{
  "artifact_id": "ONE_PATRON_HERALD_I_DYNAMICS",
  "version": "1.0.0",
  "state_domains": {
    "discrete_branch_state": "S01_TO_S29",
    "continuous_coordination_state": ["theta_A", "theta_B"],
    "phase_domain": "R_MOD_2PI"
  },
  "branch_transition_kernel": {
    "ordinary_rule": {
      "domain": "S01_TO_S28",
      "inputs": ["action_A", "action_B"],
      "rules": [
        {"when":{"action_A":"RETAIN","action_B":"DECLINE"},"offset":0},
        {"when":{"action_A":"RETAIN","action_B":"DEFER"},"offset":0},
        {"when":{"action_A":"RETAIN","action_B":"ENTER_COMPATIBLE"},"offset":1},
        {"when":{"action_A":"ADVANCE","action_B":"DECLINE"},"offset":1},
        {"when":{"action_A":"ADVANCE","action_B":"DEFER"},"offset":1},
        {"when":{"action_A":"ADVANCE","action_B":"ENTER_COMPATIBLE"},"offset":2}
      ],
      "upper_bound": "S29"
    },
    "terminal_representable_rule": {
      "domain": "S29",
      "ordinary_target": "S29",
      "limit_event_available": true,
      "limit_event": "L30"
    },
    "G0_rules": [
      {
        "from": "S07",
        "event": "INITIATE_G0",
        "recipient_action": "DECLINE",
        "to": "S07",
        "closure": false
      },
      {
        "from": "S07",
        "event": "INITIATE_G0",
        "recipient_action": "DEFER",
        "to": "S08",
        "closure": false
      },
      {
        "from": "S07",
        "event": "INITIATE_G0",
        "recipient_action": "ENTER_COMPATIBLE",
        "compatibility_required": true,
        "to": "CLOSURE_CONFIGURATION_R_AB",
        "closure": true,
        "transition_probability_given_valid_event": 1
      }
    ]
  },
  "coordination_flow": {
    "system": "HETEROGENEOUS_COUPLED_PHASE_FLOW",
    "equations": {
      "d_theta_A_dt": "omega_A+k*sin(theta_B-theta_A)",
      "d_theta_B_dt": "omega_B+k*sin(theta_A-theta_B)",
      "d_delta_dt": "delta_omega-2*k*sin(delta)",
      "delta": "theta_B-theta_A"
    },
    "parameters": {
      "omega_A": 1.0,
      "omega_B": 1.4,
      "delta_omega": 0.4,
      "k": 0.5
    },
    "derived_regime": {
      "locking_condition": "abs(delta_omega)<2*k",
      "stable_relative_phase": "asin(delta_omega/(2*k))",
      "unstable_relative_phase": "pi-asin(delta_omega/(2*k))",
      "common_angular_rate": "(omega_A+omega_B)/2",
      "recurrence_period": "2*pi/common_angular_rate",
      "transverse_stability_exponent": "-2*k*cos(stable_relative_phase)"
    },
    "attractor": {
      "full_state_description": "STABLE_PHASE_LOCKED_INVARIANT_CIRCLE",
      "quotient_by_global_phase": "STABLE_FIXED_POINT",
      "agent_phase_identity_collapsed": false,
      "basin": "ALL_RELATIVE_PHASES_EXCEPT_UNSTABLE_FIXED_POINT_MOD_2PI",
      "basin_measure_fraction": 1.0
    },
    "numerical_validation": {
      "integrator": "RK4",
      "time_step": 0.01,
      "duration": 80.0,
      "initial_relative_phases": [-2.4, -1.1, 0.0, 1.3, 2.7],
      "phase_lock_tolerance": 0.0001,
      "perturbation": {
        "at_time": 40.0,
        "delta_offset": 0.35,
        "recovery_tolerance": 0.001
      }
    }
  },
  "transport_invariant": {
    "state_path": ["S03", "S08", "S13", "S18", "S23", "S28"],
    "transport_maps": [
      {"id":"T_03_08","matrix":[[0,-1],[1,0]]},
      {"id":"T_08_13","matrix":[[-1,0],[0,1]]},
      {"id":"T_13_18","matrix":[[0,1],[-1,0]]},
      {"id":"T_18_23","matrix":[[1,0],[0,-1]]},
      {"id":"T_23_28","matrix":[[0,-1],[1,0]]}
    ],
    "invariant": "SQUARED_EUCLIDEAN_NORM",
    "tolerance": 0.000000000001
  },
  "structural_modes": {
    "operator": "WEIGHTED_VERTEX_LAPLACIAN_FROM_TOPOLOGY",
    "eigenpairs": "COMPUTED_NOT_STORED",
    "reference_unweighted_modes": [
      {
        "mode_index": 3,
        "eigenvalue_formula": "2-2*cos(2*pi*3/21)",
        "spatial_period_in_boundary_cells": 7
      },
      {
        "mode_index": 6,
        "eigenvalue_formula": "2-2*cos(2*pi*6/21)",
        "spatial_period_in_boundary_cells": 3.5
      }
    ]
  },
  "resonance_probe": {
    "system": "COUPLED_DAMPED_SECOND_ORDER_MODAL_RECURRENCE",
    "modal_indices": [3, 6],
    "retention": 0.96,
    "angular_frequencies": {
      "mode_3": "2*pi/7",
      "mode_6": "4*pi/7"
    },
    "symmetric_coupling": 0.03,
    "drive": {
      "target_mode": 3,
      "type": "PERIODIC_IMPULSE",
      "resonant_period": 7,
      "comparison_period": 5,
      "amplitude": 1.0
    },
    "steps": 700,
    "measurement_window": [350, 699],
    "observable": "RMS_MODAL_ENERGY",
    "resonance_criterion": "RMS_ENERGY_PERIOD_7>1.5*RMS_ENERGY_PERIOD_5"
  },
  "structural_persistence_score": {
    "components": [
      {"name":"PERTURBATION_SURVIVAL","weight":0.35},
      {"name":"PHASE_RECURRENCE","weight":0.25},
      {"name":"BASIN_FRACTION","weight":0.25},
      {"name":"TRANSPORT_INVARIANT_RETENTION","weight":0.15}
    ],
    "range": [0, 1],
    "physical_interpretation": "NONE"
  }
}