{
  "experiment": "same-field-action-tradeoff",
  "created_utc": "2026-09-24T11:16:02.839913+00:00",
  "case": "depth-ten index 23 inner and outer radii at b=1.34",
  "action": "Per canonical norm, sum D_i(R)*(q_i-J_i/D_i)^2/2 + sum beta_i*q_i*k + F0(k), where J_i=sqrt(r*gamma*w_i), beta_i=sqrt(gamma*w_i/r).",
  "reduced_action": "F_eff(k,R)=g(R)*k-g(R)*k^2/(2*r)+F0(k), with exact zero-current offset cancellation.",
  "tradeoff": "Without square completion, E_offset=-r*g/2 and current curvature=-g/r, so 2*abs(E_offset)*abs(curvature)=g^2. Cauchy gives >=g^2 for general two-channel coefficients.",
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  "zero_current_curvature_match_scope": "Requires the exact inverse law to continue smoothly to zero current at both radii and one R-independent F0''(0).",
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        {
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        {
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        {
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        },
        {
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        {
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          "branch": "outer",
          "harmonic": 5
        },
        {
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          "F0": 0.0,
          "F0_prime": 0.0,
          "branch": "zero",
          "harmonic": 0
        }
      ]
    }
  ],
  "scope": "Homogeneous retained-mode reduction at two radius samples. Convex Hermite tests are necessary sampled conditions for one radius-independent F0, not proof of a smooth spatial action. Radial force is for fixed canonical norm at inherited radii; nearby equilibria, full spatial/metric stability and master origin remain untested.",
  "sources": {
    "experiments/same-field-action-tradeoff.py": "e5f9a636ef3a8253fad80903239ab931a660ecf7a32aa37bab34dcfc4404fc12",
    "experiments/results/light-tau-branch-batch-20260924T102749_642908Z.json": "f76f1eafaacb1214f4673ef0a491ddc921c50e713f26168fd986d32147301901",
    "experiments/results/two-channel-tau-test-20260924T105124_408062Z.json": "9230b7910d6a1c14fb79ad3f4acd0404d9b131fa4d2899703024e26cad9cd343",
    "experiments/rational-common-law-probe.py": "c5c1d814e6f89023d9fa7a27a83f6f52360ff958af3f3f98287118ed1a196cc4",
    "experiments/nonmonotone-common-law-probe.py": "43a676540502034807ba79aa3835e5bf767ec06fbd77fe4a0c3ef5293beb4bd1"
  }
}