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[2602.13587] A First Proof Sprint
Summary
This paper presents a multi-agent proof sprint addressing ten research-level problems, utilizing rapid draft generation and adversarial verification to enhance mathematical validation processes.
Why It Matters
The findings contribute to the field of artificial intelligence by demonstrating improved methodologies for proof validation, which is crucial for advancing research reliability and efficiency. This work highlights the importance of structured verification in complex problem-solving scenarios.
Key Takeaways
- Introduces a novel workflow combining rapid draft generation and adversarial verification.
- Demonstrates improved reliability in proof validation through structure-aware verification.
- Identifies specific mathematical outcomes and remaining obligations for various problems.
- Highlights the importance of explicit provenance in collaborative research.
- Suggests that layer-switching strategies can enhance calibration in proof sprints.
Computer Science > Artificial Intelligence arXiv:2602.13587 (cs) [Submitted on 14 Feb 2026] Title:A First Proof Sprint Authors:Joseph Corneli View a PDF of the paper titled A First Proof Sprint, by Joseph Corneli View PDF HTML (experimental) 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 structur...
