A Deterministic Discrete Dynamical System with Emergent Constant 1836: Mathematical Foundations of the Energy Ontology

We define a deterministic discrete dynamical system, called the ConstraintNetwork Model, governed by three axioms: energy units move at constant speed,upon encounter they undergo symmetric collision, and in asymmetric encountersa residual unit may merge if directional alignment occurs. We prove that thissystem, formalizable in ZFC, has the following properties: (1) the evolutionis well-posed and total energy is conserved; (2) merging is irreversible andmonotonic; (3) the system must converge to a steady state; (4) a saturatednode (a "sealed node") has a maximal aggregate number bounded by a sphere-covering problem; (5) the sealed node's aggregate number must be even and,for a tolerance angle of 1 degree, emerges uniquely as the constant 1836;(6) an odd neighbor 1837 inevitably appears near a sealed node, exhibitingconditional stability depending on the existence of a linking chain; (7) thesealed node of size 1836 is a global attractor when total energy exceeds acritical threshold; (8) multiple sealed nodes can coexist, each fixed at1836, connected by chains to form a stable network. These theorems transformthe empirically observed proton-electron mass ratio 1836 from a physicalcontingency into a mathematical necessity within the defined system.