First Push to the Complete 77-Cell Necessity Atlas: Common Depth d=36 Reaches 51/77, a Unified Global-Pad Proposal Vetoed by Its Own Audit Data Before Activation

Round 26 (AMRAL-LUC-FC-R26, 2026-09-20) is the first time this research line has pushed its search scope to the complete 77-cell necessity atlas — all depth-40 base cells flagged by the Round 19 necessity segmentation, each satisfying U_base(q_j)<0.835. To prevent different cells from contaminating each other's comparison baseline by using different maximum depths, this round fixes a common checkpoint budget of d=36, and advances wave by wave through a common depth wave (22→24→26→28→30→32→34→36), so that a small number of difficult cells cannot occupy the queue and block the rest from advancing fairly; the closure curve is strictly monotonically non-decreasing: Γ_B7(30)=7, Γ_B7(32)=19, Γ_B7(34)=38, Γ_B7(36)=51. Checkpoint result: of the 77 cells, 51 (66.23%) achieve strict reference B₇ closure at the common depth d=36, while the remaining 26 residual cells — divided by unresolved volume into three classes, terminal dust (5), thin (7), and broad (14) — are all still contracting: the contraction ratio for all 26 cells is <1, with the largest at ρ_max≈0.57615, and none shows a volume plateau, so joint-witness necessity evidence is not yet established. This round also formally establishes a production arithmetic ABI: a COMPLETE determination at the reference floating/exact-kernel level cannot be directly promoted to publication proof, and all current reference leaves are uniformly marked ARITHMETIC-PENDING until interval arithmetic migration is complete. The document records a methodological self-correction: a proposal had argued for handling all leaves' floating-point uncertainty at once with a unified 10⁻⁸ global pad, but after this round actually audited the completed complete trees, the smallest observed leaf slack among them turned out to be only about 2.8982×10⁻⁹ — far smaller than 10⁻⁸, meaning that if this unified pad were really applied, it would silently reopen some leaves whose closure was already legitimate; this proposal was therefore vetoed before it was ever put into use. Research direction was chosen and led by Neo.K; this round's execution was carried out by Aletheia / ChatGPT, GPT-5.6 Sol.