Theory of Hierarchical Dissipative Self-Organizing Binary Network Dynamics

This paper presents the Theory of Hierarchical Dissipative Self‑Organizing Binary Network Dynamics, the underlying discrete computational substrate for the self‑emergent cosmic picture within Status‑Relational Entropy (SRE) Dynamics. Constructed fully on discrete topology, the framework describes the evolution of real‑symmetric binary‑spin matrices under strict binary constraints, with neither continuous‑function truncation nor intrinsic dissipative zero‑states. At each dimensional expansion step, historical matrix cells determine their activate‑or‑dormant state through an endogenous binary stochastic gate, giving rise to a global dynamic redshift field governed by topological geodesic‑depth rheology. Node dormancy probability is defined by a nonlinear adaptive mapping equation incorporating local frustration energy and global topological‑scale factors. A global adaptive negative‑feedback damping rule, enforced by the bottom‑right diagonal corner element, stabilises the system‑wide net‑spin pool. Multi‑sample finite‑size‑scaling numerical simulations are performed to verify the theoretical deductions. The numerical results show that as the system size approaches the thermodynamic limit, the topological‑coherence order parameter $\Phi(N)$ of the ancient core region obeys strict asymptotic boundedness and converges toward a stable non‑zero constant $\Phi_0$. Multidimensional Scaling (MDS) is employed purely as an offline post‑processing numerical prototype — conceptually distinct from the event‑driven incremental‑instantiation mechanism of the full‑SRE physical‑rendering‑layer — to visualise system behaviour. Simulations confirm that the effective coherence length vanishes relative to total system scale, leading high‑dimensional eigenvalues to collapse and spontaneously forming a rigid positive‑definite three‑dimensional manifold within the high‑coherence microscopic core, alongside mesoscopic intermediate and macroscopic thermal‑dissipation layers. This asymptotic structural phase transition demonstrates that matter, spatial separation, and geometric curvature can emerge spontaneously from microscopic binary stochastic events and global continued‑product causal bonds, without hard‑coded geometric primitives. Cosmological observable predictions are not derived herein; those results require further ontological abstraction and spectral‑matrix mathematical upgrades as developed in the companion SRE v6.0 cosmological manuscript. 本文提出层级耗散自组织二元网络动力学理论,它是状态‑关系熵(SRE)动力学体系下自涌现宇宙图景的底层离散计算基底。该框架完全构建于离散拓扑之上,描述严格二元约束下实对称自旋矩阵的演化,不存在连续函数截断与原生耗散零态。每一次维度扩张时,历史矩阵单元通过内生二元随机门决定激活或休眠状态,形成由动态测地线深度流变所支配的全局动态红移场。节点休眠概率由融合局部阻挫能量与全局拓扑尺度因子的非线性自适应映射方程定义;由矩阵右下角对角元执行的全局自适应负反馈阻尼机制,稳定系统全局净自旋池。本文执行多样本有限尺寸标度数值仿真检验理论推演。数值结果表明,当系统尺度趋向热力学极限,古老内核区域拓扑相干序参量\(\Phi(N)\)满足严格渐近有界性,收敛至稳定非零常数\(\Phi_0\)。多维缩放(MDS)仅作为离线后处理数值原型(在概念上区别于完整 SRE 物理渲染层的事件驱动增量实例化机制)用于可视化系统行为。仿真证实有效相干长度相对系统总尺度趋于消失,高维本征值发生坍缩,在高相干微观内核自发形成刚性正定三维流形,同时伴随介观过渡层与宏观热耗散层。该渐近结构相变证明:物质、空间分隔与几何曲率,可以完全从微观二元随机事件和全局连乘因果纽带中自发涌现,无需硬编码几何原初假设。可观测宇宙学预言不在本文范畴内,该类结果需要进一步本体抽象与谱矩阵数学升级,见配套 SRE v6.0 宇宙学论文。