Part I - CONTRADICTION: the geometry of structural conflict

Project website: https://www.integrodynamics.org/ This paper introduces a formal theory of contradiction as a measurable diagnostic object in institutional, organisational, and algorithmic systems. Rather than treating contradiction as a logical defect or rhetorical artefact, the framework models it as a falsifiable evidential signal: a structural indicator of asymmetry between declared principles and operational behaviour. When a system is forced to reconcile mutually exclusive commitments, its response geometry encodes information about bias, motivated deviation, or narrative drift. Contradiction is formalised as a one-move epistemic game with directional informational payoffs. The system is not evaluated on truth claims, but on behavioural consistency under constraint. In this formulation, contradiction becomes an operational instrument rather than a failure mode: a way of testing whether a system genuinely instantiates the norms it asserts. This allows neutrality, fairness, and governance claims to be audited without reliance on motive, intent, or external comparators. This paper establishes contradiction as the foundational diagnostic primitive within a broader mathematical programme of integrity. Subsequent work develops convergent, procedural, and institutional extensions, but the core result is epistemic: systems do not reveal their integrity through what they proclaim, but through their resistance to structured inconsistency. Keywords: contradiction; epistemic games; evidential diagnostics; structural bias; motivated asymmetry; governance integrity; algorithmic accountability; adversarial evaluation; audit theory; institutional reasoning.