{
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    },
    {
      "definition": "rho(s)=first_window_mean+slope*(s-H/2)",
      "profile_id": "constant-mean-reference",
      "first_window_mean": {
        "numerator": 9,
        "denominator": 8
      },
      "initial_clock_rate": {
        "numerator": 9,
        "denominator": 8
      },
      "slope": {
        "numerator": 0,
        "denominator": 1
      },
      "observed_window_boundaries": [
        {
          "numerator": 0,
          "denominator": 1
        },
        {
          "numerator": 1,
          "denominator": 50331648
        },
        {
          "numerator": 1,
          "denominator": 25165824
        },
        {
          "numerator": 1,
          "denominator": 16777216
        },
        {
          "numerator": 1,
          "denominator": 8388608
        }
      ],
      "aperture_windows": [
        [
          {
            "numerator": 0,
            "denominator": 1
          },
          {
            "numerator": 1,
            "denominator": 50331648
          }
        ],
        [
          {
            "numerator": 1,
            "denominator": 50331648
          },
          {
            "numerator": 1,
            "denominator": 25165824
          }
        ],
        [
          {
            "numerator": 1,
            "denominator": 25165824
          },
          {
            "numerator": 1,
            "denominator": 16777216
          }
        ],
        [
          {
            "numerator": 1,
            "denominator": 16777216
          },
          {
            "numerator": 1,
            "denominator": 8388608
          }
        ]
      ],
      "sampled_rates": [
        {
          "numerator": 9,
          "denominator": 8
        },
        {
          "numerator": 9,
          "denominator": 8
        },
        {
          "numerator": 9,
          "denominator": 8
        },
        {
          "numerator": 9,
          "denominator": 8
        },
        {
          "numerator": 9,
          "denominator": 8
        }
      ],
      "global_rate_bounds": [
        {
          "numerator": 9,
          "denominator": 8
        },
        {
          "numerator": 9,
          "denominator": 8
        }
      ],
      "derivative_upper_bound": {
        "numerator": 0,
        "denominator": 1
      },
      "cumulative_structural_exposures": [
        {
          "numerator": 0,
          "denominator": 1
        },
        {
          "numerator": 3,
          "denominator": 134217728
        },
        {
          "numerator": 3,
          "denominator": 67108864
        },
        {
          "numerator": 9,
          "denominator": 134217728
        },
        {
          "numerator": 9,
          "denominator": 67108864
        }
      ],
      "structural_segment_durations": [
        {
          "numerator": 3,
          "denominator": 134217728
        },
        {
          "numerator": 3,
          "denominator": 134217728
        },
        {
          "numerator": 3,
          "denominator": 134217728
        },
        {
          "numerator": 9,
          "denominator": 134217728
        }
      ],
      "signed_averaged_exposure_differences": [
        {
          "numerator": 0,
          "denominator": 1
        },
        {
          "numerator": 0,
          "denominator": 1
        },
        {
          "numerator": 0,
          "denominator": 1
        },
        {
          "numerator": 0,
          "denominator": 1
        }
      ],
      "admitted": true,
      "first_window_mean_identity": true
    }
  ],
  "source_recipe": "A=4*pi-8*b; d=(2*pi-c)/8; zeta=(A-c)/2; D0=0,Dj=A+(j-1)*b; R0=zeta,Rj=zeta+c+(j-1)*d. Subtract full degree-weighted mean and add common phase plus centered residual. Form=common form+centered residual; mathematical pi outward enclosed. Same complete 36D source for every history.",
  "observation": {
    "aperture_windows": [
      [
        {
          "numerator": 0,
          "denominator": 1
        },
        {
          "numerator": 1,
          "denominator": 50331648
        }
      ],
      [
        {
          "numerator": 1,
          "denominator": 50331648
        },
        {
          "numerator": 1,
          "denominator": 25165824
        }
      ],
      [
        {
          "numerator": 1,
          "denominator": 25165824
        },
        {
          "numerator": 1,
          "denominator": 16777216
        }
      ],
      [
        {
          "numerator": 1,
          "denominator": 16777216
        },
        {
          "numerator": 1,
          "denominator": 8388608
        }
      ]
    ],
    "readout": "A_i=G*(1/width_i)*integral_Wi q^T*x(s)ds+O+eta_i",
    "sensor": "Same held gain, offset and four realized scalar errors in both actual histories and reference",
    "association": "Four normalized finite boxcar averages, not endpoint, midpoint or structural-exposure averages",
    "curvature_coefficients": [
      {
        "numerator": 9,
        "denominator": 4
      },
      {
        "numerator": -9,
        "denominator": 2
      },
      {
        "numerator": 9,
        "denominator": 4
      },
      {
        "numerator": 0,
        "denominator": 1
      }
    ],
    "contrast_pairs": [
      [
        1,
        0
      ],
      [
        3,
        2
      ]
    ],
    "numerical_band": "Shared validated full-state integral increments divided by exact observed window width; never inverse or leading-response target"
  },
  "numerics": {
    "actual_histories": 2,
    "reference_histories": 1,
    "producer_call_cap": 3,
    "windows_per_history": 4,
    "total_step_cap": 12,
    "steps_per_window": 1,
    "order": 4,
    "picard_iteration_cap": 16,
    "interval_bits": 128,
    "dimension": 38,
    "observed_window_starts": [
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 50331648
      },
      {
        "numerator": 1,
        "denominator": 25165824
      },
      {
        "numerator": 1,
        "denominator": 16777216
      }
    ],
    "observed_window_durations": [
      {
        "numerator": 1,
        "denominator": 50331648
      },
      {
        "numerator": 1,
        "denominator": 50331648
      },
      {
        "numerator": 1,
        "denominator": 50331648
      },
      {
        "numerator": 1,
        "denominator": 16777216
      }
    ],
    "phase_increments": [
      {
        "numerator": 1,
        "denominator": 4
      },
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 2
      }
    ],
    "max_recorded_average_halfwidth": {
      "numerator": 1,
      "denominator": 19807040628566084398385987584
    },
    "policy": "One new four-window producer call per history, each window one order 4 source-box Taylor step with order 5 whole-tube remainder. Carry all 38 including cumulative z. No time subdivision, clock reset, quadrature approximation, accumulator reset, retry or retuning. Global smooth domain separate from exact affine clock positivity."
