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        {
          "numerator": 7,
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        {
          "numerator": 19,
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        {
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        {
          "numerator": 1,
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        {
          "numerator": 23,
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      ],
      "form_residual": [
        {
          "numerator": -163,
          "denominator": 90071992547409920
        },
        {
          "numerator": -143,
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        },
        {
          "numerator": -123,
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        },
        {
          "numerator": -103,
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        },
        {
          "numerator": -83,
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        },
        {
          "numerator": -63,
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        },
        {
          "numerator": -43,
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        {
          "numerator": -23,
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        {
          "numerator": -3,
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        },
        {
          "numerator": 17,
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        {
          "numerator": 37,
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        {
          "numerator": 57,
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        {
          "numerator": 77,
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        {
          "numerator": 97,
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        {
          "numerator": 117,
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        {
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        {
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        },
        {
          "numerator": 177,
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      ],
      "phase_residual": [
        {
          "numerator": -51,
          "denominator": 180143985094819840
        },
        {
          "numerator": -1,
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        },
        {
          "numerator": 49,
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        },
        {
          "numerator": 99,
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        },
        {
          "numerator": -81,
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        },
        {
          "numerator": -31,
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        },
        {
          "numerator": 19,
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        {
          "numerator": 69,
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        },
        {
          "numerator": -111,
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        },
        {
          "numerator": -61,
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        },
        {
          "numerator": -11,
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        },
        {
          "numerator": 39,
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        },
        {
          "numerator": 89,
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        },
        {
          "numerator": -91,
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        {
          "numerator": -41,
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        {
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        },
        {
          "numerator": 109,
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      ],
      "hidden_gain": {
        "numerator": 15,
        "denominator": 8
      },
      "hidden_offset": {
        "numerator": 7,
        "denominator": 11
      },
      "reading_errors": [
        {
          "numerator": 1,
          "denominator": 2305843009213693952
        },
        {
          "numerator": -1,
          "denominator": 2305843009213693952
        },
        {
          "numerator": 1,
          "denominator": 2305843009213693952
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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. Subtract the single full degree mean, add common_phase and centered phase residual; form=common_form+form_residual. Mathematical pi outward enclosed; supplied source, no equilibrium or acquisition premise.",
  "observation": {
    "readout": "r_j=G*(x4(j*h)-x5(j*h))+O+eta_j, j=0,1,2",
    "sensor": "G and O fixed within each trajectory; broad supplied gain prior only, no separate calibration",
    "middle": "one middle recorded interval and one error reused in both differences; form continuous at second phase event",
    "numerical_band": "Three full-law reading intervals, never leading-response formula or chosen midpoint",
    "history": "All36 first endpoint interval pairs initialize second full flow; common means and phase drift retained without reset"
  },
  "numerics": {
    "steps_per_window": 1,
    "windows": 2,
    "order": 4,
    "picard_iteration_cap": 16,
    "interval_bits": 128,
    "dimension": 36,
    "max_recorded_reading_halfwidth": {
      "numerator": 1,
      "denominator": 1152921504606846976
    },
    "window_starts": [
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 2097152
      }
    ],
    "reading_times": [
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 2097152
      },
      {
        "numerator": 1,
        "denominator": 1048576
      }
    ],
    "policy": "Local solver time starts0 in each window; absolute starts retained separately. No retry, split, tuning or reduction; full-box jets and whole-tube order5 remainder."
  },
  "public_packet": {
    "schema": "tnfr.sine-two-pulse-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"
    ],
    "worker": "build/two-pulse-inference-freeze/invert_public_packet.py",
    "scope": "Fresh process receives only public primitives and fixed controls through stdin; software information exclusion, not cryptographic blindness or independent execution authentication"
  },
  "controls": {
    "false_bulk_angle_bounds": [
      {
        "numerator": 11,
        "denominator": 8
      },
      {
        "numerator": 353,
        "denominator": 256
      }
    ],
    "false_gain_bounds": [
      {
        "numerator": 31,
        "denominator": 16
      },
      {
        "numerator": 2,
        "denominator": 1
      }
    ],
    "equal_phase_increments": [
      {
        "numerator": 1,
        "denominator": 4
      },
      {
        "numerator": 1,
        "denominator": 4
      }
    ]
  },
  "thresholds": {
    "primary_actual_angle_width": {
      "numerator": 1,
      "denominator": 1024
    },
    "primary_gain_width": {
      "numerator": 1,
      "denominator": 1024
    }
  },
  "phase_blind_alternative": {
    "rows": "x'=-A*x; theta'=gamma*A*x",
    "preparation": "same complete source, support, capacity, clock, both phase events and held observation model",
    "recorded_increment_bound": "2*gain_upper*h*X+2*readout_error for each window",
    "scope": "Heat contraction retains original centered form bound through both windows; excludes only this declared alternative"
  },
  "prediction": "All three primary marginal intervals cover original nominal angle, actual pre-probe arc mean and held gain; actual-angle and gain widths<1/1024. Both false priors incompatible; equal amplitudes unavailable through rank; both recorded increments exclude declared phase-blind alternative.",
  "stopping_rule": "All source norms/priors/errors; two strict36D complete horizons; exact full endpoint handoff and phase-only jumps; same middle readout; all reading halfwidths<=delta; public packet hash; primary/rank availability; original nominal/actual angle and gain coverage; strict requested widths; false-angle and false-gain exclusion; equal-amplitude rank abstention; both heat exclusions. Preserve first failure or unavailability without changing protocol or rerunning responses. Whole-window acuteness is optional and is not a stopping criterion.",
  "runtime": {
    "python": "3.13.6 (tags/v3.13.6:4e66535, Aug  6 2025, 14:36:00) [MSC v.1944 64 bit (AMD64)]",
    "platform": "Windows",
    "backend": "exact Fraction and shared outward dyadic128 Picard/Taylor intervals",
    "seed": null,
    "seed_scope": "fully specified deterministic source and error realizations"
  },
  "scope": "Finite conditional software evidence under supplied law, clock, preparation and held affine sensor. Necessary outer marginals, not joint realizability, physical calibration, full-state reconstruction, source formation, maintenance or unique law selection."
}