SRE Dynamics: Rigorous Reconstruction of Maxwell's Field Equations via Purely Dimensionless Graph Cohomology and Global Evolutionary Steps

Abstract

This paper presents a formal, background‑independent topological reconstruction of Maxwell's field equations entirely decoupled from continuum space‑time manifolds, pre‑imported empirical physical constants, and empirical differential metrics. Grounded in Status‑Relational Entropy (SRE) Dynamics, macroscopic time is fundamentally discarded and re‑indexed as the emergent statistical consequence of global, synchronous global evolution steps ${\Delta S}$. Physical field interactions are formulated as localized algebraic projections of a singular synchronized‑network intersection kernel onto discrete 1‑chain (edge) and 2‑chain (cycle) chain‑complex layers. Faraday's law and the Ampere‑Maxwell relation are mathematically derived as exact topological tautologies required to maintain matrix‑condition stability. Furthermore, fundamental physical constants ($e$, $h$, $Z_0$) and the fine‑structure constant ($\alpha$) emerge natively as discrete graph‑cohomological invariants and spectral‑radius ceilings of the underlying network complex. This manuscript delivers the pure dimensionless 0‑State ontological formulation; mapping onto laboratory SI engineering units is not performed here, the corresponding observational‑mapping‑anchor conversion layer is documented in the companion electrodynamics paper v1.1‑rev. The topological definition of fine‑structure constant is given herein, while the numerical value $1/137.03599$ serves merely as real‑world observational reference; fitting against the true cosmic‑network configuration lies outside manuscript scope. To break circular‑verification loops inherent to finite‑difference schemes, an independent, non‑cyclic cross‑validation protocol is established. This metric matches the spatial dual‑divergence of the dynamically‑evolved electric field against static structural invariants derived strictly from Laplacian null‑space and boundary‑drive‑shock tensors. Parametric scanning across multi‑loop non‑planar bipartite graphs demonstrates that topological validation residuals collapse identically toward machine double‑precision limits ($\le 5.68\times10^{-14}$) across infinite state‑refresh cycles, rigorously securing dynamical gauge‑invariance and mathematical exactness of un‑extended causal electrodynamics. 本文对麦克斯韦场方程开展形式化、与背景无关的拓扑重构,完全脱离连续时空流形、预先导入的经验物理常数以及经验微分度量。基于状态‑关系熵(SRE)动力学,宏观时间被彻底舍弃,重新定义为全局同步全局演化步${\Delta S}$的统计涌现结果。将物理场相互作用表述为单一同步网络交核向1‑链(边)、2‑链(圈)离散链复形层的局域代数投影;法拉第定律与安培‑麦克斯韦关系被数学推导为维持矩阵条件稳定性所必需的严格拓扑重言恒等式。此外,基础物理常数$e、h、Z_0$以及精细结构常数$\alpha$,作为底层网络复形的离散图上同调不变量与谱半径上界内生涌现。本文为0‑State纯无量纲本体层表述,不完成向实验室SI工程单位的映射;对应的观测映射锚转换层参见配套电学论文v1.1‑rev。文中给出精细结构常数的拓扑形式定义,$1/137.03599$仅作为现实世界观测参考,针对真实宇宙网络组态的拟合不在本文工作范围内。为破除有限差分方案固有的循环验证环路,本文建立一套独立、非循环的交叉验证协议。该验证度量将动力学演化后电场的空间对偶散度,与严格由图拉普拉斯零空间、边界驱动冲击张量导出的静态结构不变量做比对。跨多闭环非平面二部图的参数扫描表明,拓扑验证残差在无穷状态刷新周期下收敛至机器双精度极限($\le 5.68\times10^{-14}$),严格保证非延拓因果电动力学的动力学规范不变性与数学精确性。