{ "experiment": "controlled gamma detuning and gamma parameter-step/return", "headline_result": "Negative local-detuning result: gamma=4.47, exact 4.570078733 baseline, and 4.67 deg all retain the same passive broad attractor for 200 s. No qualitative loss of the existing broad, persistently winding regime occurs across this +/-0.10 deg interval.", "phase_guardrail": "All three cases show persistent transverse relative-phase winding at about -59 turns/s and low circular concentration (~0.205), despite an average phase near 180 deg and positive mean magnetic potential. Thus routine wrapped crossings are not classified as genuine phase slips from a coherent 1:1 lock.", "local_detuning_ranges": { "theta_mean_deg": [ 103.2411243932942, 103.67661182661773 ], "theta_span_deg": [ 146.8145789855411, 146.92934396909095 ], "physical_spin_mean_rad_s": [ -6.9227522805083, -6.6416717465362 ], "anti_parallel_fraction": [ 0.6691333086669133, 0.6741232587674123 ], "baseline_theta_mean_deg": 103.44775435892885 }, "state_provenance_and_rephasing": { "source_npz": "MBS-Sim-private/tmp/passive_cylinder_index19_strict200/excited_strict200.npz", "source_time_s": 200.0, "source_drive_frequency_hz": 60.0, "completed_drive_cycles": 12000, "clock_reset_preserves_rotating_azimuth": true, "identical_initial_state_for_every_fixed_gamma_case": true, "canonical_initial_state_qw_qx_qy_qz_wx_wy_wz": [ 0.880103425832763, -0.20221196324571478, -0.4226839508795747, -0.07659346856345738, 87.59264815074225, 47.2098891762353, -15.833355421134897 ], "initial_symmetry_spin_rad_s": -6.675704318866007, "note": "Quaternion sign was canonicalized only; that does not change physical attitude." }, "held_fixed_inputs": { "name": "passive-cylinder-index19-stable-angular-excited", "field_frequency_hz": 60.0, "inertia_1": 1.0021731111381967e-07, "inertia_2": 1.0022090307856679e-07, "inertia_3": 1.4767799979617656e-07, "magnetic_coupling": 0.002184760832934153, "field_tilt_deg": 4.570078733480211, "damping": 0.0982787764237392, "spin_acceleration": 0.0, "theta_deg": 114.27084371195292, "phi_deg": 174.52211520353944, "psi_deg": 38.367429382075514, "theta_rate": 81.31110257042322, "phi_rate": 124.34984521684584, "psi_rate": 39.44536471991236, "duration": 200.0, "solver_method": "LSODA", "relative_tolerance": 1e-10, "absolute_tolerance": 1e-12, "maximum_step": 0.00020833333333333335, "steps_per_second": 2500.0, "inertia_12": 2.1909973539360762e-10, "inertia_13": 3.2188443951832836e-09, "inertia_23": 3.245337722777423e-09 }, "numerics": { "production_solver": "LSODA", "duration_s": 200.0, "saved_samples_per_s": 2500.0, "rtol": 1e-10, "atol": 1e-12, "maximum_internal_step_s": 0.00020833333333333335, "minimum_internal_steps_per_drive_period": 80 }, "phase_definition": { "definition": "delta=atan2(m dot e_quadrature, m dot e_parallel), where e_parallel is the rotating field's normalized transverse direction and e_quadrature=z cross e_parallel", "coordinate_safe": "Uses lab-vector dot/cross projections, not Euler azimuth; transverse radius is stored as a reliability measure.", "rho_min_for_slip_count": 0.01, "winding_crossing_rule": "Accumulate atan2 increments of the rotating-frame complex projection only across edges whose endpoint radii exceed rho_min; count signed complete 2pi winding-index changes.", "terminology_correction": "Legacy raw-report keys containing 'phase_slip' hold winding-boundary crossings. Public artifacts use the conservative term transverse winding crossing." }, "detuning_cases": { "4.470000\u00b0": { "gamma_deg_exact": 4.47, "late_window_s": [ 160.0, 200.0 ], "theta_mean_deg": 103.2411243932942, "theta_min_deg": 