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This is a raw source document. Integrity tags [E] [M] [O] [F] are coloured for readability. Content is as written in the research file.

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]

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. `

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 ``

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.
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