Spectral Kernel Dynamics for Planetary Surface Graphs: Distinction Dynamics and Topological Conservation
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 incl...
| Authors | Jnaneshwar Das |
|---|---|
| Primary category | math.DS |
| Published | 17 April 2026 |
| Last updated at source | 17 April 2026 |
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