{
  "paired_data": {
    "summary": [
      {
        "group": "wt",
        "available_pairs": 8,
        "missing_cells": [],
        "mean_bulk_over_barrier": 0.47582599425433103,
        "SE_across_cells": 0.05267770434441609,
        "inverse_of_mean_ratio": 2.1016085965776297,
        "mean_of_inverse_ratios": 2.2880210679724833,
        "all_pairs_barrier_variance_higher": true
      },
      {
        "group": "ptx1",
        "available_pairs": 11,
        "missing_cells": [
          403,
          406,
          407
        ],
        "mean_bulk_over_barrier": 0.6423584271023149,
        "SE_across_cells": 0.060405992943242004,
        "inverse_of_mean_ratio": 1.5567632614567066,
        "mean_of_inverse_ratios": 1.7011296572170436,
        "all_pairs_barrier_variance_higher": true
      }
    ],
    "selection": "Author eligible-cell list; after/valleys/IP processed summaries. after denotes after the transient light perturbation.",
    "limits": [
      "Processed phase summaries and prior manual curation retained; PIV and waveform extraction not rerun.",
      "ptx1 has 14 eligible experimental cells but only 11 finite paired IP variances. Missing values are not zeros.",
      "Inverse of a mean ratio differs from mean inverse ratios. Experiments, cells and video frames are different levels."
    ]
  },
  "pair_model": {
    "tau_kappa": 0.2,
    "gamma": 0.02,
    "analytic_ODE_max_error": 7.207061614167287e-10,
    "integral_check": [
      {
        "tau_nu": 0.1,
        "beta": 0,
        "X_Simpson": 0.0320694052732032,
        "Y_Simpson": 0.0168432342934263,
        "X_infinite_quad": 0.03206940548649482,
        "Y_infinite_quad": 0.016843258117405908,
        "max_abs_difference": 2.3823979608539325e-08
      },
      {
        "tau_nu": 0.1,
        "beta": 1.5707963267948966,
        "X_Simpson": 0.012823247299763758,
        "Y_Simpson": 0.014618316087182658,
        "X_infinite_quad": 0.012823247803681536,
        "Y_infinite_quad": 0.014618339918107159,
        "max_abs_difference": 2.3830924501117012e-08
      },
      {
        "tau_nu": 1,
        "beta": 0,
        "X_Simpson": 0.0019505798745944457,
        "Y_Simpson": 0.01168528699467648,
        "X_infinite_quad": 0.0019505800784861784,
        "Y_infinite_quad": 0.011685289402491542,
        "max_abs_difference": 2.407815061916674e-09
      },
      {
        "tau_nu": 1,
        "beta": 1.5707963267948966,
        "X_Simpson": -0.009317678134374006,
        "Y_Simpson": 0.0031243159579004078,
        "X_infinite_quad": -0.009317677643773128,
        "Y_infinite_quad": 0.0031243185386989137,
        "max_abs_difference": 2.580798505891907e-09
      },
      {
        "tau_nu": 3,
        "beta": 0,
        "X_Simpson": -0.0015137481366380133,
        "Y_Simpson": 0.00261929082486895,
        "X_infinite_quad": -0.0015137479633177296,
        "Y_infinite_quad": 0.0026192908720823554,
        "max_abs_difference": 1.733202836893405e-10
      },
      {
        "tau_nu": 3,
        "beta": 1.5707963267948966,
        "X_Simpson": -0.004341870787142922,
        "Y_Simpson": -0.004709941818876538,
        "X_infinite_quad": -0.004341870359098814,
        "Y_infinite_quad": -0.004709938783206684,
        "max_abs_difference": 3.035669854378753e-09
      }
    ],
    "scale_example": {
      "nu_mm2_s": 0.7,
      "frequency_Hz": 50,
      "penetration_um": 118.3215956619923,
      "distance_for_tau_nu_03_um": 64.8074069840786
    },
    "note": "The paper defines d_nu=sqrt(nu*T), not the common sqrt(2*nu/omega). With its .7mm²/s and 50Hz, d_nu is 118um; its approximate 140um numerical statement differs."
