On Evidence and Proof: A Recursive Model

We propose a formalization of evidence and proof as mutually recursive constructs, grounded not in logic or correspondence, but in performance and instituted threshold. Evidence is defined as the output of a confirmation bias acting on a prior proof. Proof is defined as a threshold—a discontinuity in the accumulation of evidence—that interrupts the performance of confirmation bias. The result is a non‑foundational, self‑referential model of epistemic practice. The successor axiom of arithmetic is used throughout as a study case.