# 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]**

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## 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*.

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## 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**.

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## 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`

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## 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.**