{
  "schema": "tnfr.sine-port-form-tracking-protocol.v1",
  "evaluation_kind": "conditional_analytic_uniform_form_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": "fixed_stiffness_heat_convolution_form_gain_v1",
    "baseline": "Re-admit the fourteen original primitives and freshly derive the original all-time phase certificate, including both traps, exact gap, parity defects and conserved mean allowances. No incoming cached report supplies a premise.",
    "fixed_stiffness": "B0 has class cosine internal weights and unit bridge weights. In each centered parity sector (lambda/6)I <= B0 <= 2I. A and B0 need not commute.",
    "bridge_remainder": "Odd bridge variation is zero. For the even channel, add B_edge_squared times the original even phase norm bound to the original even defect; B_edge_squared=12E_H bounds every full and surrogate bridge gap squared.",
    "heat_integral": "For spectrum in [b,M], integrate the spectral upper envelope to obtain integral norm(B0 exp(-B0 t)) <= 1+log(M/b)/e. Use M=2, b=lambda/6 and the least nonnegative integer n with 2^n*b>=M; log2<7/10 and 1/e<3/8 give H=1+21n/80 and derivative-kernel gain G=1+H.",
    "form_comparison": "With y=delta_phase+gamma*delta_form and z=gamma*delta_form, retain z_prime=-A*z+y_prime. The ordered heat convolution gives loop gain rho=gamma_upper^2*2*G/lambda. Require rho<1. The form bound is [N+gamma_upper*2*(1+gamma_upper)*N/lambda+gamma_upper*G*D/lambda]/(1-rho). This includes initial exchange and requires no commutation or forcing derivative.",
    "outputs": "Use the same heat method for both parity sectors, combine their weighted form norms orthogonally, divide by lower sqrt2 and restore the same global mean uncertainty once. Retain the freshly derived original phase bound unchanged. Use strict outward channel margins and the original fractions1/2.",
    "interval_method": "rational_outward_dyadic128_machin_trigonometry_v1",
    "trajectory_integration": false
  },
  "stopping_rule": "Freeze this proof, protocol, source and evaluator before the reserved assessment. Require every original mathematical premise and supplied-work policy, both heat small-gain conditions and both original strict channel-resolution margins. Preserve the outcome without changing thresholds, source, support, model, precision, horizon or method after evaluation. Failure of this sufficient bound is not an observed trajectory error.",
  "source_base_commit": "36fc3f36b0fc1e1450feda56819cac82842ff3a6",
  "source_overlay_archive": "port-form-tracking-v1.source.zip",
  "frozen_theory_owner": "theory/nodal/SINE_PORT_FORM_TRACKING.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": "Uniform form and phase error assessment for the unchanged degree-aware surrogate under its supplied complete model. The previous phase-only result remains immutable. No zero asymptotic-error claim, sensor/clock bridge, autonomous contact, source selection or physical identification follows.",
  "prior_evidence": "port-relaxation-v1.json remains phase_only with false joint stopping. This separate method changes no preparation, dynamics, surrogate, observation, clock, support, resolution fraction or numerical precision."
}