{
  "schema": "mlcmd-public-data-v1",
  "units": "dimensionless model units; hbar = 1",
  "sampling_scope": "independent fixed-centroid PIMC chains; conditional mean labels on a fixed grid, not ordinary-PIMD-distribution force matching",
  "dynamics_scope": "each learned or reference PMF uses its own canonical centroid distribution; physical mass",
  "attachment_scope": "stored-label/model/curve reproduction; no fresh PIMC sampling, CMD propagation or quantum diagonalization",
  "models": {
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      "mass": 1.0,
      "ml": {
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        "seed": 173,
        "max_nfev": 2000,
        "loss_weight": "inverse_quartic"
      },
      "dynamics": {
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        "dt_stricter": 0.005,
        "tmax": 8.0,
        "q_bounds": [
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          3.5
        ],
        "q_bounds_stricter": [
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          4.0
        ],
        "n_q": 64,
        "n_q_stricter": 96,
        "n_p": 12,
        "n_p_stricter": [
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          20
        ]
      },
      "quantum": {
        "n_grid": 96,
        "n_grid_stricter": 128,
        "bounds": [
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          6.0
        ],
        "larger_bounds": [
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      "coefficients": [
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      "sampling": {
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          "production": 32,
          "stricter": 64
        },
        "nsteps_train": 2048,
        "nsteps_reference": 4096,
        "nchains": 4,
        "burnin": 0.25,
        "sample_stride": 1,
        "master_seed": 20261005,
        "reference_frequency": "local_curvature",
        "gates": {
          "min_ess_per_chain": 200,
          "max_rhat": 1.05,
          "max_force_stderr": 0.005,
          "centroid_tolerance": 1e-11
        }
      },
      "force_loss": "sum normalized weights*(model force-label)^2, weights=1/(1+q^2)^2; same total-label normalization and initialization for both modes",
      "correlation_definition": "quantum position Kubo correlation; canonical q(0)q(t) counterpart for centroid dynamics",
      "validated_force_error_threshold": 0.01,
      "expected_checks": [
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          "name": "P_production_stricter_force",
          "value": 1.4055452968501052e-20,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "P_production_stricter_width",
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          "threshold": 0.005,
          "status": "passed"
        },
        {
          "name": "direct_energy_drift",
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          "threshold": 0.05,
          "status": "passed"
        },
        {
          "name": "direct_dt",
          "value": 1.2369784836707698e-05,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "direct_nq",
          "value": 9.992007221626409e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "direct_q_bounds",
          "value": 9.19507686614196e-06,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "direct_np16",
          "value": 4.440892098500626e-16,
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          "status": "passed"
        },
        {
          "name": "direct_np20",
          "value": 3.3306690738754696e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_energy_drift",
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          "status": "passed"
        },
        {
          "name": "delta_dt",
          "value": 1.2369782774246385e-05,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_nq",
          "value": 5.551115123125783e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_q_bounds",
          "value": 9.195039184783926e-06,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_np16",
          "value": 6.106226635438361e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_np20",
          "value": 3.3306690738754696e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "cmd_energy_drift",
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          "threshold": 0.05,
          "status": "passed"
        },
        {
          "name": "cmd_dt",
          "value": 1.2369782774204752e-05,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "cmd_nq",
          "value": 3.552713678800501e-15,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "cmd_q_bounds",
          "value": 9.195039182618991e-06,
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          "status": "passed"
        },
        {
          "name": "cmd_np16",
          "value": 6.106226635438361e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "cmd_np20",
          "value": 4.440892098500626e-16,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "CMD_P_production_stricter",
          "value": 0.0,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "CMD_q_table_stricter",
          "value": 1.4988010832439613e-15,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "direct_refined_independent_force",
          "value": 2.1934761671893455e-05,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "direct_unseen_centroid_force",
          "value": 2.490196809645795e-06,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "delta_refined_independent_force",
          "value": 8.881784197001252e-16,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "delta_unseen_centroid_force",
          "value": 8.881784197001252e-16,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "CMD_independent_chain_range",
          "value": 0.0,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "exact_grid",
          "value": 1.1721179639471178e-13,
          "threshold": 1e-06,
          "status": "passed"
        },
        {
          "name": "exact_box",
          "value": 8.340858143052188e-10,
          "threshold": 1e-06,
