The First Concrete Counterexample Appears While the Global Bound Remains Unshaken: B23's Single-Cell Disqualification and the Witness Counterexample Theorem

Round 20 (AMRAL-LUC-FC-R20, 2026-09-19) formally writes Round 19's proposed Necessity Marker and Dual Base/Lift Frontier into the mixed base/lift shard grammar, and proves the Witness Counterexample Theorem: if, for a given base cell's configuration q, there exists a legal placement g for witness K such that the resulting one-sided upper bound falls below the target T, then K cannot be the sole closing witness for that cell; the theorem also explicitly rejects the tempting but invalid converse inference — "no counterexample has yet been found" does not mean "this witness is viable" — and this round tags that converse inference as REJECTED AS INFERENCE. This round's single most important concrete result is the only counterexample that the numerical-attack line — Rounds 1–27 of the research line — has, up to now, actually found and fully proved: at reference cell-00, a 3-D placement search found an explicit placement of the regular 23-gon witness B₂₃ (φ≈0.22598188, x≈-5.68×10⁻⁵, y≈-3.14×10⁻⁴), with exact-kernel area 0.83492540, whose 20k support outer bound gives 0.83494439<0.835 — on this basis B₂₃ is judged unable to be the sole closer for that single marked cell. This currently remains at the pilot floating-point tier as VERIFIED-COMPUTATIONAL-PILOT, not yet a publication-tier arithmetic theorem. This round's other methodological finding: in the shallow lift-depth-12 8-cell pending count, B₇ has mean pending≈160.6 — the highest of that batch of witnesses, and seemingly the least efficient — but once the same tracked base cell is deepened to lift depth 18 and 20, B₇'s pending fraction shrinks in turn to about 0.249% and 0.0968%, in fact the lowest among the witnesses being tracked at that point, and by depth 26 it falls further to u₂₆≈3.193×10⁻⁵ — proving that shallow-depth rankings can be misleading, and that witness strength must be evaluated dynamically against the projected search horizon, giving rise to the escalation state machine Necessity→Negative Filter→Shallow Probe→Tail Estimate→Pareto Choice→Deepen/Switch/Batch. The overall status ledger plainly records theorem_ready=false; the global bound a_Leb≥0.8350 remains COMPUTE-DEFERRED, and this round does not change that status. Research direction is chosen and led by Neo.K; this round's execution was carried out by Aletheia / GPT-5.6 Sol.