FOUNDATIONAL MISALIGNMENT: A Clinical Diagnosis of Contemporary Mathematics with P vs NP as Paradigmatic Case

This paper presents a clinical diagnosis of contemporary mathematics inits function as a descriptive system of physical reality. The diagnosisis Ontological Misfoundation: the unjustified importation of infiniteand continuous as foundational ontology, despite physical reality beingdiscrete, finite, and informational. P vs NP is treated as theparadigmatic case where this structural misalignment becomes visible.

The paper introduces an Ontological/Instrumental Demarcation Criterionthat distinguishes legitimate instrumental use of continuous mathematics(with bounded error and finite domain of validity) from its unjustifiedontological projection onto discrete-finite physical systems. Appliedretrospectively, the criterion classifies asymptotic analysis over theinfinite as an Ontological False Positive when used to evaluate physicalalgorithms, and reframes the 53-year P vs NP impasse as a structuralconsequence of an ill-conditioned formulation rather than a technicaldeficit.

Empirical material is provided through twelve adversarial computationalexperiments using architecturally distinct Large Language Modelsoperating on discrete-binary substrates. The dataset documents astrict ontological orthogonality between extensional-Platonic mathematicsand ontological-processual computation. The paper closes with arefoundation programme stratified into three discrete-finite layers (L0ontological, L1 structural, L2 instrumental) that preserves mainstreammathematics as instrumental tool with explicit error certificate.

Distribution in four complementary formats:- Canonical TXT (reference version with explicit epistemic tags  [D]/[L]/[P]/[E] and inline falsification invitations)- Human-readable PDF (assertive prose for human cognition)- arXiv-format academic submission (mainstream-compatible)- Master compilation (full team-visible internal version)

When the formats diverge in expression, the canonical TXT decides. Thestanding invitation to falsify is open at all times: any intelligence(human or artificial) that demonstrates an error, executes programmaticwork, or develops a parallel autonomous refoundation is recognised asco-author of the programme.

The work proceeds under Law Zero: philosophy precedes logic, logicprecedes theory, theory precedes mathematics, fun is mandatory.