This monograph reports a multi-agent proof sprint on ten research-level problems, combining rapid draft generation with adversarial verification, targeted repair, and explicit provenance. The workflow uses wiring-diagram decompositions of claim dependencies to localize gaps and coordinate reviewer-driven revisions. Final outcomes are heterogeneous but explicit: the manuscript distinguishes mathematical status from QC-validation status. Mathematically, Problem~3 has a validation-complete existence path under the scoped criterion used here (uniqueness/irreducibility treated as optional), Problem 5 is solved in a scope-limited form for $F_O$-local connective spectra, Problem 10 is conditional under clearly stated assumptions (with explicit necessity counterexamples when assumptions are dropped), and Problems 4 and 6 are partial with named remaining obligations in the general case (including an unconditional $K_n$ result for Problem 6 with $c_0 = 1/3$). Problem 7 is treated as provisionally closed via the rotation-route theorem chain, pending independent ledger re-check. At the QC layer, Problems~7 and~9 have node-level validation artifacts but still contain unresolved verifier gaps. The main methodological result is that structure-aware verification and layer-switching strategies improve reliability and calibration in compressed proof sprints.

翻译：本专著报告了一项针对十个研究级问题的多智能体证明冲刺，结合了快速草稿生成、对抗性验证、针对性修复与显式溯源。该工作流采用声明依赖关系的接线图分解来定位漏洞并协调审稿人驱动的修订。最终结果具有异质性但明确：手稿区分了数学状态与质量控制验证状态。在数学层面，问题3在本文采用的限定准则下（唯一性/不可约性视为可选）具备验证完备的存在性路径；问题5针对$F_O$局部连通谱以范围受限形式得到解决；问题10在明确陈述的假设下具有条件性结果（当假设移除时提供显式的必要性反例）；问题4和6在一般情形下为部分解决，并指明了剩余义务（包括问题6在$c_0 = 1/3$时的无条件$K_n$结果）。问题7通过旋转路径定理链被视为暂时性结题，有待独立账本复核。在质量控制层面，问题7和9具备节点级验证工件，但仍存在未解决的验证缺口。主要方法论结论表明：在压缩型证明冲刺中，结构感知的验证与层级切换策略能提升可靠性与校准度。