Truth-Known Recovery of Local Diffusion Geometry and Jacobian-Derived Dynamical Summaries
Year: 2026
Type: preprint
Abstract: Candidate local dynamical measurements are difficult to validate when the latent state and its local laws are not known. This preprint reports a simulator-side qualification chain in which the truth is available by construction and every estimator is compared with a declared latent target. Stage O1 tests recovery of local diffusion geometry under finite support, orientation, timestep, bandwidth, and observation-noise perturbations. Stage J1 tests Jacobian-derived summaries of local continuous-time dynamics (spectral abscissa, numerical abscissa, a derived reactivity gap, and a simulator-only finite-time propagator functional) using a discrete-transition fit followed by exact logm conversion on held-out constant-linear truth systems. Stage J2 compares estimator-specific observation-noise envelopes. O1-A and O1-B pass; O1-C maps predictable breakdowns; J1 and J2 pass within restricted validity ranges. These results validate measurement objects only under the tested truth-known conditions. They do not validate empirical MNPS coordinates, biological Noetic Diffusion Theory, or the literal NeuralManifoldDynamics ingest implementation. MNJ is reserved for a Jacobian estimated on an MNPS chart.
Author: Langell, Robin
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204479165
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