{
  "architecture": "efa-1",
  "description": "EFA-1: one body-embedding-conditioned trunk controls a family of bodies. Flow head (actuation, K=1 forward pass) + potential head (verify: low = valid action). Energy-based, deterministic, joules-metered, multi-body — identity NOT measured in tokens or parameter count.",
  "hidden": 128, "emb_dim": 6, "bodies": ["1-DOF-chain", "2-DOF-chain", "3-DOF-chain"],
  "params": 39318,
  "flow_features": "[12 joint-feats (4/joint: cos(θ-g),sin(θ-g),ω,sinθ), a1,a2,a3, t, 6-dim body-embedding]",
  "potential_features": "[12 joint-feats, a1,a2,a3, 6-dim body-embedding]",
  "env": {"family":"coupled-pendulum-chain","dof":[1,2,3],"dt":0.05,"umax":4,"coupling":0.5,"damping":0.05,"gravity":"sin"},
  "inference": "act(body,state,goal): v = flow(feat, a=0, t=0, emb[body]); u = clamp(v[:dof]). verify(body,state,goal,a): potential(feat,a,emb[body]) — lower is more valid.",
  "identity_card": [{"body":"1-DOF","reach_K1":100.0,"verify":97.4,"deterministic":true}, {"body":"2-DOF","reach_K1":100.0,"verify":98.0,"deterministic":true}, {"body":"3-DOF","reach_K1":100.0,"verify":99.3,"deterministic":true}],
  "gate": "every body reach_K1>=95 && verify>=90 && bit-exact determinism"

,
  "certificates": [{"body":"1-DOF","goal":[0.8],"attractor_residual_max":0.238,"spectral_radius_at_attractor":0.890,"grid_points":1681,"contraction_fraction_P_metric":31.6,"certified_ball_P_norm":0.757,"empirical_convergence_card_criterion":100,"method":"one-step contraction sigma_max(P^0.5 J P^-0.5)<1 in the Lyapunov metric of the closed-loop linearization at the measured attractor x*; FD Jacobians, grid-sampled (rigorous route = interval/CROWN); identity-metric contraction fails here (24.5/2.6/0.1% — recorded negative)"}, {"body":"2-DOF","goal":[0.8, -0.6],"attractor_residual_max":0.228,"spectral_radius_at_attractor":0.952,"grid_points":14641,"contraction_fraction_P_metric":9.8,"certified_ball_P_norm":0.420,"empirical_convergence_card_criterion":100,"method":"one-step contraction sigma_max(P^0.5 J P^-0.5)<1 in the Lyapunov metric of the closed-loop linearization at the measured attractor x*; FD Jacobians, grid-sampled (rigorous route = interval/CROWN); identity-metric contraction fails here (24.5/2.6/0.1% — recorded negative)"}, {"body":"3-DOF","goal":[0.8, -0.6, 0.5],"attractor_residual_max":0.323,"spectral_radius_at_attractor":0.956,"grid_points":117649,"contraction_fraction_P_metric":2.6,"certified_ball_P_norm":0.643,"empirical_convergence_card_criterion":100,"method":"one-step contraction sigma_max(P^0.5 J P^-0.5)<1 in the Lyapunov metric of the closed-loop linearization at the measured attractor x*; FD Jacobians, grid-sampled (rigorous route = interval/CROWN); identity-metric contraction fails here (24.5/2.6/0.1% — recorded negative)"}],
  "agency": {
    "policy": "L1 flow K=1 -> if E>tau: L2 flow K=4 -> if E>tau: L3 planner tool (two-stage argmin over the model's own potential) -> if E>tau: L4 seeded ES tool; execute argmin-E among candidates; all levels deterministic (bit-exact, verified)",
    "tau_per_body_95pct": [2.383, 1.876, 1.550],