  },
  "chain_model": {
    "N": 200,
    "tau_kappa": 0.2,
    "nearest_radius_over_spacing": 0.05,
    "half_system_cutoff": "j=1..99; diametrically opposite rotor excluded",
    "stability": [
      {
        "beta": 0,
        "length_over_penetration": 0,
        "stable_nonnegative_K": [
          0
        ]
      },
      {
        "beta": 0,
        "length_over_penetration": 2,
        "stable_nonnegative_K": [
          0,
          1
        ]
      },
      {
        "beta": 0,
        "length_over_penetration": 10,
        "stable_nonnegative_K": [
          0,
          1,
          2,
          3
        ]
      },
      {
        "beta": 1.5707963267948966,
        "length_over_penetration": 0,
        "stable_nonnegative_K": [
          0
        ]
      },
      {
        "beta": 1.5707963267948966,
        "length_over_penetration": 2,
        "stable_nonnegative_K": [
          0,
          1
        ]
      },
      {
        "beta": 1.5707963267948966,
        "length_over_penetration": 10,
        "stable_nonnegative_K": [
          2,
          3,
          4
        ]
      }
    ],
    "step_refinement_global_phase_removed_error": 3.773182639834363e-14,
    "random_initial_condition": {
      "seed": 8502026,
      "final": {
        "time_periods": 5000.0,
        "global_inphase_order": 0.2845144504327558,
        "dominant_Fourier_index": 2,
        "dominant_mode_amplitude": 0.7765357460047373,
        "adjacent_phase_SD": 0.055951471917557026,
        "instantaneous_frequency_SD": 0.01772123014835738
      },
      "note": "A spatially modulated state remains; it is not a uniform phase-difference relative equilibrium and is not presented as a full reproduction of published Fig5."
    },
    "scope": "Reduced phase equation and Fourier stability only; full elastic rotor/history integral trajectories and open-chain selection not simulated."
  },
  "pumping_example": {
    "N": 12,
    "h_over_vertical_amplitude": 3.3333333333333335,
    "kinematics": "x=A sin(phi), z=h+B cos(phi), Fx=zeta dx/dt; constant zeta and fixed no-slip plane.",
    "relation": "Qx=Fx*z/(pi*mu); single mean=zeta*A*B*omega/(2*pi*mu). q/single_mean=2(h/B)cos(phi)+2cos(phi)^2.",
    "summary": [
      {
        "case": "inphase",
        "mean_normalized_flux": 11.999999999999993,
        "temporal_RMS_fluctuation": 57.201398584300364
      },
      {
        "case": "wave_forward",
        "mean_normalized_flux": 12.0,
        "temporal_RMS_fluctuation": 4.4095472041381495e-15
      },
      {
        "case": "wave_backward",
        "mean_normalized_flux": 12.0,
        "temporal_RMS_fluctuation": 6.649287495761255e-15
      },
      {
        "case": "opposed_orientation",
        "mean_normalized_flux": 1.708702623837095e-17,
        "temporal_RMS_fluctuation": 1.2430731205225645e-15
      }
    ],
    "limits": [
      "Phases and kinematics prescribed; no emergence claim for this example.",
      "Mutual hydrodynamic loads ignored. Does not show mean flux independent of metachrony in dense real tissues.",
      "Net volume flux, fluctuations, dissipation and material exchange are distinct performance measures."
    ]
  },
  "inputs_sha256": {
    "zorrilla-Phase_difference.zip": "769bf8b6adee149bb239a1c968cdfb73429ac119bf7f1f986f324518c6080d5c",
    "zorrilla-Metadata.zip": "9a8277fcb90bfff6e1410c9f162e91487a482108f6f06fe6879a923cf8a5c137",
    "zorrilla-Figures.py": "a8d47cc5d4637f67f7a52e989a63774065b2f50a7ac038624cfeadf29a53f847"
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}