{
  "model_version": "0.3-candidate-revision-1",
  "status": "Computational verification; no material fit, measured validation or novelty claim.",
  "parameters": {
    "L": 1.0,
    "alpha": 0.1,
    "beta": 1.5,
    "tau": 15.0,
    "zeta": 0.12
  },
  "writing_laws": {
    "drive": "alpha*u^2*(1-m)-m/tau",
    "strain": "alpha*q^2*(1-m)-m/tau",
    "dissipation": "alpha*c*p^2*(1-m)-m/tau"
  },
  "damping_laws": {
    "ratio": "c=2*zeta*sqrt(k)",
    "coefficient": "c=2*zeta/L"
  },
  "rest_caveat": "State-written variants can keep writing during mechanical ring-down even when u=0. Their rest law is not generally pure exponential decay.",
  "manufactured_solution": [
    {
      "writing": "drive",
      "damping": "ratio",
      "near_boundary": false,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 4.4606086397624284e-05,
          "observed_order": null
        },
        {
          "dt": 0.1,
          "max_state_error": 2.604476584136539e-06,
          "observed_order": 4.098175204453859
        },
        {
          "dt": 0.05,
          "max_state_error": 1.6496530985676827e-07,
          "observed_order": 3.9807588856828304
        },
        {
          "dt": 0.025,
          "max_state_error": 1.0440895037433506e-08,
          "observed_order": 3.9818453794181865
        }
      ]
    },
    {
      "writing": "drive",
      "damping": "coefficient",
      "near_boundary": false,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 4.758355935536793e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 2.799198276098175e-06,
          "observed_order": 4.087377606264367
        },
        {
          "dt": 0.05,
          "max_state_error": 1.6921362396005168e-07,
          "observed_order": 4.048096046704482
        },
        {
          "dt": 0.025,
          "max_state_error": 1.0396808487050935e-08,
          "observed_order": 4.024633092685144
        }
      ]
    },
    {
      "writing": "strain",
      "damping": "ratio",
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      "rows": [
        {
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          "max_state_error": 4.773653026494615e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 2.793686427023795e-06,
          "observed_order": 4.094851705887358
        },
        {
          "dt": 0.05,
          "max_state_error": 1.6894169078268684e-07,
          "observed_order": 4.04757279684103
        },
        {
          "dt": 0.025,
          "max_state_error": 1.052899700759724e-08,
          "observed_order": 4.004085477954181
        }
      ]
    },
    {
      "writing": "strain",
      "damping": "coefficient",
      "near_boundary": false,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 5.0723355855302604e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 3.006703124818627e-06,
          "observed_order": 4.076395865728174
        },
        {
          "dt": 0.05,
          "max_state_error": 1.8212743560855338e-07,
          "observed_order": 4.045162255605734
        },
        {
          "dt": 0.025,
          "max_state_error": 1.1195640029632026e-08,
          "observed_order": 4.023939354424322
        }
      ]
    },
    {
      "writing": "dissipation",
      "damping": "ratio",
      "near_boundary": false,
      "rows": [
        {
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          "max_state_error": 4.544744667068709e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 2.657772879999243e-06,
          "observed_order": 4.095909513697043
        },
        {
          "dt": 0.05,
          "max_state_error": 1.679919970909438e-07,
          "observed_order": 3.983753412631839
        },
        {
          "dt": 0.025,
          "max_state_error": 1.0629429225694764e-08,
          "observed_order": 3.9822564717490763
        }
      ]
    },
    {
      "writing": "dissipation",
      "damping": "coefficient",
      "near_boundary": false,
      "rows": [
        {
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          "max_state_error": 4.8240274763227536e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 2.8377172985281918e-06,
          "observed_order": 4.087435348167548
        },
        {
          "dt": 0.05,
          "max_state_error": 1.716240586174811e-07,
          "observed_order": 4.047407159054108
        },
        {
          "dt": 0.025,
          "max_state_error": 1.0546060108529431e-08,
          "observed_order": 4.0244757772261615
        }
      ]
    }
  ],
  "comparisons": [
    {
      "writing": "drive",
      "damping": "ratio",
      "dt": 0.01,
      "probe_entry_q_p_m": [
        0.0721352136329491,
        -0.07594605131144651,
        0.1109155396513032
      ],
      "probe_rms": 0.873555668883637,
