{
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      "raw_phase_residual": [
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      "form_residual": [
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          "numerator": -163,
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          "numerator": -143,
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      "phase_residual": [
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        {
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          "numerator": -41,
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        {
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      ],
      "hidden_gain": {
        "numerator": 7,
        "denominator": 4
      },
      "hidden_clock_rate": {
        "numerator": 7,
        "denominator": 8
      },
      "hidden_offset": {
        "numerator": 7,
        "denominator": 11
      },
      "reading_errors": [
        {
          "numerator": 1,
          "denominator": 2475880078570760549798248448
        },
        {
          "numerator": -1,
          "denominator": 2475880078570760549798248448
        },
        {
          "numerator": 1,
          "denominator": 2475880078570760549798248448
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        {
          "numerator": 1,
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      ]
    }
  ],
  "source_recipe": "s=4*pi-8*b; d=(2*pi-c)/8; zeta=(s-c)/2; D0=0,Dj=s+(j-1)*b; R0=zeta,Rj=zeta+c+(j-1)*d. Remove one full M-weighted mean, add common phase and centered residual; form=common form+centered residual. Mathematical pi outward enclosed. All36 coordinates retained.",
  "observation": {
    "times": [
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 33554432
      },
      {
        "numerator": 1,
        "denominator": 16777216
      },
      {
        "numerator": 1,
        "denominator": 8388608
      }
    ],
    "readout": "r_i=G*q^T*x(s_i)+O+eta_i",
    "sensor": "One held positive gain and offset per complete history, with four declared bounded errors",
    "association": "Single intervals at0,H/2,H,2H; clock child consumes0,2,3, curvature consumes0,1,2",
    "curvature_coefficients": [
      1,
      -2,
      1,
      0
    ],
    "numerical_band": "Independent full-law endpoint enclosures, never inverse or leading-response targets"
  },
  "numerics": {
    "segments": 3,
    "steps_per_segment": 1,
    "order": 4,
    "picard_iteration_cap": 16,
    "interval_bits": 128,
    "dimension": 36,
    "observed_segment_starts": [
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 33554432
      },
      {
        "numerator": 1,
        "denominator": 16777216
      }
    ],
    "observed_segment_durations": [
      {
        "numerator": 1,
        "denominator": 33554432
      },
      {
        "numerator": 1,
        "denominator": 33554432
      },
      {
        "numerator": 1,
        "denominator": 16777216
      }
    ],
    "phase_increments": [
      {
        "numerator": 1,
        "denominator": 4
      },
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 2
      }
    ],
    "max_recorded_reading_halfwidth": {
      "numerator": 1,
      "denominator": 1237940039285380274899124224
    },
    "policy": "Multiply each duration by hidden rho for the shared structural-time solver. Three fixed source-box order4 steps with whole-tube order5 remainder. All36 endpoint bounds carried unchanged; no midpoint reset, artificial kick, retry, subdivision or budget adaptation."
  },
  "public_packet": {
    "schema": "tnfr.sine-curvature-public-inference.v1",
    "inverse_keys": [
      "bulk_angle_bounds",
      "receiver_short_angle_bounds",
      "form_radius",
      "phase_radius",
      "phase_increments",
      "probe_duration",
      "recorded_reading_bounds",
      "readout_error_bound",
      "readout_gain_bounds",
      "clock_rate_bounds"
    ],
    "worker": "build/curvature-inference-freeze/invert_public_packet.py",
    "scope": "Fresh process receives only10 public primitives and fixed controls through stdin; no hidden source, rate, gain, errors or producer report. Software 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_clock_width": {
      "numerator": 1,
      "denominator": 80
    }
  },
  "phase_blind_alternative": {
    "structural_rows": "x_tau=-A*x; theta_tau=gamma*A*x",
    "preparation": "Same original complete source, both events, held clock/sensor and priors",
    "recorded_increment_bound": "2*G_plus*rho_plus*H*X+2*delta for each complete observed window",
    "scope": "Heat contraction preserves original centered form norm; no alternative trajectory reset"
  },
  "prediction": "Each primary contains original nominal/actual angle, J, G and rho at declared strict widths. False angle excluded; false gain and clock excluded by curvature while their coarse clock reports remain available. Equal-input rank abstention. Both increments exclude phase-blind law. First two identical-source/equal-J cases have disjoint recorded finite-curvature intervals.",
  "stopping_rule": "All full source/sensor priors, original actual-angle association,3 complete36D strict Picard steps,2 exact endpoint handoffs,no event atH/2,phase-only events at0,H,one held sensor with shared readings,halfwidth<=delta,public-only packet hash,primary certificates/coverage/widths,all fixed inverse controls,2 heat exclusions percase and paired-source/effective-scale identity with finite-curvature separation. Optional whole-window acuteness is not required. No retuning on failure.",
  "first_attempt": "Exclusive attempt ledger precedes first flow; any existing ledger forbids another run. Preserve partial responses and first verdict, including exception/unavailability; no retry or overwritten attempt.",
  "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 source and error realizations"
  },
  "scope": "Finite software constraints under supplied complete law/source and held sensor/clock. No physical calibration, full uncertain-state identification, unique law, autonomous formation or maintenance claim."
}