All 77 Cells of the Necessity Atlas Complete Exact-Rational Upper Migration, First Whole-Shard Prototype Closes: Marker 70 Confirmed as Round 28's Complete Lift Cell

Round 29 (AMRAL-LUC-FC-R29, 2026-09-20) fills in the other half that Round 28 had not yet handled: the necessity marker's base-hull upper bound (upper certificate), dual to the witness-tree lower bound migrated in Round 28. This round migrates every marker of the complete 77-cell necessity atlas, in one pass, into "directed support upper + exact rational outer polygon" form; the result is 77/77 PASS with zero UPPER-INCONCLUSIVE — precisely confirming 77 as the necessity atlas's complete total cell count, i.e. the baseline total that every "N/77" progress figure across the site is measured against. In terms of quantization density, the 77 markers are distributed across four densities — 4096 (21 markers), 8192 (39), 16384 (16), and 32768 (1) — none requiring 65536; the thinnest new upper margin occurs at marker 6 (about 6.1062×10⁻⁷), and the median margin is about 3.5043×10⁻⁵, noticeably thicker than the order of magnitude of the witness-tree lower bound. Another key confirmation of this round: the base cell corresponding to Round 28's complete witness tree (9278/9278 leaves PASS) has, within the complete 77-cell atlas, the official index of marker 70 — the marker index and Round 28's cell/path index are thus confirmed to be one and the same indexing space, not two systems that merely happen to overlap. As a result, marker 70's base-hull upper bound (margin about 9.24985×10⁻⁵) and Round 28's B7 lower bound are joined end to end for the first time, forming this research line's first ARITHMETICALLY-CLOSED-WHOLE-SHARD-PROTOTYPE. Of the 77 markers, only three — 6, 47, and 70 — have been replayed and cross-checked via a second, independent polygon path (not relying on the emitter's scipy candidate reduction); all three PASS, but this round explicitly states that it does not yet claim independent cross-verification of all 77/77. Throughout, the document self-labels publication_candidate=false: the production backend is still a prototype, and neither the full independent lower A1 replay nor the global atlas closure has been completed. Research direction is chosen and led by Neo.K; this round's execution was carried out by Aletheia / GPT-5.6 Sol.