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| author | YurenHao0426 <blackhao0426@gmail.com> | 2026-06-29 12:15:51 -0500 |
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| committer | YurenHao0426 <blackhao0426@gmail.com> | 2026-06-29 12:15:51 -0500 |
| commit | a6ec4288a2232988b130b2f00bb2565f81706966 (patch) | |
| tree | 1bb86e7f0b899b823b9e7fdf383e832d30a181e0 /paper/validation/validation_results.md | |
Recursive reasoning dynamics: analysis pipeline, paper drafts, toy models
Failure=more-chaotic (task-general under validity labeling) reduces to convergence/completeness
detection; mechanism (transient chaos vs multistability vs input-induced) under investigation.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Diffstat (limited to 'paper/validation/validation_results.md')
| -rw-r--r-- | paper/validation/validation_results.md | 17 |
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diff --git a/paper/validation/validation_results.md b/paper/validation/validation_results.md new file mode 100644 index 0000000..008a73a --- /dev/null +++ b/paper/validation/validation_results.md @@ -0,0 +1,17 @@ +# T0.1 estimator validation (QR/Benettin core vs known spectra) + +(a) diagonal linear: known [ 0.4055 -0.2231 -1.204 -2.9957] + recovered [ 0.4047 -0.2236 -1.2032 -2.9953] max|err|=7.99e-04 PASS +(b) symmetric linear: known [-0.1054 -0.6391 -0.9467 -1.4414 -3.074 ] + recovered [-0.1055 -0.6392 -0.9465 -1.4415 -3.0738] max|err|=1.85e-04 PASS +(c) non-normal shear: known asymptotic log|eig| [ 0.0953 -0.5108] + recovered (T=40000) [ 0.0953 -0.5109] max|err|=3.84e-05 PASS + single-step log singular values [ 1.6396 -2.0551] (finite-time transient ref) + recovered (T=5, finite-time) [ 0.5468 -0.9623] (should sit between sv and asymptotic -> confirms finite-time != asymptotic) +(d) Henon (a=1.4,b=0.3): literature [ 0.4192 -1.6232] (sum=-1.2040) + recovered [ 0.4193 -1.6233] (sum=-1.2040) |err λ1|=8.44e-05 PASS + +Interpretation: (a)(b) confirm exact recovery for normal maps; (c) confirms the +estimator converges to log|eig| asymptotically while finite-time windows reflect +singular-value growth (the regime our paper operates in); (d) confirms correct +recovery on a known chaotic nonlinear system. The QR core is validated.
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