[theon199]

PR5673's normalized eight-field escape circuit uses eight rank-one, square-zero thin queries in three bursts. This contribution supplies a complete two-burst schedule (four queries per burst) with the same six full-call matrices, eight fields and exact polynomial endpoint. Two occupied gaps are optimal for those fixed full matrices, even when all 720 full-call orderings and arbitrary constant thin matrices are allowed.

The lower bound is a corollary of PR5673's aggregate-map theorem; this package corroborates it with 5,040 literal linear contradiction certificates, each using at most three equations. The distinct construction is the two-burst word and its explicit rank-one square-zero decomposition. The checker covers every polynomial coefficient, replays the source and changed word, checks complete order/gap coverage, and rejects six corruptions. No solver is needed for replay.

Scope and cost: normalized characteristic-two algebra only. The one-burst certificates hold over every characteristic-two field. No changed full matrices, stage-dependent connector entries, physical/native lift, compiler, outer admission or new kappa is claimed. This does not settle the seven-query search. The unchanged complete optimistic P104 bill has linear margin -336 and rejects every concave moment, so no bound improvement is asserted. Required native adapters and implementation costs remain unimplemented and cannot repair that favorable negative budget.

Base: df0137efd35e11b4445734bf612bdd4c7ebc330c. Source: PR5673 at c10f75f09e41803ae8efe478331a7509b7379b2f; source Git blob aae71c6ad294d6bc9ca5e2216a7785b9e6611afd. The PR5599 tariff is pinned to the base. SHA256 pins are in research/connector-single-burst/SOURCES.json. Selected kappa remains 0.00310045.

Reproduce:

python3 -B research/connector-single-burst/verify.py

Expected PASS_SINGLE_BURST_OBSTRUCTION, 720 orders, 5,040 certificates, eight thin queries in two bursts, and all rejection controls passing. Python standard library only; standalone without Git/network. Deterministic regeneration is documented in the package README. Normal and optimized replay, certificate regeneration, a Git-free export replay and publication guards are checked in the handoff. This is not proof-assistant or independent human verification. Shared predecessor packages and upstream/ are unchanged; no unrelated suite or selected-frontier replay is claimed.

Coordination and credit: complex-supplier track, OS assignment seed 26; three candidate tasks, overlap and stopping rule are in CLAIM.md. No pinned sprint issue was available, so the claim and result are local. Credit Ali Romman for PR5673 and PR5599, Cinna Davis and the PR5617/5631/5649 controller lineage, and the cumulative P104/native/helper/compiler contributors. PR5681's static rank construction is complementary; it is not an implementation dependency. No priority claim over the one-burst theorem is made.

Prepared for theon199 with substantial OpenAI Codex assistance in analysis, code, tests and writing. No subagents. New work is Apache-2.0; copied source data retains attribution in NOTICE.