Published August 30, 2026 | Version 1.1
Working paper Open

A Proposed Temporal Difficulty Diagnostic for Hamiltonian Systems

Authors/Creators

  • 1. Independent Researcher

Description

We propose a finite-window temporal diagnostic for selected near-integrable Hamiltonian systems. It compares a normalized Fourier statistic of the perturbation Hessian along trajectories with a separately normalized finite-time redistribution estimator. We derive the log-frequency quotient derivative and state the positivity, calibration, coordinate, trajectory, and window dependencies that limit its interpretation. A deterministic 36-trajectory exploratory run compares four proxy statistics against an exploratory spectator-advantage label. After correcting the canonical modal projection and fixing the physical window, the best proxy has AUC 0.51029 (bootstrap 95% interval 0.30864--0.71193; one-sided permutation p=0.474). It exceeds the input-coordinate baseline by 0.05350, but a paired score-swap test gives p=0.401. The experiment therefore supplies no evidence of predictive value beyond that baseline. The proposed threshold must be fit and tested out of sample against an independent invariant-torus or chaos diagnostic.

Maturity: Short Draft. Part of The Latent research program.

Related papers in this program: Universal.

Notes

Topic: three_body_temporal_flow. Source: topics/three_body_temporal_flow/paper.md. Status: Short Draft. Related topics: universal.

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Additional details

References

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Subjects

Quantitative finance
http://id.loc.gov/authorities/subjects/sh2003001188
Stochastic processes
http://id.loc.gov/authorities/subjects/sh85128175