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          "knot_values_as_coefficients": {
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        },
        {
          "source_knots": 64,
          "target_knots": 24,
          "direction": "coarsen",
          "batch": 32,
          "compiled_solve_seconds": 1.5584053471684456e-05,
          "exact_cross_gram": {
            "median_relative_l2": 0.02584229519211252,
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            "worst_integral_drift": 9.71445146547012e-17
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          "coefficient_interpolation": {
            "median_relative_l2": 0.05183511594632412,
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          "knot_values_as_coefficients": {
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        {
          "source_knots": 64,
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          "compiled_solve_seconds": 1.4874967746436596e-05,
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          "coefficient_interpolation": {
            "median_relative_l2": 0.08466504103402438,
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      "nested_refine_coefficient_roundtrip_relative_error": 1.1840502680382411e-15,
      "conclusions": {
        "nested_refinement_exact": true,
        "projection_never_worse_than_controls": true,
        "interpretation": "Cross-Gram projection is an exact, deterministic grid-update primitive; it removes function drift for nested refinement and is L2-optimal for coarsening or nonnested transfer."
      }
    }
  },
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        "sampled_refit_relative_error": 2.5927250036716308e-15,
        "projection_orthogonality": 1.67674463101405e-16
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        "sampled_refit_relative_error": 4.692096199310518e-15,
        "projection_orthogonality": 1.8499173682619173e-16
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    "new_training": false,
    "archived_sources": {
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