# 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.