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E-025 — lambda-flow: discretization floor found; locking correction; channel response confirmed but machinery-limited

08-19-2026 · 16560 rows · script research/numerics/scripts/E-025-lambda-flow.py

Metadata

Validation checks

V1_lambda_a_positive_law FAIL
V2_baseline_matches_E022 PASS
V3_solve_residuals FAIL
V4_sister_reported PASS

Key values

4{'lambda_a': 5.147476282756457e-11, 'lambda_law_ratio': 3.783885052191424e-08, 'sister_corr': -0.2997460393487147, 'sister_crossings': 57, 'sister_cross_err': 16.71385138849778, 'ladder': {'-1': {'lambda': -1.0, 'Delta': 2.1593140478568413, 'floor': -0.106956845297883, 'plateau': 2.0523572025589583, 'z1_times_a': 4.504293602793437, 'n_zeros': 381, 'lock_metric': 0.10068828882668726, 'residual': 48.3075476074236, 'mass_pm0.1': 116.6477713523963, 'solve_resid': 1.588314368200427e-16}, '0': {'lambda': 0.0, 'Delta': 6.988266234191322, 'floor': 4.4061523727558125, 'plateau': 11.394418606947134, 'z1_times_a': 6.9816622297266715, 'n_zeros': 381, 'lock_metric': 7.623144158814413e-05, 'residual': 10.718615266368445, 'mass_pm0.1': 127.66723750632949, 'solve_resid': 5.831210378871265e-10}, '0.5': {'lambda': 2.5737381413782287e-11, 'Delta': 6.988147390288639, 'floor': 4.40643861356427, 'plateau': 11.39458600385291, 'z1_times_a': 7.529134813217906, 'n_zeros': 381, 'lock_metric': 7.612992319993416e-05, 'residual': 10.708784969160092, 'mass_pm0.1': 127.66507880386828, 'solve_resid': 2.2679633796708461e-07}, '0.9': {'lambda': 4.632728654480812e-11, 'Delta': 6.987816911690756, 'floor': 4.407352992396391, 'plateau': 11.395169904087147, 'z1_times_a': 8.199973337356482, 'n_zeros': 381, 'lock_metric': 7.609529464864893e-05, 'residual': 10.693566680716287, 'mass_pm0.1': 127.66305186152309, 'solve_resid': 5.74001354100028e-08}, '0.99': {'lambda': 5.096001519928893e-11, 'Delta': 6.985923725722728, 'floor': 4.413501470282933, 'plateau': 11.39942519600566, 'z1_times_a': 8.385279853786248, 'n_zeros': 381, 'lock_metric': 7.613585558613195e-05, 'residual': 10.687862236134379, 'mass_pm0.1': 127.66303788362372, 'solve_resid': 7.885784848149343e-08}, '0.999': {'lambda': 5.142328806473701e-11, 'Delta': 6.981356415160433, 'floor': 4.428696114419206, 'plateau': 11.41005252957964, 'z1_times_a': 8.40265274248596, 'n_zeros': 381, 'lock_metric': 7.614180518407809e-05, 'residual': 10.687276136059936, 'mass_pm0.1': 127.66306304014373, 'solve_resid': 4.3024270231059637e-07}}}
8{'lambda_a': -0.028701446327309428, 'lambda_law_ratio': -15509.255243545844, 'sister_corr': 0.00255772313467671, 'sister_crossings': 118, 'sister_cross_err': 18.633851388497806, 'ladder': {'-1': {'lambda': -1.0, 'Delta': 2.7352201581877043, 'floor': 0.030554703235580436, 'plateau': 2.7657748614232847, 'z1_times_a': 4.496810102477515, 'n_zeros': 763, 'lock_metric': 0.057829797607063305, 'residual': 58.651149793527864, 'mass_pm0.1': 133.51693635274552, 'solve_resid': 3.0889933849343203e-16}, '0': {'lambda': -0.0, 'Delta': -33.528034311582985, 'floor': -423.8211920422485, 'plateau': -457.3492263538315, 'z1_times_a': 1.8093924166647792, 'n_zeros': 548, 'lock_metric': 0.0003714172395450807, 'residual': 11.144052463580522, 'mass_pm0.1': 127.82233169936302, 'solve_resid': 0.00020060867988680158}, '0.5': {'lambda': -0.014350723163654714, 'Delta': 5.2473962964853165, 'floor': 1.7336013999547513, 'plateau': 6.980997696440068, 'z1_times_a': 4.498199381863492, 'n_zeros': 