Adversarial Theorem Development: A Theorem Assurance Protocol for Structured Pre-Publication Falsification

Mathematical publications typically emphasize finalized proofs rather than the development process. Failed proof attempts, corrected definitions, dependency analyses, and systematic attempts to falsify a theorem rarely appear in the record. This paper proposes Adversarial Theorem Development (ATD): a research operations protocol for systematically attempting to falsify, weaken, or reformulate a mathematical theorem before publication, and for preserving the results of that process as part of the theorem's assurance record. ATD complements proof and peer review by inserting an explicit pre-publication phase: structured adversarial development. The protocol has six stages (conjecture, definition audit, counterexample campaign, cross-paradigm attacks, dependency audit, correction log), eleven attack types, and produces five assurance artifacts. Nine applicability criteria (Table 1) define when ATD is most cost-effective and when it is not warranted. The protocol is illustrated through the development of the Edge Pretopology Characterization Theorem (G4) for injective aperiodic dynamical systems. Over the course of that development, G4 underwent four definitional errors, 13 adversarial attacks from eight independent mathematical paradigms, a 23-step dependency audit, and four corrections before the final theorem was reached. The G4 case study is included as an illustrative example of the protocol in practice, not as the primary subject of this paper. The paper proposes that negative mathematical knowledge — failed attacks, corrected definitions, counterexamples to earlier statement versions, dependency analyses, abandoned proof strategies — is a first-class mathematical artifact, as worth preserving as the proof itself. The assurance record of the G4 case study is available at DOI 10.5281/zenodo.21560157.