      "max_abs_energy_residual": 9.263585898366955e-09,
      "final_state": [
        -0.898949012897435,
        -1.3008528400570825,
        0.2066235965161772
      ],
      "fine_energy_residual": 5.882670461865303e-10,
      "fine_probe_rms": 0.8735553888938039,
      "probe_rms_refinement_difference": 2.7998983309629466e-07,
      "rms_difference_from_no_memory": 0.1710399820486349
    },
    {
      "writing": "drive",
      "damping": "coefficient",
      "dt": 0.01,
      "probe_entry_q_p_m": [
        0.09459205681103462,
        -0.12085870557433975,
        0.1109155396513032
      ],
      "probe_rms": 0.9348820199737993,
      "max_abs_energy_residual": 9.18153386653131e-09,
      "final_state": [
        -0.9034508080671805,
        -1.4942707537411233,
        0.2066235965161772
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      "fine_energy_residual": 5.848352913062627e-10,
      "fine_probe_rms": 0.9348817168647787,
      "probe_rms_refinement_difference": 3.0310902054964117e-07,
      "rms_difference_from_no_memory": 0.23236631001960972
    },
    {
      "writing": "strain",
      "damping": "ratio",
      "dt": 0.01,
      "probe_entry_q_p_m": [
        -0.05225612545958028,
        -0.04752717424400836,
        0.18719113005892105
      ],
      "probe_rms": 0.8951625626766607,
      "max_abs_energy_residual": 7.516199662660483e-09,
      "final_state": [
        -1.1800670366678643,
        0.7021646252178759,
        0.5860743157543258
      ],
      "fine_energy_residual": 4.832039213198414e-10,
      "fine_probe_rms": 0.8951627557283435,
      "probe_rms_refinement_difference": 1.930516827508555e-07,
      "rms_difference_from_no_memory": 0.19264734888317447
    },
    {
      "writing": "strain",
      "damping": "coefficient",
      "dt": 0.01,
      "probe_entry_q_p_m": [
        -0.12994764114074558,
        0.01043037486695356,
        0.21698768057456969
      ],
      "probe_rms": 1.0290481111320329,
      "max_abs_energy_residual": 6.56732712656094e-09,
      "final_state": [
        -0.8932021692061397,
        1.3337424989669717,
        0.6485689423884466
      ],
      "fine_energy_residual": 4.310356516157299e-10,
      "fine_probe_rms": 1.0290483512992186,
      "probe_rms_refinement_difference": 2.4016718569441764e-07,
      "rms_difference_from_no_memory": 0.32653294445404957
    },
    {
      "writing": "dissipation",
      "damping": "ratio",
      "dt": 0.01,
      "probe_entry_q_p_m": [
        0.06856462909931343,
        -0.0873735342796733,
        0.1335532396718413
      ],
      "probe_rms": 0.8795260116464704,
      "max_abs_energy_residual": 1.1350696119127868e-08,
      "final_state": [
        -1.4102792285545378,
        -0.541474144283482,
        0.40173183966781345
      ],
      "fine_energy_residual": 7.206566732254061e-10,
      "fine_probe_rms": 0.8795258294506212,
      "probe_rms_refinement_difference": 1.821958491854403e-07,
      "rms_difference_from_no_memory": 0.1770104226054522
    },
    {
      "writing": "dissipation",
      "damping": "coefficient",
      "dt": 0.01,
      "probe_entry_q_p_m": [
        0.1165179158322562,
        -0.12299325498816803,
        0.13242049676757006
      ],
      "probe_rms": 0.9621876390188794,
      "max_abs_energy_residual": 1.144615233150681e-08,
      "final_state": [
        -1.6477983732867851,
        -0.7058972152579621,
        0.41437659065510357
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      "fine_energy_residual": 7.289903541929377e-10,
      "fine_probe_rms": 0.9621873842978363,
      "probe_rms_refinement_difference": 2.5472104303592147e-07,
      "rms_difference_from_no_memory": 0.25967197745266735
    }
  ],
  "relaxation_family": {
    "max_abs_rhs_difference": 5.551115123125783e-17,
    "rate": 0.3556666666666667,
    "target": 0.8125585754451734,
    "caveat": "Embedding in a generic relaxation family; not equality to all voltage-dependent CALM circuits or experimental fits."
  },
  "matched_history": {
    "histories": [
      {
        "amplitude": 1.0,
        "duration": 0.7231171515224715,
        "terminal_m": 0.30000000000000004
      },
      {
        "amplitude": 2.0,
        "duration": 0.17893939348394008,
        "terminal_m": 0.3
      }
    ],
    "scope": "Equal terminal scalar states. Equal q and p and identical future input must also be imposed to obtain equal oscillator readouts. Any mechanical reset is an intervention with an unaccounted implementation cost."
  },
  "primary_candidate": {
    "id": "M03-D",
    "writing": "dissipation",
    "damping": "coefficient",
    "reason": "Fixed research choice for prospective comparisons, not selected by largest RMS or a measured fit."