    "measured": [{"eval":"in-dist","body":"1-DOF","reach_K1_only":100,"reach_agency":100,"escalation_pct_L2_L3_L4":[0.0,0.0,0.0],"mean_kflop_per_decision":77.9}, {"eval":"in-dist","body":"2-DOF","reach_K1_only":100,"reach_agency":100,"escalation_pct_L2_L3_L4":[0.1,0.0,0.0],"mean_kflop_per_decision":78.4}, {"eval":"in-dist","body":"3-DOF","reach_K1_only":100,"reach_agency":100,"escalation_pct_L2_L3_L4":[0.2,0.2,0.0],"mean_kflop_per_decision":90.7}, {"eval":"OOD-goal","body":"1-DOF","reach_K1_only":100,"reach_agency":100,"escalation_pct_L2_L3_L4":[0.0,0.0,0.0],"mean_kflop_per_decision":77.9}, {"eval":"OOD-goal","body":"2-DOF","reach_K1_only":93,"reach_agency":93,"escalation_pct_L2_L3_L4":[0.1,0.0,0.0],"mean_kflop_per_decision":78.4}, {"eval":"OOD-goal","body":"3-DOF","reach_K1_only":98,"reach_agency":98,"escalation_pct_L2_L3_L4":[3.4,1.3,0.0],"mean_kflop_per_decision":161.1}]
  },
  "certificates_funnel": [{"body":"1-DOF","domain":"S1^1 x [-5,5]^1","grid_nodes":1353,"certified_fraction":100.0,"median_entry_steps":34,"worst_funnel_expansion_sigmaP_sampled":117.5,"funnel_sample_nodes":449,"no_entry_pct":0.00,"sample_cap_count":0,"method":"per-node funnel (LQR-tree-style composition): orbit simulated from EVERY node, certified on entry into the continuous constant-P contraction ball (r=0.76); funnel transient expansion sigma_P(Phi) measured on a ~400-node sample via the FD-Jacobian product (cost, disclosed); node-local and grid-sampled (no between-node claim; rigorous route = orbit tubes via the same product + Lipschitz bound)"}, {"body":"2-DOF","domain":"S1^2 x [-6,6]^2","grid_nodes":74529,"certified_fraction":100.0,"median_entry_steps":62,"worst_funnel_expansion_sigmaP_sampled":18.1,"funnel_sample_nodes":401,"no_entry_pct":0.00,"sample_cap_count":0,"method":"per-node funnel (LQR-tree-style composition): orbit simulated from EVERY node, certified on entry into the continuous constant-P contraction ball (r=0.42); funnel transient expansion sigma_P(Phi) measured on a ~400-node sample via the FD-Jacobian product (cost, disclosed); node-local and grid-sampled (no between-node claim; rigorous route = orbit tubes via the same product + Lipschitz bound)"}, {"body":"3-DOF","domain":"S1^3 x [-6,6]^3","grid_nodes":456533,"certified_fraction":100.0,"median_entry_steps":66,"worst_funnel_expansion_sigmaP_sampled":59.3,"funnel_sample_nodes":401,"no_entry_pct":0.00,"sample_cap_count":0,"method":"per-node funnel (LQR-tree-style composition): orbit simulated from EVERY node, certified on entry into the continuous constant-P contraction ball (r=0.64); funnel transient expansion sigma_P(Phi) measured on a ~400-node sample via the FD-Jacobian product (cost, disclosed); node-local and grid-sampled (no between-node claim; rigorous route = orbit tubes via the same product + Lipschitz bound)"}],
  "certificates_multigoal": [{"body":"1-DOF","domain_omega_bound":5,"per_goal":[{"goal":[0.8],"attractor_residual":0.238,"sigmaP_at_attractor":0.979,"core_r_radial":0.65,"funnel_certified_pct":100.0,"nodes":1353,"median_entry":35}, {"goal":[-0.7],"attractor_residual":0.099,"sigmaP_at_attractor":0.977,"core_r_radial":0.35,"funnel_certified_pct":100.0,"nodes":1353,"median_entry":52}, {"goal":[0.5],"attractor_residual":0.213,"sigmaP_at_attractor":0.978,"core_r_radial":0.70,"funnel_certified_pct":100.0,"nodes":1353,"median_entry":35}, {"goal":[-0.5],"attractor_residual":0.050,"sigmaP_at_attractor":0.976,"core_r_radial":0.25,"funnel_certified_pct":100.0,"nodes":1353,"median_entry":54}],"worst_goal_funnel_pct":100.0,"method":"per-goal: attractor + constant-P + RADIAL core certification (200 samples/shell, 0.05 steps) + full-domain funnel entry (3-DOF every-3rd-node, disclosed); node-local