s1112 — CT/knot lens: three walls, one clock

(1) THE CLOCK'S CRT FACTORS ARE THE THREE FRAMING DATA (appendix_m :235 — U₆₀ = U₃² ⊗ U₄⁻¹ ⊗ U₅⁻²)
  [PASS] C₅ component of the registered clock generator, U₅⁻² = e^(−4πi/5), equals θ_τ⁻¹ (|diff| = 0.0e+00) — the P1 twist IS a clock element
  [PASS] θ_τ = ω₆₀^24: k = 24 is EVEN ⇒ θ_τ is NOT in the odd spectrum of U₆₀ (U³⁰ = −I) but IS in the spectrum of U₆₀² (one FULL turn = two moments)
    reading: C₃ (U₃²)  ↔ the 3:1 grading rate (singlets:matter)         — a RATE (continuous-time datum)
             C₄ (U₄⁻¹) ↔ T⁴ = +1 four-tick return = M2 closure order 4 (s1088) — a COUNT (the α cell's double cover)
             C₅ (U₅⁻²) ↔ θ_τ, the annular ribbon twist                      — a PHASE (P1's framing)
    Knot lens: these are the three components of a FRAMING — rate, twist count, twist phase. Călugăreanu–White: Lk = Tw + Wr.

(2) P1 TEST — does the clock's twist PHASE have the right n-profile for the ²⁴Mg/²⁸Si deficit?
    data window (|deficit| > 0.05 T₃): ON = [6, 7] · OFF = [3, 4, 5, 8, 9, 10]
    ribbon full-twist phase θ_τ^(1−n): n=6: +0×2π/5 · n=7: -2×2π/5 · n=8: +1×2π/5 · n=9: -1×2π/5 · n=10: +2×2π/5  (c1112 ✓: 0, −2, +1, −1, +2)
    the twist phase CLOSES (=1) at n ≡ 1 mod 5: n = [6, 11] — i.e. exactly at n = 6 (²⁴Mg) and n = 11 (= N★)
  [PASS] ANTI-CORRELATION: the phase is trivial at n=6 where the deficit is LARGEST (−0.1007) ⇒ a twist-PHASE energy has the WRONG profile for P1
  [PASS] NO single residue class of any clock factor (m ∈ 2..60) gives the window ON={6,7} — the P1 support is a THRESHOLD, not a cyclic closure (found: [])
    CT reading: a threshold in n is the signature of a FILTRATION, not a grading. The registered candidate is the through-string
    filtration of annular TL modules (Graham–Lehrer W_{k,z}: k through-strings, twist parameter z) — the module with k through
    strings is EMPTY for n < k. P1's window (on at 6,7, off at ≥8) is the MIRROR of that: something present at n ≤ 7 that a
    k = 8 object kills. Plan P1-CT: compute the second-order shift sector-by-sector in W_{k,z}, k = 0..3 (Fibonacci truncation),
    with z = θ_τ (now a registered clock element); the coefficient is then a matrix element, not a unit coupling.

(3) ⁶⁴Ge TEST — is the radius deficit a framing (discrete) or a writhe (continuous) object?
  [PASS] deficit ⁶⁴Ge→¹⁰⁰Sn is monotone (s1101 PASS line) and its second differences on the target line are 0 — no oscillation, no residue-class structure
    Knot lens: a smooth accumulating term is WRITHE (geometry, coiling, overlap) — not TWIST (counted ticks). Lk = Tw + Wr:
    the ladder that is sharp to Ca is the TOPOLOGICAL part (Lk, additive over cells); the deficit is the non-additive part.
    CT reading: the length functor ℓ on cells must be ADDITIVE under cell concatenation (a monoidal functor) for the ladder
    to be sharp; the curvature deficit is the FAILURE of monoidality — a natural transformation ℓ(A⊗B) → ℓ(A)⊗ℓ(B) that is
    not an isomorphism. That object is the OVERLAP (c_R/R_α = 0.914, c1110) — continuous, not a count.
    Plan Ge-CT: (i) get the ADDITIVE part from the clock count (D1228 N_α); (ii) the non-additive part is a writhe integral
    over the packing — the one place a CONTINUOUS geometric input is honest, because Wr is not quantised.

(4) CLOCK LEAD — the count is the C₄ factor's job
    D1228 asks for N_α = ticks per α cell. Lens: the α cell is M2 (closure order 4 = the C₄ factor, T⁴ = +1). A closure count
    lives in C₄ × (full cycles); N_α = 180 = 3 × 60 = C₃-rate × one U₆₀ cycle sits −0.82% off. The forcing question for the
    lane, sharpened by the lens: does M2 closure require ONE full U₆₀ cycle per grading unit (3 units ⇒ 180), or ONE C₄ return
    per cell (4 ticks ⇒ R_α = L_depth/4 = 96 fm, absurd)? The lens PREDICTS the answer must involve the full 60-cycle, because
    only the full cycle carries all three framing data; a single factor cannot price a length that is also a phase carrier.
    3 × 60 → +0.8% · 60 → -66.4% · 4 × 60 → +34.4% · 5 × 60 → +68.0% · 12 × 15 → +0.8% · 4 → -97.8%

(5) THE COMMON OBJECT
    One registered clock, three CRT factors, three walls: P1 = the C₅ PHASE (but with a filtration, not a grading, setting
    its support) · ⁶⁴Ge = the WRITHE the count cannot see · the clock lead = the C₄ COUNT. The single missing map is a
    FRAMING FUNCTOR F: (ClockSector, ⊗) → (Framings, +), F = (rate, count, phase), monoidal on the count, NOT monoidal on
    the writhe. Every wall this arc hit is one component of F evaluated where F is not yet defined.

s1112: ALL CHECKS PASS
