{
  "protocol_id": "20260907-frozen-magnetic-texture-v1",
  "purpose": "Test whether the existing six-dimensional magnetic response supports its uniform-polarization preparation when spatial polarization textures are admitted.",
  "status": "Frozen before computing texture Hessians or nonlinear texture energies",
  "dimension": 6,
  "density": "n(x)=(2*pi)^(-3)*exp(-|x|^2/2), integral n=1, fixed envelope",
  "polarization": "Unit four-component positive-band chiral spinor z(x); reference z0=(1,0,0,0)",
  "kernel": "P_k M=P_k*M+M*P_k with P_k=k*k^T/|k|^2 for nonzero k on R^6",
  "energy": "tau*integral n*|gradient z|^2 - kappa/2*integral |P_k Fourier[n J(z)]|^2 dk/(2*pi)^6",
  "coefficients": "tau=1/(2*m), g=e/(2*m), kappa=g^2/Z; hbar=1; no added restoring interaction",
  "reference_parameters": {"mass": 1.3, "charge": 0.7, "maxwell": 1.8, "width": 1.0},
  "parameter_scope": "Inherited illustrative Dirac-Maxwell benchmark, not measured six-dimensional electron parameters",
  "dimensionless_strength": "lambda=kappa*integral n^2/tau, integral n^2=(4*pi)^(-3)",
  "stress_strengths": [1.0, 8.0, 32.0, 128.0],
  "texture_family": "z=cos(epsilon*f(x))*z0 + sin(epsilon*f(x))*v, v any normalized ray-orthogonal complex spinor; f=sin(q*x0) or cos(q*x0)",
  "wave_numbers": [0.25, 0.5, 1.0, 2.0, 4.0],
  "reference_prediction_under_test": "The inherited benchmark is stationary and has no negative energy curvature in the specified texture family",
  "stronger_claim_under_test": "Uniform polarization remains a local minimum throughout the predeclared positive-coupling stress cases",
  "failure_rules": {
    "stationarity_norm_above": 1e-9,
    "resolved_negative_hessian_eigenvalue_below": -1e-7,
    "near_zero": "Within 1e-7 is unresolved, not stable",
    "independent_hessian_agreement_absolute_plus_relative": [1e-7, 0.002],
    "nonlinear_negative_witness": "A refined direct texture energy below the uniform reference confirms failure for that prepared state"
  },
  "numerical_controls": {
    "epsilon_values": [0.02, 0.01, 0.005],
    "fourier_harmonics": [8, 12],
    "phase_sample_counts": [256, 512],
    "quadrature_absolute_tolerances": [1e-11, 1e-13]
  },
  "interpretation": "A failed preparation does not refute spatial depth six. Survival is only for this perturbation family and does not prove full field or molecular stability.",
  "exclusions": ["changing the kernel after a failure", "retuning the reference parameters after seeing results", "adding compensating vector or scalar channels", "identifying polarization fields with particle orbits", "claiming experimental validation"]
}