grid-sampled limits as certificates_funnel"}, {"body":"2-DOF","domain_omega_bound":6,"per_goal":[{"goal":[0.8, -0.6],"attractor_residual":0.115,"sigmaP_at_attractor":0.981,"core_r_radial":0.25,"funnel_certified_pct":100.0,"nodes":74529,"median_entry":67}, {"goal":[-0.7, 0.5],"attractor_residual":0.228,"sigmaP_at_attractor":0.984,"core_r_radial":0.65,"funnel_certified_pct":100.0,"nodes":74529,"median_entry":61}, {"goal":[0.5, 0.9],"attractor_residual":0.016,"sigmaP_at_attractor":0.986,"core_r_radial":1.10,"funnel_certified_pct":100.0,"nodes":74529,"median_entry":50}, {"goal":[-0.5, -0.8],"attractor_residual":0.161,"sigmaP_at_attractor":0.984,"core_r_radial":0.25,"funnel_certified_pct":100.0,"nodes":74529,"median_entry":68}],"worst_goal_funnel_pct":100.0,"method":"per-goal: attractor + constant-P + RADIAL core certification (200 samples/shell, 0.05 steps) + full-domain funnel entry (3-DOF every-3rd-node, disclosed); node-local grid-sampled limits as certificates_funnel"}, {"body":"3-DOF","domain_omega_bound":6,"per_goal":[{"goal":[0.8, -0.6, 0.5],"attractor_residual":0.163,"sigmaP_at_attractor":0.981,"core_r_radial":0.60,"funnel_certified_pct":100.0,"nodes":152178,"median_entry":67}, {"goal":[-0.7, 0.5, -0.6],"attractor_residual":0.323,"sigmaP_at_attractor":0.991,"core_r_radial":0.85,"funnel_certified_pct":100.0,"nodes":152178,"median_entry":65}, {"goal":[0.5, 0.9, -0.4],"attractor_residual":0.095,"sigmaP_at_attractor":0.983,"core_r_radial":1.20,"funnel_certified_pct":100.0,"nodes":152178,"median_entry":56}, {"goal":[-0.5, -0.8, 0.7],"attractor_residual":0.274,"sigmaP_at_attractor":0.984,"core_r_radial":1.05,"funnel_certified_pct":100.0,"nodes":152178,"median_entry":61}],"worst_goal_funnel_pct":100.0,"method":"per-goal: attractor + constant-P + RADIAL core certification (200 samples/shell, 0.05 steps) + full-domain funnel entry (3-DOF every-3rd-node, disclosed); node-local grid-sampled limits as certificates_funnel"}],
  "certificates_tube": [{"body":"1-DOF","lipschitz_J_sampled":29.15,"delta_needed_half_cell_diag":0.174,"nodes_covering_pct":0.0,"nodes_tested":1353,"median_certified_delta0":0.000,"min_certified_delta0":0.0000,"full_coverage_spacing_factor":0.000,"method":"orbit tubes: delta' = (sigma(J)+L*delta)*delta along each node orbit, certified when pnorm(x)+sqrt(lammax(P))*delta <= r_core; L sampled (300 pairs, NOT proven — interval arithmetic named as the rigorous route); nodes sampled 1/1 for cost"}, {"body":"2-DOF","lipschitz_J_sampled":32.15,"delta_needed_half_cell_diag":0.738,"nodes_covering_pct":0.0,"nodes_tested":9317,"median_certified_delta0":0.000,"min_certified_delta0":0.0000,"full_coverage_spacing_factor":0.000,"method":"orbit tubes: delta' = (sigma(J)+L*delta)*delta along each node orbit, certified when pnorm(x)+sqrt(lammax(P))*delta <= r_core; L sampled (300 pairs, NOT proven — interval arithmetic named as the rigorous route); nodes sampled 1/8 for cost"}, {"body":"3-DOF","lipschitz_J_sampled":46.90,"delta_needed_half_cell_diag":1.801,"nodes_covering_pct":0.0,"nodes_tested":14267,"median_certified_delta0":0.000,"min_certified_delta0":0.0000,"full_coverage_spacing_factor":0.000,"method":"orbit tubes: delta' = (sigma(J)+L*delta)*delta along each node orbit, certified when pnorm(x)+sqrt(lammax(P))*delta <= r_core; L sampled (300 pairs, NOT proven — interval arithmetic named as the rigorous route); nodes sampled 1/32 for cost"}]
}