零存储过程式神经合成：基于边界动力学的 Lean 4 形式验证与裸机验证
Zero-Storage Procedural Neural Synthesis via Boundary Dynamics: Formal Verification in Lean 4 and Bare-Metal Gauntlet Validation
浏览论文内容
中文总结 AI 辅助
提出基于Mandelbrot集边界动力学的零存储过程式神经合成范式WERR与OED，通过Lean 4形式验证其终止性与算术不变量，并在裸机上实现15.15倍加速和100%对抗尖峰抑制。
中文摘要 AI 辅助
当代神经推理架构依赖于存储在高带宽内存（VRAM）中的稠密浮点权重矩阵，这导致了严重的内存墙瓶颈，并阻碍了在确定性虚拟机（如以太坊虚拟机 EVM）中的原生执行。在 Blum-Shub-Smale 模型中，验证连续域上递归动力系统的终止性和算术不变量通常是不可判定的。在此，我们提出了 WERR（波与误差）和第三阶段轨道误差动力学（OED）的形式验证与裸机实证验证，这是一种非张量决策范式，它根据 24 字节坐标种子 $\Theta = (c_x, c_y, \text{zoom})$ 在 Mandelbrot 集边界（$\partial\mathcal{M}$）上按需过程式合成非线性决策边界。通过将递推关系 $z_{n+1} = z_n^2 + c$ 投影到模剩余环 $\mathbb{Z}/9\mathbb{Z}$ 和定点域 $\mathbb{Q}_{16.16}$ 上，我们在 Lean 4（v4.34.1）与 Mathlib4 中建立了十个机器验证定理，且没有未证明的猜想（sorry）：证明了 $\mathcal{I}_3 = \{0,3,6\} \subset \mathbb{Z}/9\mathbb{Z}$ 的理想闭包、通用燃料有界停机（$\le 9$ 和 $\le 12$ 步）、低于 $2^{63}-1$ 时 $\mathbb{Q}_{16.16}$ 平方溢出不存在、非恒定边界逃逸敏感性，以及参数化 EVM 气体上界（$\le 22,557 \le 24,000$ 气体）。在 40 核双 Intel Xeon 服务器上评估，向量化的 36 次迭代 CPU 内核在 6.49 秒内处理 100,000 个决策（15,397 决策/秒，0 字节 VRAM，15.15 倍加速），而 sigmoid 离群值门抑制了 100.00% 的对抗性尖峰，同时保留了 89.60% 的干净基线信号。
英文摘要
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 ($\le 9$ 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.
