提出谱核动力学模型，实现行星表面图的拓扑保真压缩
Spectral Kernel Dynamics for Planetary Surface Graphs: Distinction Dynamics and Topological Conservation
- 构建区别动力学方程，通过补偿项修复谱场能量守恒缺陷
- 证明保留至少 beta_0 + beta_1 个谱模式可完全保持贝蒂数拓扑电荷
- 提出三重谱诊断法，适用于行星排水网络的高效拓扑检测
谱核场方程 R[k] = T[k] 缺乏守恒律类比。我们证明：(i) 固定点流严格体积膨胀（tr DF > 0），无法自动实现守恒；(ii) 每模式的守恒缺陷恰好等于海森稳定性裕度：D_m = -Delta'。修复缺陷需场景侧补偿贡献，我们形式化为区别动力学方程 dc/dt = G[c, h_t]，并给出 MaxCal 最优实现 G_opt。在固定拓扑的三维表面图上，推导出条件拓扑保持压缩定理：在谱序假设下，保留 k >= beta_0 + beta_1 个模式可保持全部贝蒂数电荷；附带一个图八短环反例，校准假设失效情况。针对行星排水网络，提出三重谱诊断法——费德勒模集中、提升旋度能量、异常 beta_1，计算成本为 O(N)。两个内部真实数据序列作为初步一致性检验；完整基准测试与自适应拓扑扩展留待后续。
原文摘要 · Abstract (English)
The spectral kernel field equation R[k] = T[k] lacks a conservation-law analog. We prove (i) the fixed-point flow is strictly volume-expanding (tr DF > 0), precluding automatic conservation, and (ii) the conservation deficit per mode equals the Hessian stability margin exactly: D_m = -Delta'. Closing the deficit requires a scene-side compensating contribution, which we formalise as the distinction dynamics equation dc/dt = G[c, h_t], with MaxCal-optimal realisation G_opt. On fixed-topology 3D surface graphs we derive a conditional topology-preserving compression theorem: retaining k >= beta_0 + beta_1 modes (under a spectral-ordering assumption) preserves all Betti-number charges; we include a worked short-cycle counterexample (figure-eight) calibrating when the assumption fails. A triple necessary spectral diagnostic -- Fiedler-mode concentration, elevated curl energy, anomalous beta_1 -- is derived for planetary drainage networks at O(N) cost. Two internal real-data sequences serve as preliminary consistency checks; full benchmarks and adaptive-topology extensions are deferred.
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