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Results — HOLD-CURR: Circulating-current perturbation census

Coulomb restores bunching · Weber-INST only DRIFTs · ILC-1 is not an EOM · not hold

CPT Framework — Rail A-geom / hold companion Date: 2026-08-20 Status: BANKED · PASS_HOLD_CURR_SCORED Design: a_geom_hold_curr_current_perturbation_design.md Script: scripts/investigations/s3_geometry/hold_curr_current_perturbation_census.py Data: scripts/investigations/s3_geometry/data/hold_curr_current_perturbation_census.json Parents: DW-SG · DW-ALD · H-D5 · PB3 · ED-16

Tags: [E] · [E honesty] · [M packaging] · [O residual] · [F] · [Programme]

0. One-line

On a frozen circle, a kicked circulating current is not dynamically self-restoring under the named Weber pair book. Coulomb restores bunching (ring electrostatics). Present-time Weber only DRIFTs that restore. Common-mode \(\lvert I\rvert\) is invisible to the present pair force. ILC-1 used as an EOM drains or blows the current — it is not a retarded Green. Not hold. No promote.

1. What was run

Frozen (not shopped): \(N=16\), \(R=c=Q=m_\star=1\), \(A=0.08\), \(\delta=0.08\), \(\beta\in\{0.3,0.9\}\), \(T=6\), \(\mathrm{d}t=0.02\).

Books: COULOMB, WEBER-INST, WEBER-ILC1. Kicks: UNIFORM, BUNCH, BETA-WAVE, BETA-COMMON.

2. Scores (late/early)

Bunching \(B\) (H-D5 channel)

| Book | \(\beta=0.3\) | \(\beta=0.9\) | |------|:------------:|:------------:| | COULOMB | RESTORE \(\rho=0.27\) | RESTORE \(\rho=0.27\) | | WEBER-INST | DRIFT \(\rho=0.77\) | DRIFT \(\rho=0.77\) | | WEBER-ILC1 | GROW \(\rho=5.8\) | GROW \(\rho=5.4\) (then blows \(\lvert C\rvert\)) |

Coulomb \(B\): \(0.034\to 0.009\). Weber-INST: \(0.032\to 0.025\). Same \(\rho\) at both \(\beta\) — the restore/drift is electrostatic structure, not a \(v=c\) miracle.

Speed wave \(S\)

| Book | \(\beta=0.3\) | \(\beta=0.9\) | |------|:------------:|:------------:| | COULOMB | RESTORE | RESTORE | | WEBER-INST | DRIFT | DRIFT | | WEBER-ILC1 | GROW (mean \(\Omega\to 0\); \(S\) blows) | GROW (blow) |

Coulomb converts a speed wave into transient bunching and then reclusters. Weber-INST again only slows that.

Common-mode \(\lvert I\rvert\) (\(C=\langle\Omega\rangle/\Omega_0\))

| Book | \(\beta=0.3\) | \(\beta=0.9\) | |------|:------------:|:------------:| | COULOMB | DRIFT \(C=1.08\) stays | DRIFT \(C=1.08\) stays | | WEBER-INST | DRIFT \(C=1.08\) stays | DRIFT \(C=1.08\) stays | | WEBER-ILC1 | drains \(C\to 0\) | drains \(C\to 0\) (gate C3 FAIL on ILC) |

Finding. A uniform boost of the whole current is invisible to present-time pair force. Nothing in this book restores \(\lvert I\rvert\).

Uniform control

Spatial \(B\) stays \(\sim 10^{-15}\) on all books (C0 PASS). ILC-1 still drains \(\lvert I\rvert\) while remaining spatially uniform — C0 does not certify the current amplitude.

3. ILC-1 is not a dynamical book

ILC-1 is the named HOLD-SURF packaging (one light-cone iterate). Used as the force in a time-stepper it is sick:

- UNIFORM already has \(C\sim 0.27\)–\(0.45\) in the early window and \(C\sim 10^{-6}\) late. The unperturbed current stops. - BUNCH / BETA-WAVE at \(\beta=0.9\): \(\lvert C\rvert\sim 10^5\), Larmor proxy \(10^{24}\)–\(10^{27}\). Blow-up, not a mild grow. - That is why C3 FAIL overall. Coulomb and WEBER-INST pass the common-mode null. ILC-1 fails because it is not a Green function (PB2 honesty: lag packaging \(\neq\) retarded theorem).

Do not retune ILC iterates, \(N\), or \(m\) to make C3 pass. The exit is: ILC-1 is not licensed as an EOM for this census.

4. What this means

1. Self-restoring circulating current is not scored. The only clean restore is Coulomb bunching on a ring — ordinary electrostatics, already known, not hold, not Schott/Goedecke. 2. Weber-INST does not help. It weakens the Coulomb restore (RESTORE \(\to\) DRIFT). There is no extra restoring channel in the present pair book. 3. Common-mode \(\delta\beta\) is a pair-force null. Restoring \(\lvert I\rvert\) would need another book (radius DOF, a second seat, or a radiation-reaction law). Jerk-in-Weber is still FORBIDDEN. 4. Bunching is the dangerous kick (H-D5). Under ILC-as-EOM it grows and then blows. That is a warning, not a radiation theorem. 5. Continuum hold, FP9, and DW-RAD-as-law stay OPEN. DW-SG stays CLOSED-NULL.

5. Integrity ledger

| ID | Claim | Verdict | |----|-------|---------| | C0 | UNIFORM \(B\) quiet | PASS | | C1 | BUNCH+COULOMB RESTORE | PASS | | C2 | BUNCH+WEBER class vs Coulomb | SCORED · INST DRIFT · ILC GROW/blow | | C3 | BETA-COMMON pair-force null | FAIL overall · PASS on Coulomb/INST · ILC drains \(\lvert I\rvert\) | | C4 | BETA-WAVE class | SCORED | | C5 | No hold / no Goedecke / no jerk / no promote | PASS | | Split | Coulomb restores bunching; Weber does not restore \(\lvert I\rvert\) | PAIR_FORCE_NO_CURRENT_RESTORE |

Exit: PASS_HOLD_CURR_SCORED

6. Do not

- Sell Coulomb ring restore as hold or as “the current is self-restoring.” - Sell ILC drain/blow as a radiation-reaction theorem. - Shop \(N,m,A,\delta\), or ILC iterate count to flip C3. - Feed Larmor / AL jerk into the EOM to “restore \(\lvert I\rvert\).” - Apply core Theorems 1–4 as the restoring force. - Promote. Flip the public hold chip.

7. One-line for agents

HOLD-CURR: Coulomb bunching RESTORE (ring ES); Weber-INST DRIFT; common-mode |I| not restored by present pair force; ILC-1 EOM drains/blows (not a Green); not hold; no promote.
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