The Symmetric Convergence Engine (SCE) generalises the logic of The Contradiction Trap into procedural form — replacing epistemic asymmetry with measurable fairness drift. Where Paper 1 tested truth by contradiction, Paper 2 tests fairness by convergence. At its core, SCE treats every allocation as an experiment in integrity. It defines a system that, when left to operate under symmetric stress, must converge toward its declared proportions without external correction. If it cannot, the deviation itself becomes evidence — not of error, but of hidden asymmetry, imbalance, or motivated bias. Built on a stochastic fairness kernel, the framework integrates entropy-certified randomness, adaptive weighting, and procedural conservation rules to ensure that fairness is not an assumption but an emergent property. This makes SCE both a procedural protocol and an evidential audit tool — a way to observe integrity directly in motion. The paper situates SCE as the procedural counterpart to The Contradiction Trap and the precursor to The PRIME Sentinel Framework. Together, these works develop a unified mathematics of integrity: from epistemic reasoning, to procedural dynamics, to institutional architecture. Keywords:mathematics of integrity; symmetric convergence; procedural integrity; stochastic governance; evidential fairness; mathematics of integrity; entropy-certified randomness; proportional drift; bounded rational dynamics; procedural audit; algorithmic accountability; fairness diagnostics; convergence testing; integrity verification; epistemic symmetry; governance design; adversarial calibration; procedural neutrality; information entropy; fairness-by-construction; systemic balance.