31.501652803711643, "theta_max_deg": 178.4309967728026, "theta_span_deg": 146.92934396909095, "physical_symmetry_spin_mean_rad_s": -6.6416717465362, "u_mean": 0.1474710866769846, "anti_parallel_fraction": 0.6691333086669133, "transverse_phase_circular_mean_deg": -176.3905533938511, "transverse_phase_resultant_length": 0.20410136105124765, "transverse_winding_rate_turns_per_s": -58.99775569437173, "coherent_1_to_1_transverse_phase_lock": false, "phase_assessment": "Persistent routine transverse winding; no coherent 1:1 lock exists from which individual genuine phase slips could be identified.", "winding_crossings": { "transverse_winding_crossing_count": 11799, "net_transverse_winding_turns": -11799.551138874347, "total_transverse_phase_travel_turns": 11799.551138873969, "projection_valid_fraction": 0.999994000012, "rho_min": 0.01, "first_crossing_times_s": [ 0.0244, 0.0388, 0.049600000000000005, 0.068, 0.092, 0.10640000000000001, 0.11760000000000001, 0.136, 0.16, 0.1748 ], "last_crossing_times_s": [ 199.8316, 199.8556, 199.87400000000002, 199.8852, 199.8992, 199.9232, 199.94160000000002, 199.9532, 199.96720000000002, 199.99120000000002 ], "complete_crossing_table": "See the transverse_winding_crossings CSV; these are not asserted to be genuine coherent-lock slips." }, "theta_spectrum_top_peaks_120_200s": [ { "frequency_hz": 14.749926250403124, "amplitude": 65.30835753717895 }, { "frequency_hz": 44.24977875120937, "amplitude": 5.780503276338683 }, { "frequency_hz": 29.49985250080625, "amplitude": 3.9385359164070635 }, { "frequency_hz": 88.51205743991909, "amplitude": 1.6178412958253956 }, { "frequency_hz": 59.012204939112834, "amplitude": 0.8350999308368326 }, { "frequency_hz": 118.01190994072533, "amplitude": 0.7624684660233674 }, { "frequency_hz": 132.76183619112845, "amplitude": 0.42505053550100247 }, { "frequency_hz": 147.51176244153157, "amplitude": 0.41432438666655397 }, { "frequency_hz": 73.76213118951596, "amplitude": 0.2744410349692683 }, { "frequency_hz": 103.26198369032221, "amplitude": 0.2706129973961378 } ], "cross_solver_8s": { "duration_s": 8.0, "DOP853_nfev": 520817, "quaternion_geodesic_max_rad": 5.960464477539063e-08, "body_omega_max_difference_rad_s": 3.1703312896287325e-06, "theta_max_difference_deg": 1.8122067757531113e-06, "symmetry_spin_max_difference_rad_s": 2.7740523570251173e-07 }, "raw_strict_npz_optional": "gamma_4p470000_strict200.npz" }, "4.570079\u00b0 baseline": { "gamma_deg_exact": 4.570078733480211, "late_window_s": [ 160.0, 200.0 ], "theta_mean_deg": 103.44775435892885, "theta_min_deg": 31.541258952853767, "theta_max_deg": 178.41008431673666, "theta_span_deg": 146.86882536388288, "physical_symmetry_spin_mean_rad_s": -6.782699670459178, "u_mean": 0.14810810829175086, "anti_parallel_fraction": 0.6715532844671553, "transverse_phase_circular_mean_deg": -176.51062514854092, "transverse_phase_resultant_length": 0.20554846703999244, "transverse_winding_rate_turns_per_s": -58.987909326616645, "coherent_1_to_1_transverse_phase_lock": false, "phase_assessment": "Persistent routine transverse winding; no coherent 1:1 lock exists from which individual genuine phase slips could be identified.", "winding_crossings": { "transverse_winding_crossing_count": 11797, "net_transverse_winding_turns": -11797.58186532333, "total_transverse_phase_travel_turns": 11797.581865323575, "projection_valid_fraction": 1.0, "rho_min": 0.01, "first_crossing_times_s": [ 0.0244, 0.0392, 0.049600000000000005, 0.068, 0.092, 0.1068, 0.11760000000000001, 0.136, 0.16, 0.1748 ], "last_crossing_times_s": [ 199.8288, 199.8528, 199.8676, 199.87800000000001, 199.8964, 199.9204, 199.9352, 199.946, 199.9644, 199.9884 ], "complete_crossing_table": "See the transverse_winding_crossings CSV; these are not asserted to be genuine coherent-lock slips." }, "theta_spectrum_top_peaks_120_200s": [ { "frequency_hz": 14.749926250403124, "amplitude": 64.61075451794629 }, { "frequency_hz": 44.23727881370903, "amplitude": 5.655386556139236 }, { "frequency_hz": 29.49985250080625, "amplitude": 3.638509636914682 }, { "frequency_hz": 88.4870575649184, "amplitude": 1.6693859019981212 }, { "frequency_hz": 58.98720506411215, "amplitude": 0.9650535337000662 }, { "frequency_hz": 117.98691006572464, "amplitude": 0.6826549505211732 }, { "frequency_hz": 147.47426262903056, "amplitude": 0.44644374608162674 }, { "frequency_hz": 132.72433637862744, "amplitude": 0.40975828527459307 }, { "frequency_hz": 162.22418887943368, "amplitude": 0.29480603519704707 }, { "frequency_hz": 176.9741151298368, "amplitude": 0.2762447936532731 } ], "cross_solver_8s": { "duration_s": 8.0, "DOP853_nfev": 520817, "quaternion_geodesic_max_rad": 5.16191365590357e-08, "body_omega_max_difference_rad_s": 2.603102686621972e-06, "theta_max_difference_deg": 6.008607442709035e-07, "symmetry_spin_max_difference_rad_s": 1.463615339970091e-07 }, "raw_strict_npz_optional": "gamma_4p570079_strict200.npz" }, "4.670000\u00b0": { "gamma_deg_exact": 4.67, "late_window_s": [ 160.0, 200.0 ], "theta_mean_deg": 103.67661182661773, "theta_min_deg": 31.578623684649326, "theta_max_deg": 178.39320267019042, "theta_span_deg": 146.8145789855411, "physical_symmetry_spin_mean_rad_s": -6.9227522805083, "u_mean": 0.1486882524880441, "anti_parallel_fraction": 0.6741232587674123, "transverse_phase_circular_mean_deg": -176.57242475286634, "transverse_phase_resultant_length": 0.20694804503835226, "transverse_winding_rate_turns_per_s": -58.97081478551549, "coherent_1_to_1_transverse_phase_lock": false, "phase_assessment": "Persistent routine transverse winding; no coherent 1:1 lock exists from which individual genuine phase slips could be identified.", "winding_crossings": { "transverse_winding_crossing_count": 11794, "net_transverse_winding_turns": -11794.162957103099, "total_transverse_phase_travel_turns": 11794.162957103055, "projection_valid_fraction": 0.9999960000079999, "rho_min": 0.01, "first_crossing_times_s": [ 0.0244, 0.0392, 0.049600000000000005, 0.068, 0.092, 0.1072, 0.11720000000000001, 0.1356, 0.16, 0.1748 ], "last_crossing_times_s": [ 199.8528, 199.8608, 199.88, 199.904, 199.9204, 199.9288, 199.94760000000002, 199.972, 199.9884, 199.9968 ], "complete_crossing_table": "See the transverse_winding_crossings CSV; these are not asserted to be genuine coherent-lock slips." }, "theta_spectrum_top_peaks_120_200s": [ { "frequency_hz": 14.737426312902782, "amplitude": 55.98416671330771 }, { "frequency_hz": 44.22477887620869, "amplitude": 5.524880496302655 }, { "frequency_hz": 29.487352563305905, "amplitude": 3.804272781277353 }, { "frequency_hz": 88.46205768991771, "amplitude": 1.701226135559219 }, { "frequency_hz": 58.97470512661181, "amplitude": 1.0653751629615216 }, { "frequency_hz": 117.94941025322362, "amplitude": 0.7996373528265732 }, { "frequency_hz": 147.43676281652952, "amplitude": 0.4623732486142227 }, { "frequency_hz": 132.6868365661264, "amplitude": 0.38552421136534365 }, { "frequency_hz": 176.92411537983543, "amplitude": 0.28327827496685576 }, { "frequency_hz": 162.1741891294323, "amplitude": 0.2528670293356459 } ], "cross_solver_8s": { "duration_s": 8.0, "DOP853_nfev": 520817, "quaternion_geodesic_max_rad": 5.16191365590357e-08, "body_omega_max_difference_rad_s": 2.2638050261548326e-06, "theta_max_difference_deg": 5.348448866016042e-07, "symmetry_spin_max_difference_rad_s": 