FNEM is an auditable framework for monitoring resource-constrained structural differentiation, grounded in a fractal-isomorphism criterion and a reproducible fiscal index (FCI-Lite).FNEM 是一套基于分形同构判据与可复算财政指数(FCI-Lite)的结构分化早期预警框架。 中文摘要本文提出并实现一套面向季度更新、可复算、可证伪的省级财政约束观测—裁决装置:分形南北朝-熵增模型(Fractal Nanbeichao-Entropy Model, FNEM)。该模型将魏晋南北朝的地缘政治拓扑抽象为可复用的结构基底,用以刻画现代政治系统在长期竞争中的相位分化。FNEM 将政治系统视为开放耗散结构:当缺乏持续做功(制度重装、技术跃迁、组织再整合)时,熵增将以不可逆的结构性症状出现。为避免类比叙事替代机制推断,FNEM V3.0 明确界定适用域与分形同构判据,并硬化资源约束模块:构造省级财政约束指数 FCI-Lite(FCI-Lite = 0.6R + 0.4D),以一般公共预算累计口径为唯一观测边界,将刚性锁定率 R 与收支缺口率 D 进行线性加权合成。需强调:本文所称“熵增/熵增压力”并非对热力学熵 S 的直接物理测算,FCI-Lite 亦不被主张为“熵值”,而被定义为财政维度的可审计代理指标(结果侧投影/风险距离指标)。基于中国 12 个典型省份 2024Q4(累计口径)基线测算显示,区域财政约束呈现“刚性支出趋同(R 高度集中)”与“缺口驱动分化(D 主导尾部风险)”的特征。装置进一步引入“4Q 方向判据”(含 δ 死区防抖)以形成最小可证伪单元,从而为资源约束下的结构性分化提供一套可审计、可复现的监测仪表盘。 English AbstractThis paper proposes and implements an auditable, reproducible, and falsifiable framework for monitoring provincial fiscal constraints: the Fractal Nanbeichao-Entropy Model (FNEM). Abstracting the geopolitical topology of China’s Northern and Southern Dynasties as a reusable structural substrate, FNEM models phase divergence in long-run systemic competition. FNEM treats political systems as open dissipative structures where, without sustained “work” (institutional reconfiguration, technological leaps, and organizational reintegration), entropy-like degradation manifests as irreversible structural symptoms. To prevent narrative analogy from substituting mechanistic inference, FNEM V3.0 defines applicability domains and fractal-isomorphism criteria, and hardens the resource-constraint module into a reproducible metric: the Fiscal Constraint Index (FCI-Lite = 0.6R + 0.4D), constructed from cumulative general public budget data by linearly combining a rigidity-locking ratio (R) and a revenue–expenditure gap ratio (D). Importantly, “entropy/entropy-like stress” here is systems-theoretic rather than a direct thermodynamic entropy measurement (S); FCI-Lite is treated as an auditable proxy (a resultant projection / risk-distance indicator) in the fiscal dimension. Baseline estimates using a 12-province sample (2024Q4, cumulative) reveal rigidity convergence (highly concentrated R) alongside deficit-driven divergence (D dominates tail risk). The framework further incorporates a “4-Quarter Direction Criterion” (with a δ dead-band) to establish a minimal falsifiable unit, providing an auditable and extensible monitoring dashboard for resource-constrained differentiation. [Major Update 2026-02-07] Section 7.3: Evolution Hypothesis “D as Time” (“Deficit as Clock”)中文补录:在 FNEM 的资源约束模块中,D 值(收支缺口率)不仅刻画缺口规模,更可被解释为系统逼近相变区间之“时间邻近性”的解释性假说(倒计时钟),而非物理时间的测量声明。若外部负熵输入强度(转移支付、再融资、资产处置等)无法跟上 D 的上升速度,系统将出现可观测的结构响应:非核心职能的功能性收缩或阶段性停摆、组织形态再整合(层级压缩、条块合并、指挥链缩短)、以及财政压力向治理压力外溢。该假说可证伪:若 D 持续走高而未出现上述任何一类结构响应(或响应方向与预测相反),则应予以拒绝或修正 “D as Time” 解释。操作化提示:可用季度滚动 D 序列与一套预注册的“结构响应清单”开展时序检验(如预算科目断裂/支出连续性变化、机构合并/层级压缩事件、公共服务供给波动代理、治理摩擦代理等)。English supplement: In FNEM, the D-value (Deficit Ratio) is re-interpreted as an interpretive hypothesis of temporal proximity to a phase-transition regime—a “deficit clock,” not a claim of physical time measurement. If negative-entropy inflows (e.g., fiscal transfers, refinancing, asset disposal) fail to keep pace with rising D, observable structural responses should emerge (non-essential shutdowns, organizational reconfiguration, spillover to governance stress). The hypothesis is falsifiable using rolling-quarter D series and a pre-registered checklist of structural responses. Note on Terminology: In this model, "Nanbeichao" (Nan-Bei-Chao) is used intentionally as a specific structural archetype of geopolitical topology and phase divergence, distinct from the mere chronological period "Northern and Southern Dynasties". We retain the pinyin to emphasize its role as a reusable model substrate rather than a historical timestamp. (术语说明:在本模型中,“Nanbeichao”被特指为一种地缘政治拓扑与相位分化的结构原型,以区别于单纯的时间断代“南北朝”。保留拼音拼写旨在强调其作为可复用模型基底的属性,而非历史时间戳。)