Title: Beyond the Hamiltonian: The Recognition Operator as Fundamental Dynamics
Author: Jonathan Washburn
Affiliation: Recognition Physics Institute, Austin, Texas
Date: \today

Abstract:
For four centuries, the Hamiltonian has been treated as fundamental, with dynamics derived from energy minimization. We prove this is an approximation. Starting from a single information-theoretic axiom (the Meta Principle: nothing cannot recognize itself), we construct a discrete Recognition Operator (R^) with minimal eight-tick period that evolves states by minimizing a unique convex symmetric cost on R_{>0}, J(x)=1/2(x+x^{-1})-1. In the small-deviation regime with r=e^{\varepsilon} and |\varepsilon|<<1, we have J(e^{\varepsilon})=\cosh(\varepsilon)-1=1/2\varepsilon^2+1/24\varepsilon^4+\cdots, yielding a quadratic effective generator H_eff; under a continuum limit \tau_0->0 we recover Schrödinger dynamics i\hbar \partial_t \psi=H\psi. This explains the empirical success of Hamiltonian mechanics: typical laboratory systems remain in the small-|\varepsilon| regime where R^\approx H to better than percent accuracy. The theory predicts measurable departures where R^\neq H: strongly non-equilibrium flows (\Delta E\neq 0 while recognition cost decreases), ultra-fast processes exhibiting eight-tick discretization, and mesoscopic measurements crossing an intrinsic collapse threshold C>=1. We state hard falsifiers (e.g., any alternate convex symmetric cost on R_{>0}, failure of eight-tick minimality, or cases where H works but R^ fails) and provide concrete experimental protocols. Lean-verified theorems in an open repository substantiate each claim; the same operator supplies bridges to measurement and gravity via C=2A.