1.6318765196778657e-07 }, "raw_strict_npz_optional": "gamma_4p670000_strict200.npz" } }, "bounded_boundary_scan": { "purpose": "Select an informative nearby upper-gamma boundary for a controlled parameter step.", "selection_rule": "Choose the smallest screened gamma failing mean(theta)>70 deg, max(theta)>120 deg, span(theta)>100 deg over 20-30 s; one midpoint refinement is added across the first retained/failed bracket.", "selected_step_gamma_deg": 5.7, "rows": [ { "gamma_deg": 5.3, "duration_s": 30.0, "saved_samples_per_s": 600.0, "internal_max_step_s": 0.00020833333333333335, "nfev": 343855, "large_branch_retained": true, "early": { "range_s": [ 0.0, 10.0 ], "theta_mean_deg": 104.50602382565367, "theta_min_deg": 28.48296088170403, "theta_max_deg": 179.9414034883982, "theta_span_deg": 151.45844260669418, "theta_slope_deg_s": 0.048190925340823934, "spin_mean_rad_s": -7.831583901994476, "spin_abs_mean_rad_s": 7.831583901994476, "spin_std_rad_s": 2.702928914717116, "spin_slope_rad_s2": 0.013561312363175326, "body_speed_mean_rad_s": 104.30474723440008, "u_mean": 0.15367007604287894, "ap_fraction": 0.6900516580569905, "phase_valid_fraction": 0.9995000833194467, "phase_circular_mean_deg": -179.01784736294513, "phase_resultant_length": 0.23296098599615464, "kinetic_mean_J": 0.0006127422143982861, "potential_mean_J": 0.0003357323633324949, "total_mean_J": 0.0009484745777307811, "field_power_mean_W": 9.0377871502132e-05, "damping_loss_mean_W": 0.00012037770160360441, "energy_rate_W": -3.055462114373961e-05, "power_closure_error_W": -5.547910422671937e-07, "phase_rho_min": 0.01, "phase_net_winding": -470.35696828236536, "phase_total_phase_travel_turns": 525.3294767510884, "transverse_winding_crossing_count": 570 }, "late": { "range_s": [ 20.0, 30.0 ], "theta_mean_deg": 105.0049789805037, "theta_min_deg": 31.179350913088758, "theta_max_deg": 179.9197134125033, "theta_span_deg": 148.74036249941454, "theta_slope_deg_s": -0.04410094881092614, "spin_mean_rad_s": -7.76966870446847, "spin_abs_mean_rad_s": 7.76966870446847, "spin_std_rad_s": 2.612156796554908, "spin_slope_rad_s2": 0.012725601964136083, "body_speed_mean_rad_s": 104.24628663924523, "u_mean": 0.1527931079702851, "ap_fraction": 0.6988835194134311, "phase_valid_fraction": 0.9990001666388936, "phase_circular_mean_deg": -176.17701954744146, "phase_resultant_length": 0.22114875869197784, "kinetic_mean_J": 0.0006107177572513791, "potential_mean_J": 0.0003338163978357581, "total_mean_J": 0.0009445341550871373, "field_power_mean_W": -9.211241948350311e-05, "damping_loss_mean_W": 0.00011998577821064784, "energy_rate_W": -0.00021738149941229792, "power_closure_error_W": -5.283301718146964e-06, "phase_rho_min": 0.01, "phase_net_winding": -531.9320290493191, "phase_total_phase_travel_turns": 571.3458473797765, "transverse_winding_crossing_count": 579 } }, { "gamma_deg": 5.5, "duration_s": 30.0, "saved_samples_per_s": 600.0, "internal_max_step_s": 0.00020833333333333335, "nfev": 350432, "large_branch_retained": true, "early": { "range_s": [ 0.0, 10.0 ], "theta_mean_deg": 104.2351539313011, "theta_min_deg": 23.74237224611792, "theta_max_deg": 179.5219587491427, "theta_span_deg": 155.77958650302477, "theta_slope_deg_s": 0.028244524528114715, "spin_mean_rad_s": -8.057452635590659, "spin_abs_mean_rad_s": 8.057452635590659, "spin_std_rad_s": 2.8079108577992677, "spin_slope_rad_s2": 0.027064979061235814, "body_speed_mean_rad_s": 104.35830800071498, "u_mean": 0.15599076642105741, "ap_fraction": 0.6810531578070321, "phase_valid_fraction": 0.9998333611064822, "phase_circular_mean_deg": 179.9407941344866, "phase_resultant_length": 0.23623620877579823, "kinetic_mean_J": 