静的显化理论:自发动力学的公理化构造 / Statics as Manifestation: An Axiomatic Theory of Spontaneous Dynamics

静的显化理论:自发动力学的公理化构造(构造数学系列第三篇·动层)。解释方向反转——动是内禀给定的(结构即因,解释链条到动本身终止),需要解释的是稳定形态如何从动中被显化。三条公理(自发动力学/双向耦合/比值可观测)+一条跨体系引用(本体一元性);静=显化从公理导出(定理 3.1);显化算子=幂等自映射三分类(投影/极限/滤波);单值读数必有损+双比值读数最小完备(联合重建 4.97e-16);对象理论=呼吸方程,其保守势从静力学结构逐字自产(墙项=柯西方程连续解/井项=线性回复必然/平衡点纯涌现;阻尼幅度=动力学公理独立性内容);特例化=动力系统理论的流对齐特例(三隐藏假设显式化)。学术对照:动力系统理论(工具层)/耗散结构(物理层)/过程哲学(哲学层)三层先例齐备而数学构造层空白——本文补上。核心代数 Lean 形式化零 sorry。中文主版。 Statics as manifestation: an axiomatic theory of spontaneous dynamics (third paper of the constructive-mathematics series, the motion layer). The explanatory direction reversed — motion is intrinsically given (the structure is the cause; explanation terminates at motion), and what needs explaining is how stable forms are manifested out of motion. Three axioms (spontaneous dynamics / bidirectional coupling / ratio observability) + one cross-system import (ontological monism); statics = manifestation derived (Theorem 3.1); manifestation operators = idempotent self-maps in three classes (projection / limit / filtering); single readings necessarily lossy + two ratio readings minimally complete (joint reconstruction 4.97e-16); the object theory is the breathing equation whose conservative potential is self-produced verbatim from the static structure (wall = continuous solution of Cauchy's equation / well = necessary form of linear restoration / pure emergence of the equilibrium; damping magnitude = the independence content of the dynamical axiom); specialization = dynamical systems theory as the flow-aligned special case. Scholarly comparison: dynamical systems theory (tool layer), dissipative structures (physics layer), process philosophy (philosophy layer) — three layers of precedent with the mathematical-construction layer blank; this paper fills it. Core algebra formalized in Lean with zero sorry. English edition.