{
  "schema": "public-kernel-observation-contract-v1",
  "definitions": {
    "Z_normwise_criterion": "r_m=max(abs(Z_residual[m,0:65])); require r_m <= 1e-12*C_m with finite scale, residual and eta and C_m>=0",
    "Z_normwise_eta": "r_m/C_m when C_m>0; exactly 0 when C_m=0 and all residual bins are exactly 0; otherwise infinity and failure, never an epsilon substitution",
    "Z_residual_and_scale": "Z_ref - Z_sum, and original-pulse-order sum(abs(Z_i)); full complex residual and real scale saved",
    "Z_time_L1_scale": "C_m: original-pulse-order binary64 scalar sum of np.sum(np.abs(weighted_input), dtype=np.float64); weighted_input is the identical rounded observer_input*h buffer passed to each FFT",
    "auxiliary_values": "Center-band values outside search_membership_by_band are auxiliary only and cannot be interpreted as fixed-event measurements",
    "axes": {
      "G_region": [
        "region",
        "cell_i",
        "cell_j"
      ],
      "Z_ref_Z_sum_Z_residual_Z_scale": [
        "saved_center",
        "FFT_bin_0_through_64"
      ],
      "Z_sparse": [
        "sparse_cell_center_row",
        "FFT_bin_0_through_64"
      ],
      "Z_time_L1_scale_Z_residual_inf_Z_normwise_eta_Z_normwise_valid": [
        "saved_center"
      ],
      "center_power": [
        "saved_center",
        "band"
      ],
      "region_cross_terms": [
        "region",
        "pair"
      ],
      "region_self_terms": [
        "region",
        "cell"
      ]
    },
    "delta_definition": "SHAPE-PML, FULL-SHAPE, FULL-PML; delta_P_ref=delta_self_sum+delta_cross_sum+delta_power_residual, with floating balance residual retained",
    "failure_locations": "Boolean gate arrays retain every coordinate; false saved_power_valid values are failures only within search_membership_by_band",
    "gram": "G_ij = sum_k(a_k * Z_i * conjugate(Z_j)) / D over the fixed band",
    "kernel_alignment": "Native post-taper samples copied into float64 input [center-40,center+40) at their absolute sample positions",
    "legacy_Z_valid": "All old per-bin booleans, scales and residuals retained unchanged; false counts and coordinates reported with required=false",
    "new_scale_limitation": "Post-failure observation-contract revision, not an FFT theoretical error bound, interval proof, or weak-bin relative-accuracy guarantee; the coefficient remains 1e-12",
    "no_S_final_algebra_gate": "The captured complex64 S arrays are retained separately; no 1e-12 test of S_FULL=c**M*S_SHAPE is imposed",
    "observer": "h is the SHA-fixed float64[80] saved by prior condition-01, never regenerated; FFT length 128, Fs 16000, all 65 bins; internal weights 2 and DC/Nyquist 1; D=128*sum(h**2)",
    "pair_allocation": "No signed cross term allocated to either cell; no output-power percentage or signed-term dB conversion",
    "power_residual": "P_ref - (self_sum + cross_sum)",
    "power_scale": "P_ref + self_sum + abs_cross_sum",
    "region_abs_cross_sum": "Sum of absolute region-mean pair terms; center_mean_abs_cross_sum separately preserves mean center-wise absolute pair sum",
    "region_gram": "Unweighted arithmetic mean of each center Gram in the fixed region; no cell rows removed",
    "region_order": [
      {
        "band_index": 0,
        "kind": "early"
      },
      {
        "band_index": 0,
        "kind": "strong"
      },
      {
        "band_index": 0,
        "kind": "search"
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      {
        "band_index": 1,
        "kind": "early"
      },
      {
        "band_index": 1,
        "kind": "strong"
      },
      {
        "band_index": 1,
        "kind": "search"
      }
    ],
    "saved_power_comparison": "P_ref-P_saved; scale=abs(P_ref)+abs(P_saved); evaluated only at that band's saved search membership",
    "self_and_cross": "d_i=real(G_ii); q_ij=2*real(G_ij) only for original pulse-order i<j; all pairs including exact zeros retained",
    "sparse_order": "Cell-major, then saved-center order; cells are in original pulse order",
    "sparse_reconstruction": "Initialize dense (N, m, 65) complex128 zeros; assign Z_sparse at sparse_cell_center_index[:,0], sparse_cell_center_index[:,1]",
    "sparse_rule": "Keep every pair with a_i < center+40 and b_i > center-40 and a_i < b_i; all other Z are exact geometric zero",
    "variant_order": [
      "PML",
      "RAW_SHAPE",
      "RAW_FULL"
    ]
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        "case": "librispeech_1188-133604-0003",
        "crossing": "first_observer_center_at_or_above_threshold; no_interpolation",
        "region_membership": "left_closed_right_open"
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