# CKM Package Rail — Closeout / PARK Freeze

### L-PKG texture banked [M] · unique geometric \(V\) FAIL · L-GEO DENIED · rail PARK

**Date:** 2026-08-11  
**Status:** **PACKAGE RAIL PARK** · `PASS_CKM_PACKAGE_RAIL_CLOSEOUT`  
**Arc:** G2-0…4 · C6–C9 · Q-op · C10–C12 · C7/C7b/C7c · §0bn186–190  
**Board:** `a_geom_ckm_status_board.md`  
**Public doctrine chips:** **UNCHANGED** (no free \(V_{\mathrm{CKM}}\); no promote)

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

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## 0. One-line

> **CKM angle/frame package rail is PARKED: bank L-PKG texture (\(\theta_{12,23,13}\), \(\delta_{\mathrm{CP}}\), reconstructed \(\lvert V_{ij}\rvert\)) as **[M]**; unique geometric \(V\) remains FAIL; L-GEO-CKM DENIED; reopen only with a new principle — not more Fano multiples of \(\theta_C\); promote NOT APPROVED.**

---

## 1. Why park now

| Reason | Detail |
|--------|--------|
| Angle rail saturated | C10–C12 fix all four physical angles under packages |
| Frame residual closed as census | C7c: L-PKG matrix contact; unique \(V\) still FAIL |
| No new principle in hand | Further Fano/\(\theta_C\) multiples are re-grinds |
| Integrity | 0 free continuous *angles* ≠ free unique \(V\) theorem |

User directive (2026-08-11): **start at (1) and park CKM.**

---

## 2. What is frozen (banked [M] / [E])

### 2.1 Structure (not mixing matrix)

| Item | Status | Docs |
|------|--------|------|
| \(G_2\) dim 14, Aut(\(\mathbb{O}\)) | **[E]** | G2-1 |
| \(14=\mathbf{8}\oplus\mathbf{3}\oplus\bar{\mathbf{3}}\) | **[E]** | G2-1 |
| Gen pack in \(\mathbf{3}\) | **[M]** PASS | G2-2 |
| \(\mathcal{U},\mathcal{D}\) triads named | PASS named · construction OPEN | G2-3 |
| \(\mathcal{J}_W^{q}\) residual CC | **PASS_NAMED** | C6 |
| Q-op \(\sigma_s\times\sigma_i\) on Fano \(U(1)\) | Operators banked | Q-op |

### 2.2 Angle package texture [M]

\[
\begin{aligned}
\theta_{12}&=\theta_C=\pi/14,\\
\sin\theta_{23}&=\lambda^2,\quad\lambda=\sin\theta_C,\\
\sin\theta_{13}&=\lambda^3/\pi,\\
\delta_{\mathrm{CP}}&=5\theta_C=5\pi/14.
\end{aligned}
\]

| Package | Law | Contact (illustrative) | Doc |
|---------|-----|------------------------|-----|
| Cabibbo | \(\theta_C=\pi/14\) | \(\sim 12.86^\circ\) vs \(\sim 13.04^\circ\) | Q-op |
| C10-W23 | \(\sin\theta_{23}=\lambda^2\) | \(\sim 2.84^\circ\) vs \(\sim 2.38^\circ\) | C10 |
| C11-T13 | \(\sin\theta_{13}=\lambda^3/\pi\) | \(\sim 0.201^\circ\) (thin \(\pi\) ontology) | C11 · C12 audit |
| C12-δ | \(\delta=5\theta_C\) | \(\sim 64.29^\circ\) vs \(\sim 65^\circ\) | C12 |

### 2.3 Reconstructed \(\lvert V_{ij}\rvert\) L-PKG texture [M]

From standard parametrization of the four packages (C7c):

| Class | Elements | Notes |
|-------|----------|-------|
| **Hard contact** | \(V_{ud},V_{us},V_{ub},V_{cd},V_{cs},V_{td},V_{tb}\) | Cabibbo block + \(1{-}3\) / \(t\) strong |
| **Soft** | \(V_{cb},V_{ts}\) | High from C10 \(A=1\) seed (\(A_{\mathrm{eff}}\sim 0.84\)) |
| Unitarity | PASS numeric | |
| Jarlskog \(J\) | \(\sim 3.4\times 10^{-5}\) vs class \(\sim 3.1\times 10^{-5}\) | order/package |

---

## 3. What stays OPEN / DENIED (do not overclaim)

| Residual | Status | Why |
|----------|--------|-----|
| Unique geometric \(V_{\mathrm{CKM}}\) | **FAIL** | C7 / C7c — SU(3) relative frame not killed by packages |
| L-GEO-CKM | **DENIED** | packages ≠ free theorems |
| \(\pi\) seat for C11-T13 | **OPEN hard** / thin ontology | alt \(2/7\) competitor banked |
| \(A\neq 1\) geometric law | **OPEN** | single \(A\) with \(r=1\) FIRE inconsistent (C11) |
| \(\mathcal{U},\mathcal{D}\) construction beyond naming | **OPEN** | G2-3 |
| Absolute quark MeV / mass-matrix seats | **OPEN** | not this rail |
| Free full \(V\) from Cabibbo alone | **FIRE** | |
| PMNS transfer of quartering | **FIRE / DENIED** | Foot \(\Delta\theta\neq\theta_C\) |
| Public promote / doctrine chip flip | **NOT APPROVED** | |

### Knowledge rule (stands)

```text
Same Fano circle φ = 2π/7
  ├─ Foot Δθ = φ sin²(φ/2)     lepton book
  └─ Cabibbo θ_C = φ/4 = π/14  CKM package [M]
Do NOT identify these quanta.
```

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## 4. Reopen criteria (only)

Reopen the CKM rail **only** if at least one **new principle** is on the table:

| Principle class | Example (not claimed) |
|-----------------|------------------------|
| Mass-matrix seats | Dial-free Weber/binding law fixing relative \(\mathcal{U}\)–\(\mathcal{D}\) frames |
| Triple LQ law | \(T(2,3)/T(3,2)\) dual extended dial-free beyond gen-1 |
| True U–D differential | Q-op or parallel transport that produces full \(3\times 3\) \(V\), not only \(\theta_C\) |
| Seat for \(\pi\) (or kill) | Geometric derivation of \(1/\pi\) in C11, or honest demote to \(2/7\) |

**Do not reopen for:** extra \(\phi/n\) halves, PDG refits, PMNS copy, “0 free angles ⇒ L-GEO”, promote pressure.

---

## 5. Document map (park index)

| Slice | Role |
|-------|------|
| `a_geom_ckm_status_board.md` | Live chip board (PARK) |
| G2-0…4 · C6 · C7 · C7b · C8/C9 | Structure + join + moduli |
| Q-op · π/14 origin · quartering | Cabibbo package |
| C10 · C11 · C12 | Angle packages |
| **C7c** | Matrix reconstruction + false-uniqueness kill |
| **This closeout** | Formal PARK freeze |

Handover: §0bn186–190 (packages + C7c); this closeout §0bn191.

---

## 6. Certificate

```text
CKM package rail:          PARK
L-PKG angle texture:       BANKED [M]
L-PKG |Vij| texture:       BANKED [M] (7 contact / 2 soft)
unique geometric V:        FAIL
L-GEO-CKM:                 DENIED
public promote:            NOT APPROVED
doctrine chips:            UNCHANGED
reopen:                    new principle only
```

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## 7. One-line (banked)

> **CKM package rail PARK: L-PKG V texture [M]; unique V FAIL; L-GEO DENIED; no promote; reopen only with new principle.**