          "status": "passed"
        },
        {
          "name": "direct_CMD_correlation",
          "value": 8.993245201316391e-08,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "direct_independent_force",
          "value": 2.1934761671893455e-05,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "delta_CMD_correlation",
          "value": 2.220446049250313e-16,
          "threshold": 0.01,
          "status": "passed"
        },
        {
          "name": "delta_independent_force",
          "value": 4.440892098500626e-16,
          "threshold": 0.01,
          "status": "passed"
        }
      ],
      "expected_curve_differences": {
        "cmd_exact": 1.799872261817881e-05,
        "direct_exact": 1.8084494170927945e-05,
        "delta_exact": 1.7998722618123297e-05
      },
      "optimizer": {
        "direct": {
          "optimizer_success": false,
          "optimizer_status": 0,
          "nfev": 2000,
          "max_nfev": 2000,
          "weighted_force_rmse": 4.782743679578855e-07
        },
        "delta": {
          "optimizer_success": true,
          "optimizer_status": 1,
          "nfev": 1,
          "max_nfev": 2000,
          "weighted_force_rmse": 1.0697320641185152e-16
        }
      },
      "optimizer_interpretation": "independent predictive checks assess the fixed-budget models; reaching the evaluation budget is not optimization convergence"
    },
    "quartic": {
      "beta": 2.0,
      "mass": 1.0,
      "ml": {
        "hidden_units": 12,
        "seed": 173,
        "max_nfev": 2000,
        "loss_weight": "inverse_quartic"
      },
      "dynamics": {
        "dt": 0.01,
        "dt_stricter": 0.005,
        "tmax": 8.0,
        "q_bounds": [
          -3.5,
          3.5
        ],
        "q_bounds_stricter": [
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          4.0
        ],
        "n_q": 64,
        "n_q_stricter": 96,
        "n_p": 12,
        "n_p_stricter": [
          16,
          20
        ]
      },
      "quantum": {
        "n_grid": 96,
        "n_grid_stricter": 128,
        "bounds": [
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          6.0
        ],
        "larger_bounds": [
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        "larger_n_grid": 128
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      "coefficients": [
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        0.1
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      "sampling": {
        "beads": {
          "diagnostic": 32,
          "production": 64,
          "stricter": 128
        },
        "nsteps_train": 2048,
        "nsteps_reference": 4096,
        "nchains": 4,
        "burnin": 0.25,
        "sample_stride": 1,
        "master_seed": 20261005,
        "reference_frequency": "local_curvature",
        "gates": {
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          "max_rhat": 1.05,
          "max_force_stderr": 0.005,
          "centroid_tolerance": 1e-11
        }
      },
      "force_loss": "sum normalized weights*(model force-label)^2, weights=1/(1+q^2)^2; same total-label normalization and initialization for both modes",
      "correlation_definition": "quantum position Kubo correlation; canonical q(0)q(t) counterpart for centroid dynamics",
      "validated_force_error_threshold": 0.01,
      "expected_checks": [
        {
          "name": "P_production_stricter_force",
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        },
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          "name": "direct_energy_drift",
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          "status": "passed"
        },
        {
          "name": "direct_dt",
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        },
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        },
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        },
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        },
        {
          "name": "direct_np20",
          "value": 1.3485091054477039e-05,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_energy_drift",
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          "status": "passed"
        },
        {
          "name": "delta_dt",
          "value": 1.2576975937324264e-05,
          "threshold": 0.0015,
          "status": "passed"
        },
        {
          "name": "delta_nq",
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        {
          "name": "CMD_q_table_stricter",
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          "name": "exact_grid",
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        {
          "name": "exact_box",
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        {
          "name": "direct_CMD_correlation",
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        },
        {
          "name": "direct_independent_force",
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        },
        {
          "name": "delta_CMD_correlation",
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        },
        {
          "name": "delta_independent_force",
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        "cmd_exact": 0.02874915001695555,
        "direct_exact": 0.028906390337310073,
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      "optimizer": {
        "direct": {
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          "optimizer_status": 0,
          "nfev": 2000,
          "max_nfev": 2000,
          "weighted_force_rmse": 0.0009846860057516687
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        "delta": {
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          "optimizer_status": 0,
          "nfev": 2000,
          "max_nfev": 2000,
          "weighted_force_rmse": 0.000988646266457102
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      },
      "optimizer_interpretation": "independent predictive checks assess the fixed-budget models; reaching the evaluation budget is not optimization convergence"
    }
  }
}