Zero-Storage Procedural Neural Synthesis via Boundary Dynamics: Formal Verification in Lean 4 and Bare-Metal Gauntlet Validation

Contemporary neural inference architectures rely on dense floating-point weight matrices stored in high-bandwidth memory (VRAM), incurring severe memory-wall bottlenecks and preventing native execution inside deterministic virtual machines like the Ethereum Virtual Machine (EVM). Verifying termination and arithmetic invariants for recursive dynamical systems over continuous domains is generally undecidable in the Blum-Shub-Smale model. Here, we present the formal verification and bare-metal empirical validation of WERR (Waves & Errors) and Phase III Orbital Error Dynamics (OED), a non-tensor decision paradigm that procedurally synthesizes non-linear decision boundaries on demand from a 24-byte coordinate seed Theta = (cx, cy, zoom) along the boundary of the Mandelbrot set (partialM). By projecting the recurrence zn+1 = zn2 + c onto the modular residue ring mathbbZ/9mathbbZ and the fixed-point domain mathbbQ16.16, we establish ten machine-verified theorems in Lean 4 (v4.34.1) with Mathlib4 and zero unproven conjectures (sorry): proving I3 = 0,3,6 subset mathbbZ/9mathbbZ ideal closure, universal fuel-bounded halting (≤ 9 and ≤ 12 steps), absence of mathbbQ16.16 square overflow below 263-1, non-constant boundary escape sensitivity, and a parametric EVM gas bound (≤ 22,557 ≤ 24,000 gas). Evaluated on a 40-core Dual Intel Xeon server, the vectorized 36-iteration CPU kernel processes 100,000 decisions in 6.49 s (15,397 decisions/s, 0 Bytes VRAM, 15.15x speedup), while a sigmoidal outlier gate suppresses 100.00% of adversarial spikes while preserving 89.60% of clean baseline signals.