0.0006163868309381609, "potential_mean_J": 0.0003408025167761063, "total_mean_J": 0.0009571893477142671, "field_power_mean_W": 0.00022908117873885747, "damping_loss_mean_W": 0.00012107590528623964, "energy_rate_W": 0.00010522862078152955, "power_closure_error_W": -2.7766526710882786e-06, "phase_rho_min": 0.01, "phase_net_winding": -460.5871896995979, "phase_total_phase_travel_turns": 499.9149445217728, "transverse_winding_crossing_count": 520 }, "late": { "range_s": [ 20.0, 30.0 ], "theta_mean_deg": 104.2446320608934, "theta_min_deg": 24.705730126559363, "theta_max_deg": 179.90375719788742, "theta_span_deg": 155.19802707132806, "theta_slope_deg_s": -0.08200405344871231, "spin_mean_rad_s": -7.942065228392845, "spin_abs_mean_rad_s": 7.942065228392845, "spin_std_rad_s": 2.710277014627732, "spin_slope_rad_s2": -0.002658430759901082, "body_speed_mean_rad_s": 104.25922744787817, "u_mean": 0.1550207931493089, "ap_fraction": 0.6825529078486919, "phase_valid_fraction": 0.999333444425929, "phase_circular_mean_deg": -179.8015720126464, "phase_resultant_length": 0.23542645653904373, "kinetic_mean_J": 0.0006151404172759925, "potential_mean_J": 0.00033868335716299704, "total_mean_J": 0.0009538237744389896, "field_power_mean_W": 0.0003338054463928412, "damping_loss_mean_W": 0.00012084167282373063, "energy_rate_W": 0.00021883097411121345, "power_closure_error_W": 5.867200542102865e-06, "phase_rho_min": 0.01, "phase_net_winding": -462.904466272365, "phase_total_phase_travel_turns": 502.6199280529553, "transverse_winding_crossing_count": 496 } }, { "gamma_deg": 5.6, "duration_s": 30.0, "saved_samples_per_s": 600.0, "internal_max_step_s": 0.00020833333333333335, "nfev": 344165, "large_branch_retained": true, "early": { "range_s": [ 0.0, 10.0 ], "theta_mean_deg": 104.52715147727713, "theta_min_deg": 20.3524722006056, "theta_max_deg": 179.3177614221685, "theta_span_deg": 158.9652892215629, "theta_slope_deg_s": 0.09860504596299205, "spin_mean_rad_s": -8.210512570105525, "spin_abs_mean_rad_s": 8.210512570105525, "spin_std_rad_s": 2.819156019716682, "spin_slope_rad_s2": 0.02033907970576998, "body_speed_mean_rad_s": 104.39987955928935, "u_mean": 0.15616513961368325, "ap_fraction": 0.6847192134644225, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": 179.96001254412658, "phase_resultant_length": 0.23691684030330812, "kinetic_mean_J": 0.0006168601507817904, "potential_mean_J": 0.000341183480497669, "total_mean_J": 0.0009580436312794592, "field_power_mean_W": 0.000239525077790335, "damping_loss_mean_W": 0.00012115704518957657, "energy_rate_W": 0.0001154716785251972, "power_closure_error_W": -2.896354075561223e-06, "phase_rho_min": 0.01, "phase_net_winding": 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-0.00018242132675490001, "power_closure_error_W": -3.927637620223417e-07, "phase_rho_min": 0.01, "phase_net_winding": -499.883123148176, "phase_total_phase_travel_turns": 557.8710497280454, "transverse_winding_crossing_count": 561 } }, { "gamma_deg": 5.7, "duration_s": 30.0, "saved_samples_per_s": 600.0, "internal_max_step_s": 0.00020833333333333335, "nfev": 363997, "large_branch_retained": false, "early": { "range_s": [ 0.0, 10.0 ], "theta_mean_deg": 94.33652604298514, "theta_min_deg": 8.06976230444314, "theta_max_deg": 179.3657234190121, "theta_span_deg": 171.29596111456897, "theta_slope_deg_s": -5.0830062069076565, "spin_mean_rad_s": -8.620357388852938, "spin_abs_mean_rad_s": 8.631641621946805, "spin_std_rad_s": 3.813268135796323, "spin_slope_rad_s2": 0.3675429088007676, "body_speed_mean_rad_s": 75.74454064991971, "u_mean": 0.12776069113811162, "ap_fraction": 