A First Proof Sprint

TL;DR

This paper reports a multi-agent proof sprint tackling ten complex research problems using rapid drafting, adversarial verification, and provenance tracking, demonstrating improved reliability through structure-aware strategies.

Contribution

It introduces a workflow combining draft generation, adversarial verification, and provenance management for efficient proof development and validation.

Findings

Validated existence path for Problem 3 under scoped criteria

Solved Problem 5 in a scope-limited form for $F_O$-local spectra

Conditional solution for Problem 10 with explicit assumptions

Abstract

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.