  },
  "public_packet": {
    "schema": "tnfr.sine-aperture-public-inference.v1",
    "inverse_keys": [
      "bulk_angle_bounds",
      "receiver_short_angle_bounds",
      "form_radius",
      "phase_radius",
      "phase_increments",
      "probe_duration",
      "averaged_reading_bounds",
      "readout_error_bound",
      "readout_gain_bounds",
      "clock_rate_bounds",
      "clock_rate_derivative_bound"
    ],
    "worker": "build/aperture-inference-freeze/invert_public_packet.py",
    "scope": "Fresh process receives only11 public primitives and fixed controls via stdin. No hidden source, clock profile, rate/exposure, sensor realization, reference averages or producer report. Software information exclusion, not cryptographic blindness."
  },
  "controls": {
    "false_bulk_angle_bounds": [
      {
        "numerator": 11,
        "denominator": 8
      },
      {
        "numerator": 353,
        "denominator": 256
      }
    ],
    "false_gain_bounds": [
      {
        "numerator": 31,
        "denominator": 16
      },
      {
        "numerator": 2,
        "denominator": 1
      }
    ],
    "false_clock_bounds": [
      {
        "numerator": 25,
        "denominator": 32
      },
      {
        "numerator": 13,
        "denominator": 16
      }
    ],
    "equal_phase_increments": [
      {
        "numerator": 1,
        "denominator": 4
      },
      {
        "numerator": 1,
        "denominator": 4
      }
    ]
  },
  "thresholds": {
    "primary_actual_angle_width": {
      "numerator": 1,
      "denominator": 1024
    },
    "primary_effective_gain_width": {
      "numerator": 1,
      "denominator": 2048
    },
    "primary_gain_width": {
      "numerator": 1,
      "denominator": 16
    },
    "primary_mean_clock_width": {
      "numerator": 1,
      "denominator": 64
    }
  },
  "phase_blind_alternative": {
    "structural_rows": "x_tau=-A*x; theta_tau=gamma*A*x",
    "preparation": "Same complete source, actual clock, phase-only events and held finite-aperture sensor",
    "recorded_average_contrast_bound": "2*G_plus*X+2*delta for both declared average contrasts, using centered heat contraction and q dual norm1"
  },
  "prospective_separation": {
    "positive_minus_reference_signs": [
      1,
      1,
      1,
      -1
    ],
    "negative_minus_reference_signs": [
      -1,
      -1,
      -1,
      1
    ],
    "true_average_separation_lower_in_delta_units": [
      {
        "numerator": 200704,
        "denominator": 84375
      },
      {
        "numerator": 372736,
        "denominator": 84375
      },
      {
        "numerator": 200704,
        "denominator": 84375
      },
      {
        "numerator": 28672,
        "denominator": 1875
      }
    ],
    "true_negative_minus_positive_curvature_lower_in_delta_units": {
      "numerator": 229376,
      "denominator": 15625
    },
    "scope": "Prospective analytic strict lower bounds, not evaluated observations; same realized sensor errors cancel between histories"
  },
  "prediction": "Both actual primaries cover original nominal/actual angle,J=G*first-window-mean,G and mean clock with fixedstrict widths; false priors exclude, equal inputs abstain and heat contrasts exclude. Positive first three averages>reference>negative; positive last average<reference<negative. Every complete difference interval lies within its rebuilt clock transfer allowance. Composed C_positive<C_negative. H nodal 36 enclosures intersect before/after event as consistency only; clock and cumulativeintegral coordinates are not expected equal.",
  "stopping_rule": "Complete source/profile/sensor admission; fixed38D window certificates and complete handoffs; phase-only/passive events; observed-time integral increment normalization; numerical recorded average halfwidth<=delta/16; public-only hash; primary availability/coverage/strict widths; fixed false/equal/heat controls; all four signed transfers and whole difference containment; H nodal 36 overlap; paired composed curvature separation. Optional acute flags are not required. No physical or pointwise clock claim.",
  "first_attempt": "Exclusive attempt ledger before first flow; refuse existing ledger/result. Preserve completed prefix and first failure; stop later acquisition after incomplete history. No retries, overwrite or inverse on reference. At most 3 producer calls and12 reserved steps; unexpected exceptions retain known prefix and declared reserved budget without inventing an internal step count.",
  "runtime": {
    "python": "3.13.6 (tags/v3.13.6:4e66535, Aug  6 2025, 14:36:00) [MSC v.1944 64 bit (AMD64)]",
    "platform": "Windows",
    "seed": null,
    "backend": "Exact Fraction and shared outward dyadic128 Picard/Taylor",
    "seed_scope": "Explicit deterministic full source, sensor and clock recipes"
  },
  "scope": "Conditional finite software geometry/gain/mean-clock inference with substantial fixed apertures. No point-sensor replacement, actual profile reconstruction, empirical kernel calibration, source formation or unique physical law."
}