{
  "schema": "tnfr.sine-reduced-class-ports-protocol.v1",
  "evaluation_kind": "conditional_analytic_reduced_model_transfer_no_trajectory",
  "inputs": {
    "formation_time": {
      "numerator": 100,
      "denominator": 1
    },
    "relaxation_duration": {
      "numerator": 10000000000000,
      "denominator": 1
    },
    "phase_origin_difference": {
      "numerator": 1,
      "denominator": 1000
    },
    "contact_duration": {
      "numerator": 1,
      "denominator": 100
    },
    "form_error_bound": {
      "numerator": 1,
      "denominator": 10000000000
    },
    "phase_error_bound": {
      "numerator": 1,
      "denominator": 10000000000
    },
    "endpoint_radius": {
      "numerator": 1,
      "denominator": 100000000000000000000000000000000
    },
    "readout_error_bound": {
      "numerator": 1,
      "denominator": 1000000000000000000000000000000
    },
    "radius": {
      "numerator": 1,
      "denominator": 12
    },
    "work_allowance": {
      "numerator": 1,
      "denominator": 1000000
    },
    "decay_power": 512,
    "error_fraction": {
      "numerator": 1,
      "denominator": 4
    }
  },
  "complete_model": "Normalized-sine law with e=1023/1024, w=1/1024, beta=1, held capacities one. tau=e*t; both rows transform. No forcing or phase probes.",
  "preparation": "Original C9 nominal forms k*(2046/9)*(355/113)^2*(j-4), initially phase-flat; donor k=1 or 2, held-out receiver k=2. Each original form/phase residual is bounded by 1e-10 with separate exact zero sums. Receiver common phase origin 1/1000 is declared from initial preparation; donor origin 0. Form origins 0. Both original sixteen-dimensional relative families remain admitted.",
  "support": {
    "nodes": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17
    ],
    "edges": [
      [
        0,
        1
      ],
      [
        0,
        8
      ],
      [
        1,
        2
      ],
      [
        2,
        3
      ],
      [
        3,
        4
      ],
      [
        4,
        5
      ],
      [
        4,
        13
      ],
      [
        5,
        6
      ],
      [
        6,
        7
      ],
      [
        7,
        8
      ],
      [
        9,
        10
      ],
      [
        9,
        17
      ],
      [
        10,
        11
      ],
      [
        11,
        12
      ],
      [
        12,
        13
      ],
      [
        13,
        14
      ],
      [
        14,
        15
      ],
      [
        15,
        16
      ],
      [
        16,
        17
      ]
    ],
    "bridge": [
      4,
      13
    ],
    "weights": "unit",
    "capacity": "held one at every node"
  },
  "schedule": "Acquire at tau=100, continue both isolated actual flows unprobed for D=10^13, attach one unit bridge at tau_c=100+D with no state reset, then hold support. No further events.",
  "observation": "Actual held-out receiver class-two form at global node 13 at tau_c+1/100; donor-two minus donor-one contrast. Independent additive readout error <=1e-30 in each record.",
  "retained_reduction": {
    "orbits": [
      [
        4
      ],
      [
        3,
        5
      ],
      [
        2,
        6
      ],
      [
        1,
        7
      ],
      [
        0,
        8
      ]
    ],
    "full_state_coordinates": 36,
    "reduced_state_coordinates": 20,
    "component_state": "Five signed forms and five real target-phase deviations, retaining both component origins; common form and phase origins are not quotiented.",
    "component_parameters": "Class index k in {1,2}; internal cosine cos(2*pi*k/9), gamma=1/(1023*pi), internal C9 mobility with the actual degree-three port. Parameters are derived independently of recipient responses and unchanged between recipient classes.",
    "composition": "Exact nonlinear sine of the relative port phases and linear port form exchange; internal sine field alone is linearized about the formed twist.",
    "discarded_information": "Four reflection-odd modes per channel per component are omitted from retained state. Their initial uncertainty and nonlinear generation are covered by explicit full-space error estimates; no exact invariant nonlinear quotient is claimed."
  },
  "prediction": {
    "recorded_class_two_minus_one_lower_threshold": {
      "numerator": 1,
      "denominator": 10000000000000000000000000
    },
    "fraction_of_certified_full_gap": {
      "numerator": 1,
      "denominator": 4
    },
    "error_criterion": "Total prediction error E must be strictly less than one quarter of the final outward recorded_contrast_bounds.lo, itself positive. This interval is built from the interval enclosure of the exact leading expression P plus [-E,E]. E includes semigroup tail, reduced nonlinear finite-response remainder, twice the lifted surrogate/full discrepancy, actual-source uncertainty and both readout errors. A positive exact fractional margin whose outward lower endpoint is zero does not certify.",
    "both_windings_retained_all_future": true,
    "recovery_modulo_actual_postevent_means": true,
    "contact_work_allowance": {
      "numerator": 1,
      "denominator": 1000000
    }
  },
  "controls": [
    "Exact projection and lift identify five reflection-even spatial modes; the odd internal nonlinear residual is retained in the error proof.",
    "The unchanged component matrices support recipient classes one and two; per-case response derivatives retain receiver-class dependence.",
    "The reduced-matrix fourth contrast coefficient is derived directly; lower donor contrasts vanish under a shared recipient.",
    "Zero phase offset and disconnected controls retain their separate scope; no contact or hidden-state selection law is inferred."
  ],
  "method": {
    "name": "reflection_even_ports_exact_bridge_correlated_interval_v1",
    "isolated_handoff": "2^-512 only if512<=kappa*D<=4096",
    "joined_identity": "Full original eighteen-node law, gap >=2/81, cosine >=1/20, radius1/12; no surrogate storage substitution.",
    "finite_response": "Derivatives through fourth order from the reduced matrices, common-semigroup tail and full nonlinear bridge remainder.",
    "ideal_surrogate_to_full_per_case": "8*gamma^5*sin(phi)^2*h^5 / (45*(1-3*h)) upper bound, using upper absolute sine and gamma bounds.",
    "actual_preparation_contrast_error": "2*epsilon/(1-3*h)",
    "interval_method": "rational_outward_dyadic128_machin_trigonometry_v1",
    "generic_forecast": "Not used. The row evaluator is a detached surrogate field, not a trajectory solver or an increased generic forecast work cap."
  },
  "stopping_rule": "Pass only if fresh formation, both actual unprobed handoffs, full joined identity, event-work allowance, strict final outward actual recorded contrast lower bound >1e-25, and a positive outward lower bound for error_fraction*recorded_contrast_bounds.lo-E all hold. Preserve an unavailable or negative result without tuning protocol primitives, coefficients, precision or thresholds.",
  "source_base_commit": "8a46511a2baa08cd431c5aeff4524b2281d3a48b",
  "source_overlay_archive": "reduced-ports-v1.source.zip",
  "frozen_theory_owner": "theory/nodal/SINE_REDUCED_CLASS_PORTS.md",
  "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": "Python exact Fraction plus fixed outward dyadic128; exact squared decay bounds below interval grid",
    "packages": {
      "numpy": "2.3.3",
      "networkx": "3.5",
      "scipy": "1.16.3",
      "mpmath": "1.3.0"
    },
    "seed": null,
    "seed_scope": "No random input or trajectory samples; pressure supplied analytically by complete law, no held-pressure approximation."
  },
  "scope": "One prospective transfer of a rigorously bounded smaller constituent model under supplied law, source preparation, clock, observation and contact. No autonomous constituent/contact selection, exact nonlinear closure, minimality, practical sensing or physical identification."
}