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

Volkan Dağlı, Zerrin Dağlı, Dağhan Dağlı

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 $Θ= (c_x, c_y, \text{zoom})$ along the boundary of the Mandelbrot set ($\partial\mathcal{M}$). By projecting the recurrence $z_{n+1} = z_n^2 + c$ onto the modular residue ring $\mathbb{Z}/9\mathbb{Z}$ and the fixed-point domain $\mathbb{Q}_{16.16}$, we establish ten machine-verified theorems in Lean 4 (v4.34.1) with Mathlib4 and zero unproven conjectures (sorry): proving $\mathcal{I}_3 = \{0,3,6\} \subset \mathbb{Z}/9\mathbb{Z}$ ideal closure, universal fuel-bounded halting…