{ "prediction_checks": [ { "prediction": "Global phase is exactly unobservable", "predicted": "error 0", "observed_max_abs_error": 6.661338147750939e-16 }, { "prediction": "At least 2n-1=11 local degrees of freedom become identifiable modulo phase once enough times are sampled", "predicted_rank_at_K2_or_more": 11, "observed_ranks": { "1": 6, "2": 11, "3": 11, "4": 11, "5": 11, "6": 11, "7": 11, "8": 11 } }, { "prediction": "Generic diagonal perturbations improve spectral identifiability conditioning versus nearly constant potential", "predicted": "pair-sum gap and sigma_min(S) increase with potential scale over small scales", "observed_scale_gap_sigma": [ [ 0.02, 9.574141116930335e-05, 0.002563127302950817 ], [ 0.1, 0.0016087870616696698, 0.01325704104551373 ], [ 0.3, 0.009286181459882137, 0.04609205351775604 ], [ 1.0, 0.03093639029452433, 0.10623320993335798 ], [ 3.0, 0.04597004606857613, 0.24691854680700215 ] ] }, { "prediction": "More time samples reduce local noise amplification after the transient sampling regime", "predicted": "1/sigma_min decreases for K>=2 overall", "observed_noise_gain": [ [ 1, 1.000000000141043 ], [ 2, 5.017408866958467 ], [ 3, 2.985295170896411 ], [ 4, 1.4874163837223315 ], [ 6, 0.8540563661036842 ], [ 8, 0.7755764490658387 ] ] } ], "classification": { "clean_accuracy": { "phaseless_K6": 0.8777777777777778, "single_time_coordinate_magnitude": 0.6027777777777777 }, "noisy_test_accuracy_phaseless_K6": 0.8583333333333333, "N": 2400, "train_test": [ 1680, 720 ] } }