755, 'lock_metric': 0.0013619017100949234, 'residual': 12.052748449542477, 'mass_pm0.1': 127.6918385778458, 'solve_resid': 6.867617904061254e-13}, '0.9': {'lambda': -0.025831301694578486, 'Delta': 5.070963483079262, 'floor': 1.333969497055245, 'plateau': 6.4049329801345065, 'z1_times_a': 4.497946694779682, 'n_zeros': 761, 'lock_metric': 0.0030658627341504153, 'residual': 13.166729243282433, 'mass_pm0.1': 127.88295027859101, 'solve_resid': 1.2366600020318642e-13}, '0.99': {'lambda': -0.028414431864036332, 'Delta': 5.037993177808347, 'floor': 1.272757105974604, 'plateau': 6.3107502837829506, 'z1_times_a': 4.5002419528288815, 'n_zeros': 761, 'lock_metric': 0.0018016901302855674, 'residual': 12.566089279144094, 'mass_pm0.1': 127.72782983544735, 'solve_resid': 2.3651958714205305e-14}, '0.999': {'lambda': -0.028672744880982117, 'Delta': 5.034476634521893, 'floor': 1.2679657032940865, 'plateau': 6.30244233781598, 'z1_times_a': 4.495276414486893, 'n_zeros': 762, 'lock_metric': 0.0026471749147504637, 'residual': 12.710218865379431, 'mass_pm0.1': 127.70661909585449, 'solve_resid': 1.413266823421088e-14}}}
12{'lambda_a': -0.0682789599667037, 'lambda_law_ratio': -27121745.659492664, 'sister_corr': -0.014045368106618201, 'sister_crossings': 137, 'sister_cross_err': 18.87885138849781, 'ladder': {'-1': {'lambda': -1.0, 'Delta': 2.9442229398281423, 'floor': 0.22834844487190686, 'plateau': 3.172571384700049, 'z1_times_a': 4.495304974166888, 'n_zeros': 1145, 'lock_metric': 0.032106115361490564, 'residual': 57.59425795470206, 'mass_pm0.1': 133.31147006008132, 'solve_resid': 5.565591099499078e-16}, '0': {'lambda': -0.0, 'Delta': 145.87233394077197, 'floor': -369.5573776739587, 'plateau': -223.68504373318672, 'z1_times_a': 47.08983339916813, 'n_zeros': 788, 'lock_metric': 0.11988236920414796, 'residual': 10.704038663232183, 'mass_pm0.1': 126.78597572681957, 'solve_resid': 0.00035380049050859374}, '0.5': {'lambda': -0.03413947998335185, 'Delta': 4.517541168837466, 'floor': 2.012961451365246, 'plateau': 6.530502620202712, 'z1_times_a': 4.495602611843745, 'n_zeros': 1127, 'lock_metric': 0.0016805564393911263, 'residual': 12.576655387504829, 'mass_pm0.1': 127.80026124326591, 'solve_resid': 2.361326934047527e-10}, '0.9': {'lambda': -0.06145106397003333, 'Delta': 4.373132705161369, 'floor': 1.5778486637685551, 'plateau': 5.9509813689299245, 'z1_times_a': 4.4955360310205545, 'n_zeros': 1141, 'lock_metric': 0.002769088717484152, 'residual': 14.752940107360544, 'mass_pm0.1': 128.0191898119376, 'solve_resid': 3.98328418223779e-14}, '0.99': {'lambda': -0.06759617036703666, 'Delta': 4.345367791047291, 'floor': 1.511240245787921, 'plateau': 5.856608036835212, 'z1_times_a': 4.495571310035841, 'n_zeros': 1143, 'lock_metric': 0.0030508525265727083, 'residual': 15.875746711965263, 'mass_pm0.1': 128.06515694909066, 'solve_resid': 2.4872731506462405e-14}, '0.999': {'lambda': -0.068210681006737, 'Delta': 4.342626921736709, 'floor': 1.505160225931791, 'plateau': 5.847787147668501, 'z1_times_a': 4.495984857538869, 'n_zeros': 1144, 'lock_metric': 0.003716572174764971, 'residual': 15.417387806155247, 'mass_pm0.1': 128.0996751837004, 'solve_resid': 6.800740851599709e-15}}}

Parameters

a_list[4.0, 8.0, 12.0]
ladder_rel[0.0, 0.5, 0.9, 0.99, 0.999]
z_max300.0

Chart

Data preview (16560 rows total)

alambda_tagzlogK
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4-114.100-0.068293
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