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This research introduces a zero-storage neural paradigm that procedurally synthesizes decision boundaries using formal verification in Lean 4, effectively eliminating VRAM dependencies and enabling native execution within deterministic environments like the EVM. By projecting dynamical systems onto modular residue rings and fixed-point domains, the authors provide machine-verified guarantees for halting conditions and arithmetic safety, addressing critical memory-wall bottlenecks in current inference architectures. The approach demonstrates significant speedups on bare-metal CPU hardware while maintaining robustness against adversarial inputs without relying on traditional weight matrices.
Zero-Storage Procedural Neural Synthesis via Boundary Dynamics: Formal Verification in Lean 4 and Bare-Metal Gauntlet Validation
arXiv:2609.33066v1 Announce Type: new Abstract: 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 $\Theta = (c_x, c_y, \text{zoom})$ 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 ($\le 9$ and $\le 12$ steps), absence of $\mathbb{Q}_{16.16}$ square overflow below $2^{63}-1$, non-constant boundary escape sensitivity, and a parametric EVM gas bound ($\le 22,557 \le 24,000$ 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.
Abstract: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 $\Theta = (c_x, c_y, \text{zoom})$ 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 ($\le 9$ and $\le 12$ steps), absence of $\mathbb{Q}_{16.16}$ square overflow below $2^{63}-1$, non-constant boundary escape sensitivity, and a parametric EVM gas bound ($\le 22,557 \le 24,000$ 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.
7 pages, 2 tables, 1 listing. Formal verification in Lean 4 (v4.34.1, Mathlib4, 0 sorry). Ancillary files include Lean 4 proofs, Solidity contracts, and bare-metal 40-core gauntlet replication scripts
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Cryptography and Security (cs.CR); Logic in Computer Science (cs.LO)
I.2.6; F.3.1; D.2.4
arXiv:2609.33066 [cs.LG]
(or arXiv:2609.33066v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.33066 arXiv-issued DOI via DataCite (pending registration)
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