s1107 — selection census of the mixing chain
  choice                               menu  bits  fixed by                          caps
  first-row ROUTE (A|B)                   2  1.00  by kaon data (override)            |V_us|, |V_ud|, |V_ub|
  θ₂₃ OCTANT (7/16 | 9/16)                2  1.00  by data (lower octant, 2.3σ)       θ₂₃, |V_cb|
  mass ORDERING (NO | IO)                 2  1.00  assumed                            θ₁₂ᴾᴹᴺˢ, δ_CP
  δ_CP FRAMING sector (1,3)               3  1.58  chosen (1,3)                       δ_CP
  Dirac | Majorana                        2  1.00  assumed Dirac                      δ_CP (phases), Σm_ν
  θ₁₃ EXPONENT (sin^n(π/8))               4  2.00  n=4 by identity/heuristic          θ₁₃
  the 9 in |V_cb| = 1/(9√7)               9  3.17  by data                            |V_cb|
  δ_CKM correction (c,k) in φ+cφ⁻ᵏ       64  6.00  by fit (5,5); 28/64 within 1σ      δ_CKM
  RAW SUM of log₂(menu) over the declared menus: 16.75 bits across 8 choices — menus are DEPENDENT (see the reverse map);
  no additive bit total is asserted (A1566 §S1107-4). The |V_cb| menu is a LOWER BOUND (1..9), so the raw sum is a lower bound too.
  fixed by looking at data: 4 · assumed/chosen without data: 4
  [PASS] every listed choice caps at least one row (this is what v1's :32 line actually tested)
  [PASS] no choice has a continuous menu — all are ℤ₂ bits or small integer labels

(0) REVERSE MAP — row → the choices it inherits, with multiplicity (v2; the v1 print 'exactly one per row' was FALSE)
  |V_us|         ← 1: first-row ROUTE (A|B)
  |V_ud|         ← 1: first-row ROUTE (A|B)
  |V_ub|         ← 1: first-row ROUTE (A|B)
  θ₂₃            ← 1: θ₂₃ OCTANT (7/16 | 9/16)
  |V_cb|         ← 2: θ₂₃ OCTANT (7/16 | 9/16); the 9 in |V_cb| = 1/(9√7)
  θ₁₂ᴾᴹᴺˢ        ← 1: mass ORDERING (NO | IO)
  δ_CP           ← 2: mass ORDERING (NO | IO); δ_CP FRAMING sector (1,3)
  δ_CP (phases)  ← 1: Dirac | Majorana
  Σm_ν           ← 1: Dirac | Majorana
  θ₁₃            ← 1: θ₁₃ EXPONENT (sin^n(π/8))
  δ_CKM          ← 1: δ_CKM correction (c,k) in φ+cφ⁻ᵏ
  rows inheriting MORE THAN ONE choice: ['|V_cb|', 'δ_CP']
  [PASS] |V_cb| inherits exactly two choices — the θ₂₃ octant registration AND the integer 9 (double-capped, A1566 §6)
  [PASS] every row inherits at least one choice

(0b) MENU GATE — every selected value lies in its DECLARED menu (the v1 :19 line failed this: menu 1..8, selected 9)
  [PASS] first-row ROUTE (A|B): selected A ∈ declared menu of size 2 (= menu-size column 2)
  [PASS] θ₂₃ OCTANT (7/16 | 9/16): selected 7/16 ∈ declared menu of size 2 (= menu-size column 2)
  [PASS] mass ORDERING (NO | IO): selected NO ∈ declared menu of size 2 (= menu-size column 2)
  [PASS] δ_CP FRAMING sector (1,3): selected (1,3) ∈ declared menu of size 3 (= menu-size column 3)
  [PASS] Dirac | Majorana: selected Dirac ∈ declared menu of size 2 (= menu-size column 2)
  [PASS] θ₁₃ EXPONENT (sin^n(π/8)): selected 4 ∈ declared menu of size 4 (= menu-size column 4)
  [PASS] the 9 in |V_cb| = 1/(9√7): selected 9 ∈ declared menu of size 9 (= menu-size column 9)
  [PASS] δ_CKM correction (c,k) in φ+cφ⁻ᵏ: selected (5, 5) ∈ declared menu of size 64 (= menu-size column 64)
  Rev32.5 s1107 v1 printed for 'the 9 in |V_cb| = 1/(9√7)': menu 'integer 1..8 (×√7)' (size 8), selected 9 → 9 ∉ 1..8: the A1566 defect, reproduced here as a negative control
  [PASS] negative control: the v1 menu (1..8) does NOT contain the selected 9
  repair: Paper 3 :639 pre-declares only 'small-integer menu' (no numeric range). v2 states the smallest range containing the selection,
  1..9, and labels it a LOWER BOUND. The menu was never widened silently: this line is the disclosure.

