
354
355theorem signatureVertexTickPhase_not_eventuallyZero :
356 ¬ EventuallyZeroPhase (tickDerivedPhase signatureVertexTick) := by
357 intro hzero
358 obtain ⟨N, hN⟩ := hzero
359 let n : ℕ := 8 * N + 1
360 have hn : N ≤ n := by
361 change N ≤ 8 * N + 1
362 omega
363 have hph := hN n hn (isolatedClass n)
364 have hval : tickDerivedPhase signatureVertexTick n (isolatedClass n) =
365 2 * Real.pi * (1 : ℝ) / 8 := by
366 simp only [tickDerivedPhase, signatureVertexTick_isolated]
367 have hmod : n % 8 = 1 := by
368 change (8 * N + 1) % 8 = 1
369 rw [Nat.add_mod, Nat.mul_mod_right, Nat.zero_add, Nat.mod_eq_of_lt (by norm_num)]
370 simp only [hmod]
371 norm_num
372 have hEq : (2 * Real.pi * (1 : ℝ) / 8) = 0 := by
373 calc 2 * Real.pi * (1 : ℝ) / 8
374 = tickDerivedPhase signatureVertexTick n (isolatedClass n) := hval.symm
375 _ = 0 := by
376 simpa [zeroPhase] using hph
377 have hπ : (0 : ℝ) < Real.pi := Real.pi_pos
378 nlinarith [hπ]
379
380/-- **THEOREM.** Signature vertex-count mod 8 is an escaping tick-phase
381substrate (clears both certified dead classes). Analytic
382`OscillatoryTail` / strengthened block cancellation remain OPEN. -/
383def signatureVertexTickSubstrate : ExactShellTickPhaseSubstrate where
384 tickPhase := signatureVertexTick
385 not_shellConstant := signatureVertexTickPhase_not_shellConstant
386 not_eventuallyZero := signatureVertexTickPhase_not_eventuallyZero
387
388theorem typedResidual_shell_phase_enrichment_schema_closed :
389 TypedResidual_shell_phase_enrichment_schema :=
390 ⟨signatureVertexTickSubstrate⟩
391
392/-! ## §7. Decoy: complexity-only eight-tick phase is ShellConstant -/
393
394/-- Raw complexity tick: phase depends only on shell index `n % 8`. -/
395def complexityTick (n : ℕ) (_c : ExactPathClass n) : Fin 8 :=
396 ⟨n % 8, Nat.mod_lt n (by norm_num : (0 : ℕ) < 8)⟩
397
398def complexityTickPhase : ∀ n : ℕ, ExactPathClass n → ℝ :=
399 tickDerivedPhase complexityTick
400
401/-- **DECOY THEOREM.** The raw complexity eight-tick phase is
402shell-constant (banked dead class). -/
403theorem complexityTickPhase_shellConstant :
404 ShellConstant complexityTickPhase := by
405 intro n c
406 rfl
407
408/-- Decoy is killed by the banked `shellConstant_not_oscillatoryTail`. -/
409theorem complexityTickPhase_not_oscillatoryTail :
410 ¬ OscillatoryTail complexityTickPhase :=
411 shellConstant_not_oscillatoryTail complexityTickPhase
412 complexityTickPhase_shellConstant
413
414theorem complexityTickPhase_decoy_dead :
415 ShellConstant complexityTickPhase ∧
416 ¬ OscillatoryTail complexityTickPhase :=
417 ⟨complexityTickPhase_shellConstant, complexityTickPhase_not_oscillatoryTail⟩
418
419/-! ## §8. Status flags (no continuum flip) -/
420
421structure Gap2TickPhaseSubstrateStatus where
422 r2SchemaClosed : Bool
423 escapingWitnessLanded : Bool
424 strengthenedBalanceOpen : Bool
425 gap2ContinuumAndMeasure : Bool
426
427def gap2TickPhaseSubstrateStatus : Gap2TickPhaseSubstrateStatus where
428 r2SchemaClosed := true
429 escapingWitnessLanded := true
430 strengthenedBalanceOpen := true
431 gap2ContinuumAndMeasure := false
432
433theorem gap2TickPhaseSubstrateStatus_flags :
434 gap2TickPhaseSubstrateStatus.r2SchemaClosed = true ∧
435 gap2TickPhaseSubstrateStatus.escapingWitnessLanded = true ∧
436 gap2TickPhaseSubstrateStatus.strengthenedBalanceOpen = true ∧
437 gap2TickPhaseSubstrateStatus.gap2ContinuumAndMeasure = false := by
438 decide
439
440end
441
442end Gap2TickPhaseSubstrate
443end SevenGaps
444end Gravity
445end IndisputableMonolith
446