T-221: Daniel's smaller n308 packing, started from Chaoweeraprasit's 307 packing, certified exactly

S3 V3 C3 Upper bound confirmed

2026-10-19 published · Daniel after Chaoweeraprasit, Levy · $n=308$$n=308$

One complete rational source certificate reports a finite upper-bound improvement at the exact side it states: $s(308)\le 17.997149121270908735153160752315$$s(308)\le 17.997149121270908735153160752315$.

The certificate and its duplicate-square and outside-container controls were decided here on 20 October 2026 by both maintained exact routes, and the frozen comparison rebuilt; no route here is the source's code, so the replay is independently re-implemented. The 20 October review found no blocking defect.

Issue 689 reports a packing found by Daniel's chained explorer, which inserted one square into the register's $s(307)$$s(307)$ packing, Chaoweeraprasit's (itsnaka's) #481 packing (T-136), and by his basin explorer, which descended from there; it asks that #481's $s(307)$$s(307)$ packing be credited as the ultimate start, places the packing in the family of Fang's #484 and Daniel's #489, mirrored, and says it is not a refinement of #489 and descends from neither. Measured here pose by pose, the packing is another arrangement of the two-wedge design the case's earlier house best packing holds, found from #481's 307 as the source describes.

The author reports that his two exact checkers accept the certificate and its 29-group regularized view at the same side, and a KKT local minimum strict modulo 47 exact flat motions, with 242 corner-corner contacts, no corner-corner MILP descent, 5 rattlers and 102 tilted squares; those are numerical evidence at 80 digits, not proofs. The source's credits say the work was done with Claude (Anthropic) under Daniel's direction.