{
  "model": {
    "latent_dimension": 5,
    "generator": "fixed real skew-symmetric",
    "observation": "linear passive projection plus optional linear exposure",
    "maximum_positive_frequencies": 2
  },
  "reference": {
    "source": "NIST Handbook of Basic Atomic Spectroscopic Data, H I strong lines",
    "medium": "air wavelengths for visible Balmer lines",
    "selection": "strongest listed component for each displayed feature",
    "lines": [
      {
        "label": "H-delta",
        "upper_n": 6,
        "lower_n": 2,
        "wavelength_nm_air": 410.174,
        "relative_intensity": 15
      },
      {
        "label": "H-gamma",
        "upper_n": 5,
        "lower_n": 2,
        "wavelength_nm_air": 434.0462,
        "relative_intensity": 30
      },
      {
        "label": "H-beta",
        "upper_n": 4,
        "lower_n": 2,
        "wavelength_nm_air": 486.13615,
        "relative_intensity": 60
      },
      {
        "label": "H-alpha",
        "upper_n": 3,
        "lower_n": 2,
        "wavelength_nm_air": 656.28518,
        "relative_intensity": 180
      }
    ]
  },
  "written_result": {
    "distinct_reference_features": 4,
    "linear_model_capacity": 2,
    "capacity_deficit": 2,
    "gate_passed": false,
    "exposure_statement": "Linear exposure can attenuate or erase modes but cannot add spectral lines."
  },
  "bounded_calibrations": {
    "locked_1_to_1": {
      "ratio": 1.0,
      "scale_nm": 656.28518,
      "predicted_nm": [
        656.28518,
        656.28518
      ],
      "matched_count": 1,
      "observed_count": 4,
      "tolerance_fraction": 0.01,
      "nearest_relative_errors": [
        0.0,
        0.0
      ],
      "sum_nearest_relative_error": 0.0
    },
    "quasiperiodic_1_to_sqrt2": {
      "ratio": 1.4142135623730951,
      "scale_nm": 656.28518,
      "predicted_nm": [
        464.0637011702339,
        656.28518
      ],
      "matched_count": 1,
      "observed_count": 4,
      "tolerance_fraction": 0.01,
      "nearest_relative_errors": [
        0.045403841762777924,
        0.0
      ],
      "sum_nearest_relative_error": 0.045403841762777924
    },
    "resonant_2_to_3": {
      "ratio": 1.5,
      "scale_nm": 651.0693,
      "predicted_nm": [
        434.0462,
        651.0693
      ],
      "matched_count": 2,
      "observed_count": 4,
      "tolerance_fraction": 0.01,
      "nearest_relative_errors": [
        0.0,
        0.00794758156812252
      ],
      "sum_nearest_relative_error": 0.00794758156812252
    }
  },
  "free_two_frequency_fit": {
    "fitted_nm": [
      410.174,
      656.28518
    ],
    "exactly_matched": 2,
    "unmatched": 2,
    "reason": "A fixed linear five-coordinate skew model has at most two distinct positive frequencies; four resolved Balmer features cannot all be its linear temporal spectrum."
  },
  "claim_ceiling": "Written linear-algebra obstruction plus finite reference-data comparison; not evidence against every higher-dimensional model and not evidence for a physical fifth dimension.",
  "next_model_classes": [
    "state transitions with a validated energy operator",
    "nonlinear observation producing declared combination frequencies",
    "time-varying or interacting generators",
    "higher-dimensional linear state"
  ]
}