0.6072321279786702, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": 179.60293123636902, "phase_resultant_length": 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"end_s": 200.0, "gamma_deg": 4.570078733480211 } ], "selected_boundary_gamma_deg": 5.7, "windows": { "baseline_before_step_10_30s": { "range_s": [ 10.0, 30.0 ], "theta_mean_deg": 103.45386405652417, "theta_min_deg": 31.53620938304378, "theta_max_deg": 178.4154957316502, "theta_span_deg": 146.87928634860643, "theta_slope_deg_s": -0.01784035521804858, "spin_mean_rad_s": -6.783889215619976, "spin_abs_mean_rad_s": 6.783889215619976, "spin_std_rad_s": 2.507375380760843, "spin_slope_rad_s2": 0.00040108151188263206, "body_speed_mean_rad_s": 104.0268503731133, "u_mean": 0.14804637725584285, "ap_fraction": 0.6715065698686026, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": -176.46714824563824, "phase_resultant_length": 0.2055080104973739, "kinetic_mean_J": 0.0006049975150469435, "potential_mean_J": 0.00032344592648635915, "total_mean_J": 0.0009284434415333026, "field_power_mean_W": 0.00018502853654785113, "damping_loss_mean_W": 0.00011892948944680992, "energy_rate_W": 6.622820977619604e-05, "power_closure_error_W": 1.2916267515482554e-07, "phase_rho_min": 0.01, "phase_net_winding": -1179.8572053936093, "phase_total_phase_travel_turns": 1179.857205393615, "transverse_winding_crossing_count": 1179 }, "during_step_70_90s": { "range_s": [ 70.0, 90.0 ], "theta_mean_deg": 105.86853692662149, "theta_min_deg": 31.675409541374556, "theta_max_deg": 178.8881457123001, "theta_span_deg": 147.21273617092552, "theta_slope_deg_s": -0.006141325927437487, "spin_mean_rad_s": -8.240650180555543, "spin_abs_mean_rad_s": 8.240650180555543, "spin_std_rad_s": 2.6423679831289864, "spin_slope_rad_s2": 0.0010004117514390517, "body_speed_mean_rad_s": 104.33620029067356, "u_mean": 0.15507754824526104, "ap_fraction": 0.7105257894842103, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": -176.84991257841605, "phase_resultant_length": 0.22034459092410313, "kinetic_mean_J": 0.000613640284322888, "potential_mean_J": 0.00033880735347370283, "total_mean_J": 0.0009524476377965908, "field_power_mean_W": 0.0001258079493755887, "damping_loss_mean_W": 0.00012052499295996791, "energy_rate_W": 5.3459570109741945e-06, "power_closure_error_W": 6.300059535341328e-08, "phase_rho_min": 0.01, "phase_net_winding": -1176.3910684881216, "phase_total_phase_travel_turns": 1176.391068488128, "transverse_winding_crossing_count": 1176 }, "early_after_restore_90_120s": { "range_s": [ 90.0, 120.0 ], "theta_mean_deg": 103.49060347900553, "theta_min_deg": 30.981080180537415, "theta_max_deg": 179.93506673308283, "theta_span_deg": 148.95398655254542, "theta_slope_deg_s": 0.0011315039224780619, "spin_mean_rad_s": -6.9614363721540125, "spin_abs_mean_rad_s": 6.9614363721540125, "spin_std_rad_s": 2.5570791889725677, "spin_slope_rad_s2": 0.01427685375086813, "body_speed_mean_rad_s": 104.04076625364748, "u_mean": 0.14837295420825355, "ap_fraction": 0.6789776136318182, "phase_valid_fraction": 0.9991600111998507, "phase_circular_mean_deg": -175.89525388934737, "phase_resultant_length": 0.2106855204558371, "kinetic_mean_J": 0.0006056217942172827, "potential_mean_J": 0.00032415941902092497, "total_mean_J": 0.0009297812132382078, "field_power_mean_W": 0.00016193401950597797, "damping_loss_mean_W": 0.0001190397076613134, "energy_rate_W": 4.153979131750858e-05, "power_closure_error_W": -1.3545205271559861e-06, "phase_rho_min": 0.01, "phase_net_winding": -1628.3244794792822, "phase_total_phase_travel_turns": 1695.3352575170204, "transverse_winding_crossing_count": 1698 }, "settled_after_restore_160_200s": { "range_s": [ 