  },
  "near_boundary_manufactured_solution": [
    {
      "writing": "drive",
      "damping": "ratio",
      "near_boundary": true,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 7.350641473885533e-05,
          "observed_order": null
        },
        {
          "dt": 0.1,
          "max_state_error": 4.408760597707229e-06,
          "observed_order": 4.05942511248656
        },
        {
          "dt": 0.05,
          "max_state_error": 2.8005452468171654e-07,
          "observed_order": 3.976593496192973
        },
        {
          "dt": 0.025,
          "max_state_error": 1.7625013004618495e-08,
          "observed_order": 3.990011510159813
        }
      ]
    },
    {
      "writing": "drive",
      "damping": "coefficient",
      "near_boundary": true,
      "rows": [
        {
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          "max_state_error": 8.159248894960489e-05,
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        },
        {
          "dt": 0.1,
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          "observed_order": 4.096565946366211
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          "observed_order": 4.052268824262604
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          "observed_order": 4.005779552750796
        }
      ]
    },
    {
      "writing": "strain",
      "damping": "ratio",
      "near_boundary": true,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 7.385435975743038e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 4.415148842973338e-06,
          "observed_order": 4.064149108650908
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          "observed_order": 3.976383938023661
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        {
          "dt": 0.025,
          "max_state_error": 1.7654334993899568e-08,
          "observed_order": 3.9899118479375524
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      ]
    },
    {
      "writing": "strain",
      "damping": "coefficient",
      "near_boundary": true,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 8.208052181702882e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 4.797129722816651e-06,
          "observed_order": 4.09679654454566
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          "observed_order": 4.011388943737368
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      ]
    },
    {
      "writing": "dissipation",
      "damping": "ratio",
      "near_boundary": true,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 7.379001338525537e-05,
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        },
        {
          "dt": 0.1,
          "max_state_error": 4.4141939727904145e-06,
          "observed_order": 4.063203645180066
        },
        {
          "dt": 0.05,
          "max_state_error": 2.804227393626846e-07,
          "observed_order": 3.9764747805721186
        },
        {
          "dt": 0.025,
          "max_state_error": 1.7648847272511148e-08,
          "observed_order": 3.9899574790002235
        }
      ]
    },
    {
      "writing": "dissipation",
      "damping": "coefficient",
      "near_boundary": true,
      "rows": [
        {
          "dt": 0.2,
          "max_state_error": 8.184170180356928e-05,
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        },
        {
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          "observed_order": 4.0963296865407575
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          "observed_order": 4.052189888569361
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        {
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          "max_state_error": 1.790788539679511e-08,
          "observed_order": 4.009505863402157
        }
      ]
    }
  ],
  "scalar_saturation_check": {
    "alpha": 2.0,
    "drive": 4.0,
    "tau": 20.0,
    "equilibrium_m": 0.9984399375975039,
    "runs": [
      {
        "initial_m": 0.0,
        "runs": [
          {
            "dt": 0.02,
            "max_abs_error": 0.0008564951351262007,
            "minimum_m": 0.0,
            "maximum_m": 0.998439937597491,
            "final_m": 0.998439937597491
          },
          {
            "dt": 0.01,
            "max_abs_error": 4.219602839605763e-05,
            "minimum_m": 0.0,
            "maximum_m": 0.9984399375974918,
            "final_m": 0.9984399375974918
          },
          {
            "dt": 0.005,
            "max_abs_error": 2.3057656231006973e-06,
            "minimum_m": 0.0,
            "maximum_m": 0.9984399375974919,
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          },
          {
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            "max_abs_error": 1.3477639171366462e-07,
            "minimum_m": 0.0,
            "maximum_m": 0.9984399375974919,
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          }
        ]
      },
      {
        "initial_m": 1.0,
        "runs": [
          {
            "dt": 0.02,
            "max_abs_error": 1.3382736486766689e-06,
            "minimum_m": 0.9984399375975039,
            "maximum_m": 1.0,
            "final_m": 0.9984399375975039
          },
          {
            "dt": 0.01,
            "max_abs_error": 6.593129442400425e-08,
            "minimum_m": 0.998439937597504,
            "maximum_m": 1.0,
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          },
          {
            "dt": 0.005,
            "max_abs_error": 3.6027587579923193e-09,
            "minimum_m": 0.9984399375975042,
            "maximum_m": 1.0,
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          },
          {
            "dt": 0.0025,
            "max_abs_error": 2.1058810251162186e-10,
            "minimum_m": 0.9984399375975046,
            "maximum_m": 1.0,
            "final_m": 0.9984399375975046
          }
        ]
      }
    ],
    "boundary_derivatives": {
      "at_m0": 32.0,
      "at_m1": -0.05
    },
    "scope": "Scalar constant-drive law only; no clipping, no added forcing, not a full coupled-material saturation validation."
  },
  "no_memory_baseline": {
    "writing": "drive",
    "damping": "coefficient",
    "dt": 0.005,
    "probe_entry_q_p_m": [
      -0.3472793649505882,
      -0.10608233130285884,
      0.0
    ],
    "probe_rms": 0.702515406845169,
    "max_abs_energy_residual": 7.455582817783579e-10,
    "final_state": [
      -0.29597219289308896,
      -1.1229374982936136,
      0.0
    ],
    "definition": "alpha=0, initially m=0; otherwise same parameters, drive and initial mechanics."
  }
}