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    "shared_color_range": [
      -13.318787943322858,
      108.81952291594818
    ]
  },
  "limitations": "Uncertified FEM projections of sampled P1 targets. Finite projections disturb the trace identities; no tiling or aperiodicity claim survives by approximation alone. Neumann conditions are imposed weakly, not as pointwise zero derivatives of the P1 plots."
}