{
  "schema": "tnfr.sine-port-relaxation-protocol.v1",
  "evaluation_kind": "conditional_analytic_uniform_tracking_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
    },
    "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
    },
    "normalized_gap_lower_bound": {
      "numerator": 3,
      "denominator": 100
    },
    "phase_resolution_fraction": {
      "numerator": 1,
      "denominator": 2
    },
    "form_resolution_fraction": {
      "numerator": 1,
      "denominator": 2
    }
  },
  "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 per-coordinate errors in all27 fine forms and continuous phase lifts relative to the same lifted30-state nominal surrogate, for every subsequent time after the supplied contact. Separate conserved global mean floors remain. No time horizon, trajectory integration or fitted coefficient.",
  "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."
  },
  "prediction": {
    "phase_resolution": "Strict outward positive margin for phase_error_upper < origin_span/2 =1/2000.",
    "form_resolution": "Strict outward positive margin for form_error_upper < gamma*origin_span/2 =gamma/2000; compare against the lower outward allowance.",
    "joint_resolution": "Both separately admitted channel margins must pass under the unchanged protocol.",
    "scope": "The two channel scales are declared structural coordinate scales, not sensor errors, guaranteed signal lower bounds or the earlier donor contrast. A partial channel certificate is retained."
  },
  "method": {
    "name": "acute_storage_parity_invariant_rectangle_v1",
    "handoff": "Fresh original formation and exact guarded2^-512 unprobed decay. No incoming report, ideal reset or probe.",
    "both_traps": "Shared joined radius/storage certificate admits the actual full family and the nominal extended surrogate around the same aligned target.",
    "spectral": "Fresh exact PSD of reduced L−q*(M−mm^T/W), q=3/100. Odd blocks retain tridiagonal half-weight C9 operator with gap>7/30.",
    "acute_refinement": "From retained excess E and original acute cosine c_r obtain beta=sqrt(2E/c_r); require cos(4*pi/9+beta)>=1/6. Then squared internal edge deviation <=12E.",
    "defects": "Odd forcing <=B^2/sqrt(2); even forcing <=2B*odd_phase_norm+sqrt(2)*B^3/6, with B=sqrt(12E). Generated odd modes enter the comparison explicitly.",
    "comparison": "Use c=1/6, a=c*lambda, b=lambda/gamma_upper^2−2, det=a*b−4>0. Positive2x2 inverse gives an invariant rectangle retaining initial error and forcing. Same simple method for both parity sectors; no optional form-gain refinement.",
    "mean_floors": "Retain absolute form and phase mean differences <=2*edge_count*endpoint_radius/(18*component_count+2*edge_count).",
    "interval_method": "rational_outward_dyadic128_machin_trigonometry_v1",
    "trajectory_integration": false
  },
  "stopping_rule": "Require fresh handoff, actual and surrogate trapping, supplied work admission, exact normalized gap, refined cosine and positive stable comparison gains before claiming uniform envelopes. Preserve independent phase/form resolution and joint verdict. A failed sufficient form bound is not observed surrogate failure. Do not tune source, support, model, thresholds, precision or add a horizon search to turn a partial result into a joint pass.",
  "source_base_commit": "c16b3d8b86b05da0a52c0ba7734264d8597812ec",
  "source_overlay_archive": "port-relaxation-v1.source.zip",
  "frozen_theory_owner": "theory/nodal/SINE_PORT_RELAXATION.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, exact PSD and 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 supplied analytically; no held-pressure approximation."
  },
  "scope": "An all-time comparison on unchanged supplied support and law. Distinct source uncertainty, parity defects and conserved means remain. No asymptotic full-error zero, physical sensor/clock bridge, autonomous contact or unique-law claim."
}