{
  "schema": "tnfr.sine-port-composition-protocol.v1",
  "evaluation_kind": "conditional_analytic_degree_aware_composition_no_trajectory",
  "inputs": {
    "classes": [
      1,
      2,
      1
    ],
    "contacts": [
      [
        0,
        1
      ],
      [
        1,
        2
      ]
    ],
    "phase_origins": [
      {
        "numerator": 0,
        "denominator": 1
      },
      {
        "numerator": 1,
        "denominator": 1000
      },
      {
        "numerator": 0,
        "denominator": 1
      }
    ],
    "formation_time": {
      "numerator": 100,
      "denominator": 1
    },
    "relaxation_duration": {
      "numerator": 10000000000000,
      "denominator": 1
    },
    "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
    },
    "radius": {
      "numerator": 1,
      "denominator": 12
    },
    "decay_power": 512,
    "work_allowance": {
      "numerator": 1,
      "denominator": 500000
    },
    "approximation_allowance": {
      "numerator": 1,
      "denominator": 50000000000000000000000000000000
    }
  },
  "complete_model": "Normalized-sine rows x_prime=-K L x+gamma K S(theta), theta_prime=gamma K L x, gamma=1/(1023*pi). K uses each actual fine degree. Unit capacities, beta=1, e=1023/1024, w=1/1024, tau=e*t. Both rows transform. No forcing or phase probes.",
  "preparation": "Three original C9 form sources k_i*(2046/9)*(355/113)^2*(j-4), initially phase-flat at origins (0,1/1000,0), classes (1,2,1). Independent per-coordinate form and continuous phase-lift errors <=1e-10 on every component, with separate exact zero sums. All sixteen relative source coordinates/component and original storage ceiling1e9 are retained; source costs need not agree.",
  "support": {
    "nodes": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21,
      22,
      23,
      24,
      25,
      26
    ],
    "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
      ],
      [
        13,
        22
      ],
      [
        14,
        15
      ],
      [
        15,
        16
      ],
      [
        16,
        17
      ],
      [
        18,
        19
      ],
      [
        18,
        26
      ],
      [
        19,
        20
      ],
      [
        20,
        21
      ],
      [
        21,
        22
      ],
      [
        22,
        23
      ],
      [
        23,
        24
      ],
      [
        24,
        25
      ],
      [
        25,
        26
      ]
    ],
    "bridges": [
      [
        4,
        13
      ],
      [
        13,
        22
      ]
    ],
    "weights": "unit",
    "capacities": "held one",
    "component_order": [
      0,
      1,
      2
    ],
    "local_node_order": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8
    ],
    "central_local_port": 4
  },
  "schedule": "Fresh formation at tau=100; continue actual isolated flows unprobed for D=1e13; add both contacts simultaneously at tau_c=100+D without state reset; hold support afterward.",
  "observation": "Uniform maximum absolute error in all 27 fine form and27 continuous phase-lift coordinates between the actual fine trajectory and the lifted nominal surrogate throughout[0,1/100] after contact. This coordinate allowance is not a sensor precision or response contrast.",
  "retained_reduction": {
    "orbits": [
      [
        4
      ],
      [
        3,
        5
      ],
      [
        2,
        6
      ],
      [
        1,
        7
      ],
      [
        0,
        8
      ]
    ],
    "full_state_coordinates": 54,
    "reduced_state_coordinates": 30,
    "layer_masses": [
      [
        3,
        4,
        4,
        4,
        4
      ],
      [
        4,
        4,
        4,
        4,
        4
      ],
      [
        3,
        4,
        4,
        4,
        4
      ]
    ],
    "component_parameters": "Class cosine cos(2*pi*k_i/9); internal L0=2*L_path5; M_i=diag(2+contact_degree_i,4,4,4,4). Every bridge phase difference derives from common component origins and retained real phase deviations.",
    "composition": "Internal sine currents alone are linearized; exact bridge sine and form currents sum over all contacts. The ideal surrogate begins at zero forms/deviations. Actual original endpoint errors are bounded, never reset.",
    "discarded_information": "Four reflection-odd modes per channel/component are omitted. Initial arbitrary odd uncertainty and nonlinear odd-mode generation remain in the full-space error proof. No exact invariant nonlinear quotient."
  },
  "algebraic_control": {
    "phase_origins": [
      0,
      0,
      0
    ],
    "forms": [
      0,
      0,
      0,
      0,
      0,
      1,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0
    ],
    "phase_deviations": [
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0,
      0
    ],
    "expected_middle_form_rate": {
      "numerator": -1,
      "denominator": 1
    },
    "naive_middle_form_rate": {
      "numerator": -4,
      "denominator": 3
    },
    "naive_weighted_charge_rate": {
      "numerator": -4,
      "denominator": 3
    },
    "exact_charge_rate": 0,
    "form_storage": 2,
    "dissipation": {
      "numerator": 17,
      "denominator": 3
    }
  },
  "prediction": {
    "full_state_uniform_error_strictly_below": {
      "numerator": 1,
      "denominator": 50000000000000000000000000000000
    },
    "all_original_windings_retained_all_future": true,
    "recovery_on_actual_postevent_mean_leaf": true,
    "contact_work_allowance": {
      "numerator": 1,
      "denominator": 500000
    },
    "exact_reduced_storage_rate": "-(L_joined*x)^T*M^-1*(L_joined*x)",
    "exact_weighted_charge_rates": [
      0,
      0
    ]
  },
  "method": {
    "name": "degree_aware_even_ports_exact_bridge_full_space_defect_v1",
    "handoff": "Fresh original source library; exact2^-512 only if512<=kappa*D<=4096. Tiny squared endpoint bounds remain exact rational.",
    "joined_identity": "Actual full sine law; gap>=4/[9*m*(contact_diameter+8)], cosine>=cos(4*pi/9+sqrt(2)*r)>1/20. Strict initial quotient-radius and storage-barrier margins.",
    "sigma": "Maximum absolute signed ideal port sine sum divided by actual fine degree, interval bounded from origins.",
    "ideal_discrepancy": "2*gamma_upper^5*sigma_upper^2*h^5/[5*(1-2*gamma_upper^2*h^2/3)^2*(1-3*h)]",
    "actual_preparation_error": "epsilon/(1-3*h)",
    "interval_method": "rational_outward_dyadic128_machin_trigonometry_v1",
    "trajectory_integration": false
  },
  "stopping_rule": "Pass only if fresh formation, every actual unprobed handoff, full joined identity/recovery, declared event-work allowance, exact degree/storage/charge controls and a strictly positive outward lower margin for the whole-window error allowance all hold. Preserve failure/unavailable without tuning any input, law, horizon, precision or threshold.",
  "source_base_commit": "f9c419c42bce35df8bd94b136ac73ca9999103b1",
  "source_overlay_archive": "port-composition-v1.source.zip",
  "frozen_theory_owner": "theory/nodal/SINE_REDUCED_PORT_COMPOSITION.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 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 numerical trajectory. Complete pressure field is supplied analytically; no held-pressure approximation."
  },
  "scope": "One frozen three-component-path control of a generic simple-unit-contact theorem. Supplied law, capacities, preparation, clock, support and work. No weighted-support extension, contact selection, minimality, autonomous hierarchy, laboratory acquisition or physical identification."
}