First Full Pilot Run on the Global Master Root: Raw HARD Vastly Outnumbers the True Near-Minimizer Frontier, B7 Lift Deferred, Base-First Policy Adopted

Round 16 (AMRAL-LUC-FC-R16, 2026-09-19) is the first time this research line runs a finite-depth pilot on the full five-dimensional global master root D+B₃+B₅: phase master target T_M=0.8365, while the actual next theorem target to profile remains T=0.8350; the round runs only to finite depth and claims no complete certificate, and its purpose is not a new lower bound but answers to five questions about prune structure, split scheduler, the master root's extra domain cost, the true near-minimizer share of the raw HARD frontier, and when to activate B7. A split-scheduler A/B test compares the Mishra/official first-order-weight scheduler against Round 09's exact-τ one-step scheduler: at depth 16 the official scheduler has about 18.48% fewer nodes (23,455 vs. 28,771) and about 21.71% fewer HARD leaves (4,112 vs. 5,252), showing that one-step τ optimality is not the same as global tree-cost optimality — this is not an error in Round 09's theorem (Round 09 only proved one-step optimality for a single coordinate bisection), and is logged as R09-STRENGTHENING-EMPIRICAL-001, with the official scheduler kept as the production baseline for now. At the same depth 16 under the official scheduler, the immediate root T=0.835 (N=24,691, CORE=8,004, HARD=4,342) is compared against the phase master root T_M=0.8365 (N=23,455, CORE=7,616, HARD=4,112): the master root has larger geometric volume yet this finite-depth pilot shows slightly fewer nodes, showing that domain-volume overhead cannot be linearly converted into certificate cost. Running the full T_M=0.8365 root with the official split to depth 18 gives N=45,651 (APR=0, REP=0, CORE=12,378, HARD=10,448); the cell-center inner hull of the 10,448 HARD cells has a minimum of 0.8356828349502634 > 0.835, with #{A⁻_center<0.835}=0 — meaning raw HARD does not mean configurations below the threshold have already been observed, but that common-core/box uncertainty is still too loose. Using the distance of the center area from the target as a near-frontier compression proxy, only 8 of the 10,448 raw HARD cells fall within target+0.002; the HARD center-area quantiles (Q0.50≈0.884, Q0.99≈0.914) show that the vast majority of HARD seeds are in fact far above 0.835, a certification-resolution problem rather than an obvious-minimizer one — yet the HARD lower-bound quantiles show real heterogeneity too: Q0.50≈0.822, Q0.99≈0.835, max=0.834989575, meaning some seeds already have a core bound only about 10⁻⁵ from the target while others still fall short by about 10⁻² because of erosion loss. A margin-to-resolution profiler (reusing Round 09's τ*(m,T) formula) estimates that about 90% of HARD cells require no more than 3 full refinement cycles, with a genuine tail of only 142 seeds at ≥5 cycles, 8 at ≥7 cycles, and 2 at ≥8 cycles. Launching a full phase-master B7 root to depth 12 on each of the two base cells closest to the target (A⁻_center≈0.83568283495, with a core lower bound of only 0.79907297849, an erosion/box loss of about 3.66×10⁻²) gives an identical result for both: 2,403 nodes, 568 closed leaves, and 634 unresolved leaves — concluding B7-ACTIVATE-NOW: NO (at this base resolution), because the B7 tree is paying for the over-eroded B₃/B₅ base cores, and refining the base first is more sensible. The round therefore sets a Base-First / Lift-Later production policy (Phase A base refinement → Phase B near-frontier re-profiling → Phase C witness lifting), and retains T_M=0.8365 as the B7-phase master domain (while explicitly noting MASTER-ROOT-PERFORMANCE-NOT-A-THEOREM). This round obtains no new rigorous lower bound, and the global bound a_Leb≥0.8350 remains OPEN / 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.