All Seven Seats of the Depth-30 Batch Advance to Publication-Candidate, DFRONT Completes Its First Real Recovery: cell33's Lost Frontier Exactly Rebuilt, Zero Error

Round 36 (AMRAL-LUC-FC-R36, 2026-09-20) completes two independent closures. First, on the arithmetic side: the depth-30 batch's last two cells complete promotion to publication-candidate — cell75 (10,948 leaves, 2,627,357 rational vertices, RHCERT raw bytes 44,382,455) passes 10,948/10,948 bytes-only replay, with a minimum exact margin of 6.2517761412×10⁻⁸ and an MPFR dominance check of 1,690 unique states, 0 failures; cell76 (10,932 leaves, 2,617,252 rational vertices, raw certificate 44,229,325 bytes) passes 10,932/10,932 bytes-only replay, with a minimum margin of 2.0477267270×10⁻⁸ and MPFR dominance of 1,688 unique states, 0 failures. Both possess complete finite topology, a split-axis stream, rational marker upper and lower bounds, independent recomputation, MPFR recomputation, bytes-only replay, and an MPFR enclosure audit, bringing all seven cells {47,48,68,69,70,75,76} to complete the Depth-30 Publication Batch (7/7), contributing to the global publication-candidate tier of 7/77 (≈9.09%; relative to the 66 known geometry-complete cells, that is 7/66≈10.61%). Second, on the geometry side: this round is the first time the DFRONT-v0.1 format moves from specification into real recovery verification — cell33's previously lost depth-36 search frontier (the old Round 26 checkpoint's underlying per-box state was not persisted at the time, and only summary statistics survived) is deterministically rebuilt from the witness root, and the result exactly matches all three summary values in the Round 26 ledger: 129,401 nodes, 14,027 pending leaves, unresolved volume 2.9748317031636626×10⁻⁸, with an absolute volume error of 0; the new explicit pending frontier is only 126,327 bytes. This round also gives the most concise terminological summary of this entire arithmetic-migration series: "RHCERT = certified leaves" corresponds to "DFRONT = unresolved leaves", representing two complementary evidence formats — one already proven closed, the other still open. This recovery of cell33 is exactly what the next installment, Round 37, goes on to continue and extend — Round 37 starts from this round's recovered depth-36 checkpoint and, via its newly-proposed Compositional DFRONT Merge Theorem, advances successively to depth 38, 40, and 42. Research direction is chosen and led by Neo.K; this round's execution was carried out by Aletheia / GPT-5.6 Sol.