{
  "experiment_key": "relaxed-frame-twist-force-and-longitudinal-stiffness",
  "created_utc": "2026-10-12T12:32:12.041975+00:00",
  "sources": {
    "experiments/relaxed-frame-twist.py": "9315b5d2e542b8503f6b27fe31ff2101b481c87e720b6eb765795276eeece5e4"
  },
  "evaluations": 397,
  "conditions": {
    "full frame bulk wave equation has one common shifted restoring scale": 4,
    "both rotating vectors retain the complete time kinetic energy": 1,
    "both twisted vectors retain the complete longitudinal gradient energy": 1,
    "exact uniform twists retain the area dielectric": 1,
    "full electric variation retains the actual spatial vector source": 2,
    "balanced rotating frame satisfies the same scalar profile equation": 2,
    "complete relaxed bulk energy gives tension minus shape-gradient stress": 1,
    "endpoint torque follows from the same relaxed energy": 1,
    "force separation slope equals longitudinal phase stiffness exactly": 1,
    "actual guide moment coefficient is strictly above one on zero to one": 2,
    "pure quartic phase stiffness has the exact twist threshold": 2,
    "homogeneous rotation has positive subluminal reduced phase speed": 2,
    "finite full-frame tilt preserves its actual vector norm": 1,
    "finite full-frame tilt preserves relative orthogonality": 1,
    "exact tilted-vector kinetic metric retains orientation and tilt together": 2,
    "full-frame quadratic tilt has the exact rotation-versus-twist restoring term": 1,
    "original vector equation independently gives the exact spatial tilt frequency": 1,
    "complete rotation Routhian is the claimed positive-square decomposition": 1,
    "all unused spatial frame directions have a nonnegative rotation norm deficit": 1,
    "boosted uniform frame retains the same supported transverse restoring coefficient": 1,
    "complete bulk longitudinal momentum has positive motion-supplied linear response": 1,
    "finite shortest-angle static segment retains a positive lowest tilt frequency": 3,
    "timelike frame rotation removes this exact tilt growth channel": 5,
    "independent complete moments recover the prescribed fixed flux": 36,
    "complete guide energy gives the exact tension-to-norm relation": 36,
    "globally bound mixed guide has decreasing profile norm with restoring scale": 36,
    "relaxed mixed uniform twist has positive net inward force": 36,
    "direct full neutral and electric stress agrees with relaxed force": 36,
    "independent branch differences verify the fixed-flux envelope derivative": 36,
    "independent branch differences verify the complete profile norm response": 36,
    "positive static phase stiffness gives subluminal reduced response": 21,
    "direct finite-separation energy derivative gives the force": 30,
    "independent mixed-profile force differences give the phase stiffness identity": 30,
    "mixed force minimum remains strictly inward when phase stiffness changes sign": 6,
    "exact pure-quartic relaxed twist remains inward at all control gradients": 14,
    "occupied-sector gate remains the same without a twist-specific coefficient": 6
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  "maximum_errors": {
    "independent complete moments recover the prescribed fixed flux": 5.970931150114086e-14,
    "complete guide energy gives the exact tension-to-norm relation": 2.0097095792262884e-14,
    "direct full neutral and electric stress agrees with relaxed force": 3.76977217247901e-16,
    "independent branch differences verify the fixed-flux envelope derivative": 4.727207038224024e-09,
    "independent branch differences verify the complete profile norm response": 1.7236598830050468e-08,
    "direct finite-separation energy derivative gives the force": 2.031117690383397e-09,
    "independent mixed-profile force differences give the phase stiffness identity": 4.4245859637419116e-08
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  "pure_quartic_controls": [
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      "depth": 3,
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      "twist_over_restoring": 0,
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      "depth": 3,
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      "depth": 3,
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    {
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      "twist_over_restoring": 20,
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      "depth": 4,
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    {
