Reference Atlas Emitter End-to-End Dry Run: An 11372-Node, 5688-Leaf Nested Witness Certificate Actually Runs to Completion for the First Time, Fully Cross-Checked by a Second, Independently Rewritten Verifier; Round 10 Is the First Round in the Whole Series to Adopt the Formal Claim-Status Vocabulary Verbatim, and Pre-Emptively Excludes, Under Its Own REJECTED Category, the Misreading of "Treating the Local Dry Run as the Global 0.835 Theorem"

Round 10 (AMRAL-LUC-FC-R10, 2026-09-18) builds on Round 08–09's certificate grammar and adaptive cost logic; its goal is not to claim that the global a_Leb≥0.835 has already been completed, but to actually run the whole nested certificate pipeline through once. This round centers on the officially published D+B₃+B₅ near-minimizer placement, taking a local five-dimensional neighborhood at normalized coordinates q†=(x₃,y₃,φ₅,x₅,y₅) with halfwidth (4×10⁻⁵,4×10⁻⁵,4×10⁻⁴,4×10⁻⁵,4×10⁻⁵), cutting first along φ₅ and then along x₅ to get 4 base leaves (00/01/10/11, all labeled LIFT-CLOSED rather than BASE-PRUNED), but every base leaf expands the complete Round 08 B7 three-dimensional relevant root (φ₇∈[0,2π/7), x₇,y₇∈[-0.19693504677116785,+0.19693504677116785]), recursively split by a deterministic rule that minimizes motion radius, so the verifier can reconstruct every lift box from the root, the bitstream, and the split rule alone. For each lift leaf, 96 normal boundary points are taken on the curved core and on the radius-1/2 disk respectively, and the convex hull of all the finite points is taken as the one-sided geometric lower witness; the emitter computes this hull with scipy.spatial.ConvexHull, while the independent verifier uses no scipy at all, instead re-implementing it with a handwritten monotone chain + shoelace formula and re-checking erosion nonempty and all-disk membership — so at the convex-hull-algorithm layer alone, the two are already different code paths. The lift trees expanded from the four base leaves (node counts 2833/2853/2833/2853, leaf counts 1417/1427/1417/1427, maximum depth 21 in every case) total 11372 nodes and 5688 leaves, each satisfying N=2L-1; the independent verifier fully cross-checks the manifest and SHA-256, all four B7 bitstreams, deterministic box regeneration, core reconstruction, the handwritten convex hull, subtraction of the dry-run floating-point pad (10⁻⁸), and exact stream exhaustion — both emitter and verifier apply fail-closed semantics to conditions such as MAX_DEPTH and hash mismatch — reaching a final status of REFERENCE-VERIFIED. Round 10 is the first round in the whole series to adopt the formally mandated claim-status vocabulary verbatim — PROVED-ANALYTIC / VERIFIED-COMPUTATIONAL / CONDITIONAL / COMPUTE-DEFERRED / REJECTED — and, under its own REJECTED category, explicitly lists "treating Round 10's local dry run as a global 0.835 theorem" as a forbidden reading. Research direction is chosen and led by Neo.K; this round's execution was carried out by Aletheia / GPT-5.6 Sol.