A SRE-Dynamics Inspired Topological Paradigm for Composite Elementary Particles and Relational Space Emergence

Abstract

Within the conceptual framework of Status‑Relational‑Entropy (SRE) Dynamics, this paper presents a qualitative‑probabilistic formulation for the topological configuration and emergent geometry of composite elementary particles. Traditional physical paradigms rely heavily on fine‑tuned continuous variables and empirical constants to explain rest‑mass amplification and strong‑interaction effects in composite structures. This work strips away all a‑priori assumptions of absolute time, space and energy; space is de‑indexed and reformulated as a macroscopic geometric manifestation of status‑relational entropy and phase coherence among distinct causal chains. The underlying physical process is driven by dissipation‑compensation duality dynamics of bidirectional Möbius causal loops. Coupled evolution of two internal causal‑loops modifies mutual‑information and phase‑coherence between them. The 2×2 local cross‑spectral Hermitian operator is a characterisation tool obtained by statistical smoothing over dynamical output time‑series, capturing spectral‑evolution features of the system. When the cross‑coherence coefficient (at the representational level) asymptotically approaches unity, it corresponds to underlying dynamical saturation of phase coherence. The dimensionless eigenvalue‑spacing of the ensemble spontaneously undergoes a distribution transition from the Wigner Surmise toward a continuous Poisson process. Within the full‑rank expanded spectral regime, three‑in‑one co‑emergent phenomena appear at the macroscopic rendering‑layer: relational distance collapses toward zero due to maximised mutual information; the matrix condition‑number hits numerical truncation thresholds, characterising an abrupt logical‑pressure gradient rendered macroscopically as the strong‑interaction force; instantaneous residual resonance triggers non‑linear combinatorial explosion of secondary causal‑feedback paths. Free‑parameter tuning and pre‑existing background geometry are not required. This paradigm achieves self‑consistent mathematical unification of composite‑particle physics and relational metric space. Spectral‑matrix constructions serve purely as statistical‑analytical representations; the first‑principle physical origin resides in dissipation‑compensation duality evolution of the causal‑information network. 本文在状态‑关系熵(SRE)动力学概念框架下,给出复合基本粒子的拓扑构型与涌现几何的定性概率化表述。传统物理范式高度依赖精细调谐的连续变量与经验常数,用以解释复合结构的静质量放大效应与强相互作用。本文剥离全部绝对时间、空间、能量先验预设,对空间解除索引,将其重新表述为不同因果链之间状态‑关系熵与相位相干性的宏观几何呈现。 底层物理过程由双向莫比乌斯因果网络的耗散‑补偿对偶动力学所驱动:两条内部因果闭环发生耦合演化,耗散效应改变闭环之间的互信息与相位相干程度;2×2局域交叉谱厄米算子是对该动力学输出做统计平滑得到的表征分析工具,用于捕捉系统的谱演化特征。当表征层面的交叉相干系数渐近趋近于1时,对应底层动力学走向相位相干饱和,系综无量纲本征值间距会自发发生从维格纳猜想(Wigner Surmise)向连续泊松过程的分布转变。在满秩展开的谱表征区间,系统会在宏观渲染层触发“三合一”协同涌现现象:互信息极大化带来关系距离收敛至零;局域矩阵条件数触及数值截断阈值,表征底层生成骤然的逻辑压力梯度(宏观呈现为强相互作用力);瞬时残余共振带来次级因果反馈路径的非线性组合爆炸。 本范式无需自由参数调谐、也不依赖预先存在的背景几何,实现了复合粒子物理与关系度量空间在数学层面的自洽统一。其中谱矩阵相关数学构造仅作为统计分析表征手段,物理的第一性根源归属于因果网络的耗散‑补偿对偶演化。