{
  "schema": "tnfr.sine-two-port-compatibility-protocol.v1",
  "evaluation_kind": "conditional_static_geometry_and_local_attraction_no_trajectory",
  "inputs": {
    "classes": [
      2,
      1
    ],
    "outer_refinements": 32,
    "inner_refinements": 64
  },
  "matched_control_inputs": {
    "classes": [
      1,
      1
    ],
    "outer_refinements": 32,
    "inner_refinements": 64
  },
  "complete_model": "Fixed normalized-sine rows x_prime=-K L x+gamma K S(theta), theta_prime=gamma K L x, gamma=1/(1023*pi). K uses actual full fine degrees. Held unit capacities, beta=1, e=1023/1024, w=1/1024, tau=e*t. No forcing or events. This is the positive-loss sine model, not native resultant-direction dynamics.",
  "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
      ],
      [
        0,
        9
      ],
      [
        1,
        2
      ],
      [
        1,
        10
      ],
      [
        2,
        3
      ],
      [
        3,
        4
      ],
      [
        4,
        5
      ],
      [
        5,
        6
      ],
      [
        6,
        7
      ],
      [
        7,
        8
      ],
      [
        9,
        10
      ],
      [
        9,
        17
      ],
      [
        10,
        11
      ],
      [
        11,
        12
      ],
      [
        12,
        13
      ],
      [
        13,
        14
      ],
      [
        14,
        15
      ],
      [
        15,
        16
      ],
      [
        16,
        17
      ]
    ],
    "left_cycle": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8
    ],
    "right_cycle": [
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17
    ],
    "bridges": [
      [
        0,
        9
      ],
      [
        1,
        10
      ]
    ],
    "mixed_cycle": [
      0,
      9,
      10,
      1
    ],
    "weights": "unit",
    "capacities": "held one",
    "degree_mass": 40,
    "ports": [
      0,
      1,
      9,
      10
    ],
    "orientation": "Both internal cycles follow increasing local index, closing8 to0. Both bridge currents are oriented left to right."
  },
  "target": {
    "cycle_periods": [
      2,
      1,
      0
    ],
    "form": "Uniform zero on all18 nodes; no hidden form source.",
    "phase_gauge": "One real-lift representative with zero full degree-weighted common phase; retain exact affine correlations and closing-edge integer offsets.",
    "acute_domain": "Every principal edge gap lies strictly between -pi/2 and pi/2. Uniqueness is restricted to this full cycle-period cell, modulo the common phase."
  },
  "preparation": "No initial source family or trajectory is assessed. The previously acquired classes motivate the target labels only. This is not a handoff from either formed-family preparation, and no late attachment, work budget or basin-entry claim is inferred.",
  "observation": "Implicit equilibrium geometry, strictly positive left0-to-right0 sine current for classes(2,1), zero bridge current for matched classes(1,1), all fine nodal balance equations, strict acute margins and the local full-law stability classification. Stationary edge currents do not imply nodal motion, form transport or dissipated power.",
  "method": {
    "name": "two_monotone_turn_roots_with_full_affine_cycle_reconstruction_v1",
    "arc_constraints": "a+8b=2*pi*k_left, c+8d=2*pi*k_right, delta=(a-c)/2. Bridge gaps are delta,-delta. Complete critical equations: sin(b)-sin(a)=sin(c)-sin(d)=sin(delta).",
    "outer_variable": "For canonical classes(2,1), a/(2*pi) lies in[1/9,2/9]. Write h_k(s)=sin((2*pi*k-s)/8)-sin(s). For each outer a, solve h_1(c)+h_2(a)=0 in c/(2*pi) in[1/9,2/9].",
    "inner_endpoint": "At a=4*pi/9, h_2(a)=0 and c=2*pi/9 analytically; do not ask a strict-sign root solver to certify an endpoint zero by rounding.",
    "outer_residual": "h_2(a)-sin((a-c(a))/2) is strictly decreasing, with strictly positive/negative endpoint signs. Reuse the shared exact-turn decreasing-root bracket owner, inner64 and outer32 refinements, fixed outward interval arithmetic. Unresolved numerical signs remain explicitly unavailable.",
    "reconstruction": "Use rational-affine nodal turns in the correlated two root coordinates, exact degree-weighted gauge cancellation and exact integer cycle periods. Rebuild all20 edge currents and all18 nodal residuals, including their symbolic dependence on the two root equations. A midpoint or independent interval box is not an exact equilibrium.",
    "recovery": "Strict acute edge cosines give a positive relative phase Hessian on the actual connected support. Reuse the complete two-row positive-loss quadratic-pencil argument without commutation to infer local exponential attraction on the conserved mean leaf, with34 stable relative directions. No global attraction or specified basin entry follows.",
    "control": "Equal classes have their unchanged uniform twists and zero bridge gaps/current; construct this control analytically without an artificial root solve.",
    "interval_method": "rational_outward_dyadic128_machin_trigonometry_v1",
    "trajectory_integration": false
  },
  "prediction": {
    "unequal_classes": "Unique strictly acute critical geometry in period cell(2,1,0), positive first oriented bridge sine current, opposite second current, and local full-law attraction. Internal twists must deform; no relative origin preserves both undeformed unequal twists as an acute equilibrium.",
    "matched_classes": "Exact unchanged class-one twists, zero bridge current and strict acute local attraction in cell(1,1,0).",
    "scope": "Admission of known formed-class geometries to a new interface. General circulation and acute-cell uniqueness are reused theorems, not new universal laws. The earlier central-port reduced-model bounds do not transfer to this support."
  },
  "stopping_rule": "Require both admitted geometries, exact full-cycle and nodal-factorization consistency, strict acute/Hessian margins, the predicted nonzero-versus-zero interface-current distinction and the justified local-stability classification. Preserve an unavailable result if fixed interval signs cannot be resolved. Freeze proof, source and protocol before evaluation; do not retune support, class, precision or refinement budgets afterward. No trajectory search, initial-family capture or physical binding claim.",
  "source_base_commit": "3a313196640bfd99d2164d8c2c2e5c89cb504c50",
  "source_overlay_archive": "two-port-compatibility-v1.source.zip",
  "frozen_theory_owner": "theory/nodal/SINE_TWO_PORT_COMPATIBILITY.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 and fixed outward dyadic128 trigonometry; shared monotone phase-root brackets",
    "seed": null,
    "seed_scope": "No random state or numerical trajectory. The complete pressure law and fixed support are declared analytically."
  }
}