Round 23's Shallow 0/60 Was Not Single-Witness Infeasibility: B₇ Alone, Deepened to Depth 30–36, Fully Closes All 12 Reference Cells and Collapses the Joint Residual to Empty

Round 25 (AMRAL-LUC-FC-R25, 2026-09-20) takes the strategy Round 24 validated on only four hardest cells and pushes it across the complete 12-cell reference subset. Background: under Round 23's shallow search — 12 necessity-marked cells × 5 portfolio witnesses (B₇, H₁₁, H₁₃, H₁₇, H₁₉) at lift depth 16 — all 60 pilot edges scored zero; Round 24 then deepened only the single witness B₇ on four of the hardest cells and reached 3 COMPLETE (cell 0 at depth 30, cells 1 and 2 both at depth 32), with cell 3 still PARTIAL. Round 25 applies that same strategy — deepening the single witness B₇ alone, with no joint witness introduced — to all 12 reference cells, and every one of them reaches strict COMPLETE closure: closure depths fall between 30 and 36 (D_max=36, mean 32.5, median 32), with cell 7 the deepest (depth 36, 45,401 nodes, 22,701 CERT leaves) and cells 0, 5, and 11 the shallowest (depth 30); the 12 independent lift trees total 340,540 nodes (average ≈28,378), and all of them satisfy the forest identity N=2L-1. The budget-coverage curve reads F(30)=3/12=25%, F(32)=7/12≈58.33%, F(34)=11/12≈91.67%, F(36)=12/12=100%. Because all 12 cells satisfy I_{j,B7}=1, this round proves that on this reference subset the singleton witness {B₇} is by itself a strict witness cover — H₁₁, H₁₃, H₁₇, H₁₉, and any joint witness are not needed to complete it — and Round 24's four-state joint-admission taxonomy (JOINT-REDUNDANT / JOINT-DEFERRED-CONTRACTING / JOINT-CANDIDATE / JOINT-NECESSARY-RELATIVE-TO-PORTFOLIO) converges entirely to JOINT-REDUNDANT this round, so the joint-admissible residual collapses to empty. This round also shows that the pending-leaf count can be a misleading metric — for cell 7, pending leaves actually rise from 1793 at depth 26 to 1918 at depth 30, even as the unresolved placement volume over the same interval contracts from 3.89×10⁻⁶ to 2.60×10⁻⁷ (about 15-fold) — and so replaces pending-leaf count with the unresolved volume V_d as the measurement basis, formally proving the Unresolved-Volume Monotonicity Theorem (Theorem 9.1: V_{d+1}≤V_d) and defining the plateau metric ρ_{d,Δ}=V_{d+Δ}/V_d on that basis. The closure capacity curve is Γ_B7(30)=3, Γ_B7(32)=7, Γ_B7(34)=11, Γ_B7(36)=12; this round also proves the Reference Maximum Closure Depth Theorem — for any finite reference cell set where every D_j is finite, D*=max_j D_j (here, 36) is a common finite budget under which all cells are simultaneously COMPLETE, though the document itself states plainly that this is only a finite reference statement. On this basis, the production scheduler is updated to a B₇-first, three-stage policy (first run the B₇ deepening wave to the shared checkpoints 30/32/34/36; remove any COMPLETE cell from the residual/joint queue immediately; for a cell still unresolved at depth 36, decide by its volume-contraction ratio whether to keep deepening B₇ or move it into portfolio/joint), but H₁₁, H₁₃, H₁₇, H₁₉, and joint witnesses are not discarded — this is only a reprioritization, since the full 77-cell atlas may still contain cells where B₇ is slower, has counterexamples, or plateaus. The document repeatedly states, in boxed statements, that this is still reference/pilot arithmetic covering only the 12-cell subset flagged by Round 23, that it cannot be extrapolated to the full 77-cell atlas, still less to the global Lebesgue theorem, and hence cannot support the claim Λ(D,B₃,B₅,B₇)≥0.835; even with 12/12 complete, the full 77-cell closure wave, full base-atlas coverage, production-grade arithmetic, independent complete-edge replay for every final shard, root/shard merge, and a global theorem-ready checkpoint are all still missing, and the global bound a_Leb≥0.835 remains compute-deferred. Research direction and methodology are due to Neo.K; this round's AI collaborating researcher and primary executor was Aletheia / ChatGPT, GPT-5.6 Sol.