Tail/arc-compression search. Started from the transferable size-32 core, which at N=3360 lies entirely above N/2. Sweeps at N/4, 0.30N, N/3, 3N/8, 2N/5, 0.45N, N/2 found no direct insertion; exhaustive 1->2 at representative thresholds and exact 2->3 at N/4, 2N/5, N/2 also stalled. A deeper sampled 3->4 search at N/4 found {1802,2427,2727} -> {1062,2667,2917,2947}, giving size 33. The new set occupies an arc of span 1885, so translating by +283 repacks the full size-33 witness above 2N/5 (min 1345 > 1344). Exact direct/1->2/2->3 regrowth from the repacked state and 1200 sampled 3->4 branches at 2N/5 found no size 34.
Yongxi (Aaron) Lin · 2026-08-10 09:47:30 UTC