# Larmor \(Q\sim 1/\alpha\) is the right *class*, not the Gamow \(P\)

### \(Q=(3/(2\alpha_{\mathrm{eff}}))(mc^2/\hbar\omega)\) · named \(Q\gg 59\) · damps energy not topology · chips OPEN

**CPT Framework — C3-MODES / LEAD-5 / WOBBLE-P / DW-ALD / AL freeze**  
**Date:** 2026-09-17  
**Status:** **CONSIDERATION + PROBE** · `PASS_LARMOR_Q_HAS_1_OVER_ALPHA_FAIL_AS_P` · \(1/\alpha\) in \(Q\) **PASS** · \(Q=E_0\) **FAIL_NUM** · Larmor \(=\) \(n\to p\) **FAIL_IDENTIFY** · no promote  
**Stimulus:** User — process that sets \(P\) should scale as \(1/\alpha\); Larmor damping of internal modes, quality factor \(\sim 1/\alpha\) times geometry.  
**Parents:** `a_geom_p1_c3_lobe_normal_modes.md` · `a_geom_p1_kramers_c3_lobe_escape.md` · `a_geom_p1_wobble_period_times_probability.md` · `weber_larmor_radiation_reaction_results.md` · `a_geom_dw_sg_schott_goedecke_ontology_freeze.md`  
**Probe:** `scripts/investigations/s3_geometry/p1_larmor_q_c3_modes_probe.py`  
**Data:** `scripts/investigations/s3_geometry/data/p1_larmor_q_c3_modes.json`

Tags: **[E honesty]** · **[E algebra]** · **[E process]** · **[Programme]**

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## 0. One-line

> **The \(1/\alpha\) is real and it is the same numeral as LEAD-5; it does not pay \(P\).** Classical Abraham–Lorentz gives \(Q=(3/(2\alpha_{\mathrm{eff}}))(mc^2/\hbar\omega)\). For \(C_3\) \(E\)-modes that is \(Q\sim 10^3\)–\(10^5\), not \(E_0\approx 59\). Energy lost per cycle \(2\pi/Q\) is \(O(\alpha)\), so \(\tau=T/P\) stays \(10^{-20}\,\mathrm{s}\). \(e^{-Q}\) is the wrong size the other way. Larmor damps **oscillation energy**, not baryon topology, and AL is not the CPT radiation law. No promote.

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## 1. Why this was the right thing to try

Kramers \(B/T\) is \(\alpha\)-free once \(B\) is MeV Coulomb. A dimensionless action \(\propto 1/\alpha\) is exactly what minutes need (\(E_0=(3/(2\alpha))\varepsilon\)).

Radiation reaction of a dipole oscillator:

\[
\tau_{\mathrm{AL}}=\frac{2\alpha_{\mathrm{eff}}}{3}\frac{\hbar}{mc^2},\qquad
Q=\frac{1}{\tau_{\mathrm{AL}}\omega}=\frac{3}{2\alpha_{\mathrm{eff}}}\frac{mc^2}{\hbar\omega}.
\]

\(\alpha_{\mathrm{eff}}=\alpha(q/e)^2\). For \(q=e/3\), \(Q\) is nine times the charge-\(e\) value. The prefactor **is** \(3/(2\alpha)\).

The \(C_3\) \(E\)-mode **does** carry a linear dipole (probe: \(\partial\mathbf{d}/\partial\mathrm{amp}\neq 0\)). Dipole Larmor applies as *classical* radiation of that mode.

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## 2. Named numbers

Lobe mass \(m_0/3\). \(\hbar\omega\) from C3-MODES.

| \(R\) | \(q\) | \(Q\) | \(Q/E_0\) | \(\tau=T_{\mathrm{circuit}}/(2\pi/Q)\) |
|-------|------|------:|----------:|--------------------------------------:|
| Compton \(m_0\) | \(e\) | \(1.64\times 10^3\) | 28 | \(3.5\times 10^{-21}\,\mathrm{s}\) |
| Compton \(m_0\) | \(e/3\) | \(1.47\times 10^4\) | 248 | \(3.2\times 10^{-20}\,\mathrm{s}\) |
| \(R_p\) | \(e\) | \(1.31\times 10^4\) | 220 | \(2.8\times 10^{-20}\,\mathrm{s}\) |
| \(R_p\) | \(e/3\) | \(1.18\times 10^5\) | 1980 | \(2.5\times 10^{-19}\,\mathrm{s}\) |

To force \(Q(e/3)=E_0\) would need \(\hbar\omega\simeq 9.8\,\mathrm{GeV}\), not \(5\)–\(39\,\mathrm{MeV}\).

**Finding L0 [E algebra].** \(3/(2\alpha)\) in \(Q\) is the same writing as LEAD-5’s prefactor. That is a **clue**, not a mill of \(E_0\) (same family as the Hopf/Willmore waiter: the numeral appears, the map to the exponent is not exhibited).

**Finding L1 [E honesty].** Per-cycle radiated fraction \(2\pi/Q\) is a **prefactor** \(O(\alpha)\), the same lesson as Kramers \(\omega_0\): \(1/\alpha\) here does **not** sit in \(e^{-S}\). Putting \(P=e^{-Q}\) uses the named \(Q\sim 10^4\), not \(59\).

**Finding L2.** Radiation reaction **cools the mode**. It does not change \(T(3,2)\to T(2,3)\). Category error, plus DW-ALD: do not insert point Abraham–Lorentz as the radiation law.

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## 3. Integrity

| Gate | Verdict |
|------|---------|
| \(Q\sim(3/(2\alpha))(mc^2/\hbar\omega)\) | **PASS** |
| Named \(Q=E_0\) / \(P=2\pi/Q\) or \(e^{-Q}\) \(\to\) minutes | **NO** |
| Larmor \(=\) \(n\to p\) | **NO** |
| Mill \(\alpha\) / shop \(\omega\) | **NO** |
| Promote | **NOT APPROVED** |

**Exit:** `PASS_LARMOR_Q_HAS_1_OVER_ALPHA_FAIL_AS_P`

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## 4. Licensed next

Do not mill AL as \(\Gamma_n\). Do not shop \(\hbar\omega\) to \(9.8\,\mathrm{GeV}\). A later \(1/\alpha\) action still has to be an **exponent** (Gamow/EM path), not a quality factor. Pair EOM parked. \(T(2,3)\) not proton mass. \(\alpha\) INPUT. \(a\) INPUT. Do not name \(R\). No hub dump.

**Looked into (17 Sep, E0-READ):** accept LEAD-5 as the exponent law; mill the Coulomb-to-mass *reading*, not a primitive derivation (`a_geom_p1_e0_is_the_law_reading.md`).

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## 5. One-line for agents

> **§LARMOR-Q: classical \(Q\) carries \(3/(2\alpha)\); named \(C_3\) \(Q\gg E_0\); not \(P\); damps energy not topology; chips OPEN; no promote.**