160.0, 200.0 ], "theta_mean_deg": 103.46070330577211, "theta_min_deg": 31.482580062020503, "theta_max_deg": 178.61825445965547, "theta_span_deg": 147.13567439763497, "theta_slope_deg_s": 0.004926390187828371, "spin_mean_rad_s": -6.783982442315336, "spin_abs_mean_rad_s": 6.783982442315336, "spin_std_rad_s": 2.507723635289784, "spin_slope_rad_s2": -1.2334692383784994e-06, "body_speed_mean_rad_s": 104.03445763843793, "u_mean": 0.14815734489428647, "ap_fraction": 0.6717032829671703, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": -176.46515505983243, "phase_resultant_length": 0.20563220134579926, "kinetic_mean_J": 0.0006050801044579371, "potential_mean_J": 0.0003236883642365539, "total_mean_J": 0.0009287684686944909, "field_power_mean_W": 0.0002154990489072171, "damping_loss_mean_W": 0.00011894574433261068, "energy_rate_W": 9.673004940404793e-05, "power_closure_error_W": 1.7674482944149753e-07, "phase_rho_min": 0.01, "phase_net_winding": -2359.6208135021043, "phase_total_phase_travel_turns": 2359.6208135021056, "transverse_winding_crossing_count": 2359 } }, "response_during_step_relative_to_baseline": { "theta_mean_change_deg": 2.41467287009732, "theta_span_change_deg": 0.33344982231909626, "spin_mean_change_rad_s": -1.4567609649355662, "anti_parallel_fraction_change": 0.039019219615607725 }, "settled_restored_minus_baseline": { "theta_mean_difference_deg": 0.0068392492479461, "theta_span_difference_deg": 0.2563880490285442, "spin_mean_difference_rad_s": -9.32266953599381e-05, "anti_parallel_fraction_difference": 0.00019671309856772456 }, "interpretation": "The 5.70 deg step changes spin, AP occupancy, and the detailed orbit, but restoring baseline gamma returns the same broad statistical branch. There is no irreversible hysteresis for this schedule.", "near_boundary_state_sensitivity": "The direct 30 s scan from the original rephased microstate leaves the broad branch at gamma=5.70 deg, whereas applying the same gamma after 30 s of baseline evolution retains it. This is finite-state/basin sensitivity near a non-monotone boundary, not spontaneous decay.", "potential_energy_jump_at_30s_J": 2.2893989249139317e-05, "potential_energy_jump_at_90s_J": -4.2442568142413017e-05, "winding_crossings": { "transverse_winding_crossing_count": 11632, "net_transverse_winding_turns": -11578.419151221415, "total_transverse_phase_travel_turns": 11677.581188436225, "projection_valid_fraction": 0.9997860004279991, "rho_min": 0.01, "first_crossing_times_s": [ 0.0244, 0.0392, 0.049600000000000005, 0.068, 0.092, 0.1068, 0.11760000000000001, 0.136, 0.16, 0.1748 ], "last_crossing_times_s": [ 199.8468, 199.85520000000002, 199.87400000000002, 199.8984, 199.9148, 199.9232, 199.942, 199.966, 199.98239999999998, 199.9908 ], "complete_crossing_table": "See the transverse_winding_crossings CSV; these are not asserted to be genuine coherent-lock slips." }, "phase_assessment": "The transverse phase continues routine winding. Winding-boundary crossings are tabulated, but are not genuine slips from a coherent lock.", "tighter_LSODA_crosscheck": { "solver": "LSODA", "saved_samples_per_s": 600.0, "rtol": 1e-11, "atol": 1e-13, "maximum_internal_step_s": 0.0001388888888888889, "nfev": 3242715, "classification_agreement": { "production_final_large_branch": true, "crosscheck_final_large_branch": true }, "windows": [ { "range_s": [ 10.0, 30.0 ], "theta_mean_deg": 103.45385014498811, "theta_min_deg": 31.535745994625305, "theta_max_deg": 178.41299293906397, "theta_span_deg": 146.87724694443867, "theta_slope_deg_s": -0.0179881443640032, "spin_mean_rad_s": -6.783879799596997, "spin_abs_mean_rad_s": 6.783879799596997, "spin_std_rad_s": 