symmetry: invariance, entropy, and the conservation of integrity
how symmetry provides an objective basis for fairness
abstract
the symmetric convergence engine provides the procedural core of the mathematics of integrity, extending the evidential logic of the contradiction trap into a dynamic, falsifiable method for fair allocation under symmetric stress. sce models allocation as a stochastic governance process in which fairness is not presumed but empirically demonstrated: declared proportions must emerge through convergence across repeated, entropy-certified draws. in this framework, deviation becomes evidence, drift becomes a diagnostic signal, and convergence becomes an operational test of procedural honesty. the engine integrates three interacting components — entropy-certified randomness, symmetric weighting, and a convergence-regulating update rule — to form a stochastic dynamical system that is unpredictable at the micro level yet statistically self-correcting at the macro level. unlike deterministic quotas or naïve lotteries, SCE produces a transparent, reproducible, and adversarially robust audit trail: every draw is a symmetry test, every residual an evidential unit, every correction bounded by publicly declared commitments. SCE functions as the procedural bridge in a trilogy on evidential integrity. where the contradiction trap converts contradiction into epistemic evidence, and the adaptive sentinel framework converts symmetry into institutional evidence, SCE converts proportional drift into procedural evidence. it establishes a unified evidential paradigm for allocation systems — one in which legitimacy is not a policy declaration but an empirically verifiable pattern of symmetric convergence. low-volume systems are diagnostic only: below K_min, interval fairness bands and full provenance are published, but no proportional claims are made.