{
  "generated_at": "2026-09-23T11:28:24.166728+00:00",
  "status": "diagnostic_pass",
  "checks": 988,
  "scope": "shared positive-response controls, separate linked radial action, and whole-depth conformal current action with nine zonal metric directions and a spinor pointwise conformal positivity test",
  "assumptions": {
    "source": "(i+ell+d)/(i+2ell+d+1), even ell >= 2",
    "inverse_stiffness": "d/((ell-1)(ell+d))",
    "size_law": "E=Q*c*mu/L-g^2*Q^2*K/(2*L^(d-2))",
    "fixed_profile": true,
    "bias": "minimum-norm solution on maintained selected modes",
    "background_schur": "unit v and the same source/control inverse; reported G bound omits the nonnegative field-mixing Schur term",
    "radial_action": "H(R)+a*xi^2/2-(R-1)*(v+xi)*<psi,H'(1)psi>/v; R0=v=Q=1 and a remains a common free coefficient",
    "radial_carrier_gap_values": [
      1000,
      10000
    ],
    "conformal_current_strength_scales": [
      1000,
      10000
    ],
    "conformal_basis": "uniform log radius and the same physical q=x1^2+x2^2/R^2 shape direction within each reference sphere",
    "extended_conformal_basis": "unit-uniform-sphere L2-normalized zonal scalar harmonics of degrees 0,2,...,16; shared within each depth",
    "conformal_current_law": "eta=0 negative-current branch; g(kappa)=g0*kappa^4/(1+kappa^4), g0 in [1000,10000]; R0=1; form transport at depth two"
  },
  "route_findings": {
    "unbiased_positive_response": "The fixed-norm shift is not proportional to the simplex count at any multi-mode depth.",
    "finite_common_bias": "Selected modes are algebraically compatible, but the next mode has a nonzero residual and the response amplitude curvature is negative.",
    "scale_covariant_size": "No maintained depth has a finite positive-curvature size extremum from these two energy terms alone.",
    "nonzero_background": "An operator-level linear background cancels the finite carrier's radius force and field-radius mixed block at a common R=1. Its bare radial curvature is 2*p*omega and its relaxed background requires a*v^2>Q*p*omega/2 for each occupied mode. The angular Hessian and full field dynamics remain open.",
    "conformal_current": "The separate whole-depth current candidate has a positive bare Hessian on the original two tested metric directions at every assigned index and both common strengths. A single inverse background mode cancels its first metric force and field-metric mixing; the reported threshold is necessary and sufficient for this retained block at unit phase charge, but does not establish full stability.",
    "extended_conformal_current": "The retained metric block is positive on the nine tested zonal directions at every assigned index and both strengths. For spinors at depths 3,4,5,6,10, a pointwise positive quadratic form proves fixed-profile bare positivity for every smooth conformal direction, including non-zonal ones. The depth-two form has only the finite zonal test. The full positive-wave action has the same geometric Schur threshold at unit phase charge, not at unit wave L2 norm."
  },
  "limits": [
    "The source vectors are controls, not derived spatial particle profiles.",
    "A passing diagnostic does not establish a complete stable particle or pair coupling.",
    "Depth ten has one maintained mode and cannot test within-depth proportionality.",
    "A fixed norm removes radial variations but does not derive the norm value.",
    "The finite-carrier background action is an inverse choice; its retained field origin, nonzero v, curvature a, and physical size scale are not derived from Psi_infinity.",
    "The first-order constrained field Hessian has a negative partner direction, so positive-P Schur stability cannot be inferred from the radial block.",
    "The angular second metric derivative is not determined by first-order cancellation; no angular stability verdict follows from the radial calculation.",
    "The radius kinetic coefficient and background potential are candidate-action inputs; a threshold inequality is not their derivation from the master field.",
    "The linked radial carrier and whole-depth conformal current are distinct candidate actions; their Hessian entries must not be combined.",
    "The conformal current is on the eta=0 negative-current branch and has not been tested through zero-current perturbations.",
    "The conformal calculation does not cover traceless tensor metric directions, nonlinear profile relaxation, nested compatibility, or the full field Hessian.",
    "The extended zonal scan does not prove positivity for every depth-two form deformation; the spinor pointwise result is a fixed-profile conformal statement only.",
    "The full positive-action Schur threshold uses phase charge J=2*omega*N. At unit wave L2 norm N=1 it is 2*omega times the reported unit-phase-charge threshold."
  ],
  "sources": {
    "experiments/route-decision-checks.py": "e71988c95e141817beb07b918da8d76ea92bb5f86399a4a1c3bc446109bf8c3f",
    "experiments/results/flux-moment-20260915T033331_031324Z.json": "6ed720878d217cc502ef9d7ba94e70b3d5b0afd10e08e1a7d3410336878f21e5"
  },
  "records": [
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      "depth": 2,
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        76,
        81,
        95
      ],
      "simplex_counts": [
        2926,
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      ],
      "response_norms": [
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        "0.71198816279324300540738418583977382"
      ],
      "response_per_simplex": [
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      ],
      "background_unit_schur_penalties": [
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      ],
      "background_shared_geometric_stiffness_lower_bound": "0.71198816279324300540738418583977382",
      "response_ratio_spread": "1.526707397614251498117974",
      "bias_minimum_norm_squared": "4.97618064900007247649920217784",
      "bias_gram_condition_estimate": "1185463869.3465507083",
      "bias_selected_max_residual": "1.37048573262e-80",
      "bias_next_index": 96,
      "bias_next_residual": "0.00000111384682091369598343901997867",
      "bias_amplitude_curvatures": [
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      ],
      "size_response_power": 0,
      "size_stationary_frequency_fraction": null,
      "size_stationary_curvature_sign": "no finite stationary size",
      "angular_jacobi": {
        "0": "-1.0",
        "1": "0.0",
        "2": "2.0"
      }
    },
    {
      "depth": 3,
      "indices": [
        1,
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      ],
      "simplex_counts": [
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      "response_norms": [
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      "background_unit_schur_penalties": [
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      "background_shared_geometric_stiffness_lower_bound": "0.69064027668203223582089860488696825",
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      "bias_selected_max_residual": "9.11900122089e-80",
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      "bias_next_residual": "0.0000243434165573608154403295120663",
      "bias_amplitude_curvatures": [
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      "size_response_power": 1,
      "size_stationary_frequency_fraction": "-1.0",
      "size_stationary_curvature_sign": "flat only at equality",
      "angular_jacobi": {
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      "background_unit_schur_penalties": [
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      "bias_selected_max_residual": "0.0",
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      "size_response_power": 2,
      "size_stationary_frequency_fraction": "0.0",
      "size_stationary_curvature_sign": "negative",
      "angular_jacobi": {
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