2.5073524792178743, "spin_slope_rad_s2": 0.00039711171976236273, "body_speed_mean_rad_s": 104.02690765871402, "u_mean": 0.14804661867252325, "ap_fraction": 0.6714440463294725, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": -176.4796130389473, "phase_resultant_length": 0.20552690469456364, "kinetic_mean_J": 0.000604998510422372, "potential_mean_J": 0.0003234464539240668, "total_mean_J": 0.0009284449643464389, "field_power_mean_W": 0.0001829006234682452, "damping_loss_mean_W": 0.00011892968595472243, "energy_rate_W": 6.622820097061105e-05, "power_closure_error_W": 2.2572634570882603e-06, "phase_rho_min": 0.01, "phase_net_winding": -1179.8572054256872, "phase_total_phase_travel_turns": 1179.8572054256856, "transverse_winding_crossing_count": 1179 }, { "range_s": [ 70.0, 90.0 ], "theta_mean_deg": 105.86838370284283, "theta_min_deg": 31.668823961758488, "theta_max_deg": 178.97227837727286, "theta_span_deg": 147.30345441551438, "theta_slope_deg_s": -0.006089096489506196, "spin_mean_rad_s": -8.240642494305135, "spin_abs_mean_rad_s": 8.240642494305135, "spin_std_rad_s": 2.6424861721008956, "spin_slope_rad_s2": 0.0009659957205652612, "body_speed_mean_rad_s": 104.33612298363786, "u_mean": 0.15507752157498594, "ap_fraction": 0.7102741438213482, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": -176.836195771173, "phase_resultant_length": 0.2203525897588253, "kinetic_mean_J": 0.0006136411199404023, "potential_mean_J": 0.0003388072952055303, "total_mean_J": 0.0009524484151459328, "field_power_mean_W": 0.00012476479521720375, "damping_loss_mean_W": 0.00012052515811742166, "energy_rate_W": 5.345962760919397e-06, "power_closure_error_W": 1.1063256611373164e-06, "phase_rho_min": 0.01, "phase_net_winding": -1176.3910684927662, "phase_total_phase_travel_turns": 1176.3910684927623, "transverse_winding_crossing_count": 1176 }, { "range_s": [ 160.0, 200.0 ], "theta_mean_deg": 103.46070034876371, "theta_min_deg": 31.494046489385173, "theta_max_deg": 178.60220916713274, "theta_span_deg": 147.10816267774757, "theta_slope_deg_s": 0.0049848004277409565, "spin_mean_rad_s": -6.783983768719784, "spin_abs_mean_rad_s": 6.783983768719784, "spin_std_rad_s": 2.5076951734415354, "spin_slope_rad_s2": 2.264743841049639e-06, "body_speed_mean_rad_s": 104.0344057277983, "u_mean": 0.14815636124552994, "ap_fraction": 0.6714720219990834, "phase_valid_fraction": 1.0, "phase_circular_mean_deg": -176.4690448184158, "phase_resultant_length": 0.20562370546452874, "kinetic_mean_J": 0.000605079542660008, "potential_mean_J": 0.00032368621519927724, "total_mean_J": 0.0009287657578592852, "field_power_mean_W": 0.00021258115888369726, "damping_loss_mean_W": 0.00011894563358790338, "energy_rate_W": 9.673006351152613e-05, "power_closure_error_W": 3.0945382157322574e-06, "phase_rho_min": 0.01, "phase_net_winding": -2359.6208134307494, "phase_total_phase_travel_turns": 2359.620813430745, "transverse_winding_crossing_count": 2359 } ] }, "raw_strict_npz_optional": "gamma_step_return_strict200.npz" }, "figures": [ "03-gamma-detuning.png", "07-gamma-step-return.png" ], "compact_data": [ "03-gamma-detuning-data.npz", "07-gamma-step-return-data.npz", "03-gamma-detuning-metrics.csv", "03-gamma-boundary-scan.csv", "07-gamma-step-return-metrics.csv" ], "reproducibility_scripts": [ "run_site_round2_gamma.py", "finalize_site_round2_gamma.py" ], "optional_audit_data": { "raw_npz_files": [ "gamma_4p470000_strict200.npz", "gamma_4p570079_strict200.npz", "gamma_4p670000_strict200.npz", "gamma_step_return_strict200.npz" ], "crossing_tables": [ "detuning_transverse_winding_crossings.csv", "gamma_step_return_transverse_winding_crossings.csv" ] } }