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    {
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    {
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    {
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  ],
  "full_frame_tilt_controls": [
    {
      "endpoint_angle": 0.2,
      "length": 2.0,
      "frame_rotation": 0.0,
      "lowest_dirichlet_tilt_frequency_squared": 2.4574011002723397
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    {
      "endpoint_angle": 0.2,
      "length": 2.0,
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      "lowest_dirichlet_tilt_frequency_squared": 2.7074011002723397
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    {
      "endpoint_angle": 0.2,
      "length": 2.0,
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    {
      "endpoint_angle": 1.0,
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      "lowest_dirichlet_tilt_frequency_squared": 2.2174011002723395
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    {
      "endpoint_angle": 1.0,
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      "lowest_dirichlet_tilt_frequency_squared": 2.4674011002723395
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    {
      "endpoint_angle": 1.0,
      "length": 2.0,
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      "lowest_dirichlet_tilt_frequency_squared": 4.4674011002723395
    },
    {
      "endpoint_angle": 2.8,
      "length": 2.0,
      "frame_rotation": 0.0,
      "lowest_dirichlet_tilt_frequency_squared": 0.5074011002723398
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    {
      "endpoint_angle": 2.8,
      "length": 2.0,
      "frame_rotation": 0.5,
      "lowest_dirichlet_tilt_frequency_squared": 0.7574011002723398
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    {
      "endpoint_angle": 2.8,
      "length": 2.0,
      "frame_rotation": 1.5,
      "lowest_dirichlet_tilt_frequency_squared": 2.7574011002723395
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    {
      "endpoint_angle": 3.4,
      "length": 2.0,
      "frame_rotation": 0.0,
      "lowest_dirichlet_tilt_frequency_squared": -0.4225988997276602
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    {
      "endpoint_angle": 3.4,
      "length": 2.0,
      "frame_rotation": 0.5,
      "lowest_dirichlet_tilt_frequency_squared": -0.17259889972766018
    },
    {
      "endpoint_angle": 3.4,
      "length": 2.0,
      "frame_rotation": 1.5,
      "lowest_dirichlet_tilt_frequency_squared": 1.8274011002723398
    }
  ],
  "sectors": [
    {
      "depth": 2,
      "hodge_gate": 0,
      "twisted_guide_available": false,
      "independently_new_dimensional_selection": false
    },
    {
      "depth": 3,
      "hodge_gate": 1,
      "twisted_guide_available": true,
      "independently_new_dimensional_selection": false
    },
    {
      "depth": 4,
      "hodge_gate": 1,
      "twisted_guide_available": true,
      "independently_new_dimensional_selection": false
    },
    {
      "depth": 5,
      "hodge_gate": 0,
      "twisted_guide_available": false,
      "independently_new_dimensional_selection": false
    },
    {
      "depth": 6,
      "hodge_gate": 0,
      "twisted_guide_available": false,
      "independently_new_dimensional_selection": false
    },
    {
      "depth": 10,
      "hodge_gate": 0,
      "twisted_guide_available": false,
      "independently_new_dimensional_selection": false
    }
  ],
  "exact_equations": {
    "shifted_restoring": "s=Omega^2+k^2-varpi^2",
    "force": "tau-k^2 M",
    "phase_stiffness": "G=M+2k^2 partial_s M",
    "force_slope": "partial_L F_in=(k^2/L)G"
  },
  "limits": [
    "uniform bulk frame and supported transverse profile are exact within the retained action",
    "finite end caps and general dynamic sources are not solved",
    "effective modulated phase action is a leading long-wavelength reduction",
    "phase-channel stiffness does not prove full orientation and connection stability",
    "rotating global energetic bound does not settle the degenerate vacuum Cauchy problem",
    "bulk longitudinal inertia is a response per length with tension, not particle rest mass",
    "frame rotation frequency is not identified with the particle mass clock",
    "ground moment inputs are inherited decimal approximations, not exact rational constants",
    "three/four restriction is inherited from the guide action, not an independent new selection",
    "master-field reduction, non-Abelian confinement and physical normalization remain open"
  ]
}