Title: The Law of Existence: Proven Uniqueness of J-Cost Minimization Across Mathematics, Physics, Biology, and Consciousness
Author: Jonathan Washburn
Affiliation: Recognition Science & Recognition Physics Institute, Austin, Texas, USA

Abstract:
The Coercive Projection Method (CPM) is the universal algorithm by which possibilities collapse to actuality—the same minimum-description-length optimization Darwin discovered for biological fitness, now formalized to govern mathematical existence, quantum measurement, information flow, and physical constants. We formalize CPM with a structured set S (configurations minimizing J-cost), a defect functional Def (code surplus = squared distance to S), and an energy E (total description length). Three core theorems with explicit constants reveal the universal architecture: (A) projection–defect inequality via a finite net (K_net) and a rank-one/Hermitian projection bound (C_proj = 2); (B) coercivity factorization linking energy gap to defect, E(x) − min_S E ≥ c · Def(x) with c = (C_eng · C_proj · K_net)^{-1}; and (C) aggregation, upgrading local positivity to global existence x ∈ S. The bridge to Darwin is exact (fitness ↔ negative code length; defect ↔ surplus bits; descent ↔ coercivity; commit ↔ aggregation), with the same convex cost J(x) = (x + 1/x)/2 − 1 governing exponential weights and scaling laws. The framework is parameter-free and falsifiable via cross-domain constants and predictions.