(1) THE COMMONALITY — stated once
  Every row below theorem is a THEOREM-GRADE MAP evaluated after ONE OR MORE discrete choices: a route, an octant
  registration, an ordering, a framing sector, an exponent, an integer coefficient, a (c,k) pair. Not one of them is a
  continuous fit. Some rows share or accumulate dependencies (|V_cb| inherits two); no additive bit count follows from
  the raw menus — the raw sum ~17 bits is a dependent, lower-bound figure, printed for scale only.
  KNOT lens: all eight are FRAMING/ORIENTATION data — writhe signs (octant, ordering), a choice of braid word
  with the same closure (route), a sector label (δ_CP), an integer twist count (exponent, the 9, the 5). The knot
  TYPE (the theorem layer) is fixed; the framing is not. This is the same sentence OPEN_ITEMS already prints for
  mass ('absolute scale and generation order are framing/orientation data') — mixing has the same disease.
  CT lens: each choice is a hom-set with >1 element and NO universal property. The theorem rows are the ones
  where the hom-set is a singleton (PMNS unitarity; tanθ = √3·P_k given the eigenvalue). Promotion = exhibit the
  universal property, i.e. a selector functor whose value on the framing is forced. F-SEL(c) closed negative
  for Φ_diag (A1533) — that was one attempt at exactly this object, for one choice.

(2) LEVERAGE — which single derivation buys the most rows
  rows freed per choice derived:
    3  ← first-row ROUTE (A|B)
    2  ← θ₂₃ OCTANT (7/16 | 9/16)
    2  ← mass ORDERING (NO | IO)
    2  ← Dirac | Majorana
    1  ← δ_CP FRAMING sector (1,3)
    1  ← θ₁₃ EXPONENT (sin^n(π/8))
    1  ← the 9 in |V_cb| = 1/(9√7)
    1  ← δ_CKM correction (c,k) in φ+cφ⁻ᵏ
  ★ The ORDERING bit is the keystone: it frees θ₁₂ᴾᴹᴺˢ AND δ_CP, and s1104 shows the resolvent rung d=2 already
    predicts it (R₂ ≪ 1 ⇒ NO) with a falsifiable corollary (Σm_ν ≈ 59 meV). One PI ruling on d=2 is worth two rows.
  ★ The ROUTE bit and the 9 share a missing object (block-dependent Peirce weight: 1/√6 on J₁₂, 1/(9√7) on J₂₃):
    one rule would free |V_us|, |V_ud|, |V_ub| AND |V_cb| — four rows. s1105 shows the naive S₃-average is NOT it.
  ★ δ_CKM: s1106 shows the coincidence is one ARGUMENT (√G₇) fed to the theorem-grade angle functor; the bare φ
    argument already sits at −0.37σ. The cheapest honest move is to PRINT bare φ beside G₇ and let data decide.

(3) WHAT THE LENSES SAY TO STOP DOING
  · Stop motivating integers one at a time (the 5, the 9, the 4). They are twist counts on the same framing; a
    framing theorem fixes them together or not at all.
  · Stop scoring loaded rows by σ alone. A 1.1σ agreement reached after a data-selection among N siblings is
    evidence discounted by the selection (look-elsewhere: the best of N is expected to look good). Print the bits beside the σ.
  · Stop calling δ_CKM a phase. Its type is angle (s1106). The phase-type object is the Jarlskog area, unpredicted.

VERDICT
  Loaded + coincidence rows share one anatomy: theorem map ∘ unfixed framing. Attack order by leverage:
  (1) ORDERING via d=2 [2 rows, PI ruling + one lane build]; (2) BLOCK-WEIGHT RULE [4 rows, in-house + lane];
  (3) OCTANT registration/basepoint — a theory-fixed sign of an odd coupling, s501 is a candidate map not a selector (A1566)
      [2 rows; |V_cb| also needs the 9]; (4) θ₁₃ exponent [1 row]; (5) δ_CKM argument [1 row — and print bare φ now].

s1107: ALL CHECKS PASS
