Recorded data and provenance for the associated calculation.
| 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. |
| zero_current_curvature_match_ratio | 2.57086503762751e-16 |
| 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). |
| 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. |
View complete data
{
"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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"branch": "inner",
"harmonic": 5
},
{
"current": -5.861835859413625e-12,
"F0": 9.473936216380356e-14,
"F0_prime": -0.01943541705804038,
"branch": "outer",
"harmonic": 30
},
{
"current": -1.6925261938321563e-12,
"F0": 2.126405736380166e-14,
"F0_prime": -0.015113970415012144,
"branch": "outer",
"harmonic": 26
},
{
"current": -7.135753746884276e-13,
"F0": 7.521849583175028e-15,
"F0_prime": -0.01268560198958313,
"branch": "outer",
"harmonic": 23.5
},
{
"current": -5.947405225781063e-13,
"F0": 6.0410601280437444e-15,
"F0_prime": -0.012225032562188952,
"branch": "outer",
"harmonic": 23
},
{
"current": -4.940043566639316e-13,
"F0": 4.831771400654806e-15,
"F0_prime": -0.011772822952798995,
"branch": "outer",
"harmonic": 22.5
},
{
"current": -1.8464741488945816e-13,
"F0": 1.47752325084043e-15,
"F0_prime": -0.009637054568801939,
"branch": "outer",
"harmonic": 20
},
{
"current": -9.226134677538998e-18,
"F0": 8.900379391632988e-21,
"F0_prime": -0.0011888626857441446,
"branch": "outer",
"harmonic": 5
},
{
"current": 0.0,
"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"
}
}