Three Seats Cross the Publication Threshold While the Unresolved Boundary Keeps Widening: Depth-32 Migration and Composable DFRONT Extension

Round 37 (AMRAL-LUC-FC-R37, 2026-09-20) simultaneously advances two independent production pipelines. On the arithmetic side: the depth-32 queue's first three cells — 49, 64, 66 — each completed durable topology reconstruction, full rational lower-bound migration (cell49: 9986/9986, cell64: 10539/10539, cell66: 10636/10636, all PASS; cell49's minimum lower-bound margin is 3.15312672×10⁻⁸, and cell66 is the thinnest of the three this round, with a minimum lower-bound margin of 6.86089458×10⁻⁹), independent marker upper-bound recomputation, marker upper-bound recomputation and enclosure-dominance checking rerun with a second arbitrary-precision library, MPFR (all three with 0 failures), and a concrete RHCERT-v0.1 byte-level replayable certificate (cell49/64/66 with 2,441,597 / 2,624,186 / 2,646,674 vertices respectively) — and each passed bytes-only replay. These three cells thus advance to publication-candidate, raising that tier from Round 36's 7/77 to 10/77 (≈12.99%; relative to the 66 known geometry-complete cells, that is 10/66≈15.15%). On the geometry side: cell33's durable frontier, starting from the previously recovered depth-36 checkpoint, successively produced three durable checkpoints at depth 38, 40, and 42 via this round's newly-proposed Compositional DFRONT Merge Theorem — which cuts an oversized frontier into pairwise-disjoint, individually hash-identified immutable segments, so that merging only needs to combine hashes rather than rerun the expensive global disjoint scan. The absolute volume of the unresolved region shrank from depth-36's 2.9748×10⁻⁸ to depth-42's 2.6015×10⁻⁹ (V₄₂/V₃₆≈8.745%), but the number of pending boxes in that same interval rose, counter to the trend, from 14,027 to 78,507 — the document itself states plainly that this result is "still no plateau evidence," and cell33 remains PARTIAL. Across the global 77-cell atlas, 66 cells are known geometry-complete, 51 reach the shared common depth d=36, and only 10 have entered publication-candidate. Research direction is chosen and led by Neo.K; this round's execution was carried out by Aletheia / GPT-5.6 Sol.