s1088 — electron as 'two-diameter width of time circles': closure arithmetic
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[1] Candidate dial models on R² ⊗ R^27 (future winding ⊕ past winding)
  [PASS] carrier dimension = 54 = 27 future ⊕ 27 past
  [PASS] M1 (plain): P² = +1
  [PASS] M2 (spinor): J² = −1
  [PASS] M1 swaps future→past winding
  [PASS] M1 swaps past→future winding
  [PASS] M2 swaps future→past winding
  [PASS] M2 swaps past→future winding
  [PASS] M2 carries the one-way reflection sign (fwd∘bwd = −1); M1 does not (+1)

[2] Closure arithmetic (half-turn = one diameter step; 2 steps = 1 circle)
  [PASS] M1 closes after 2 half-turns = ONE full circle (360°)
  [PASS] M2 closes after 4 half-turns = TWO full circles (720°)
  [PASS] M2 at one full circle (2 half-turns) = −1, NOT closed (the projective flip)
    → M2 width: 4 diameter-steps = 2 time circles. 'TWO-DIAMETER' PER CIRCLE,
      TWO CIRCLES TO CLOSE — the PI's phrase is the spinor closure, exactly.

[3] Which model is the printed clock? (appendix_h invariants; cited)
    printed: T² = −1 · T⁴ = +1 ('two moments') · symplectic · swaps windings
             · PROJECTIVE doubling (32→64).
  [PASS] M2 is Ω-symplectic: JᵀΩJ = Ω
  [PASS] M1 is NOT Ω-symplectic: PᵀΩP = −Ω (anti-symplectic — the corrected-away model)
  [PASS] M1 ELIMINATED by print (P²=+1 contradicts T²=−1)
  [PASS] M2 matches ALL printed type invariants (square −1, order 4, symplectic, swap)
  [PASS] ray-order 2 vs vector-order 4: the 2:1 (projective) cover is present in M2
    ⚠ IDENTIFICATION NOT CLAIMED: M2 shares the live T's type invariants;
      equality with the live 56 operator is the D1011-class construction.

[4] Flicker-frame cross-checks (consistency identities, NOT new physics)
  [PASS] zitter factor-2 bookkeeping: 2ω₀ completes exactly 4 cycles per closed width
  [PASS] [s500] S₀ = ln(φ²) = 2·ln(φ) (identity holds to 1e-15)
    S₀ = 2 ln φ = 0.962423650119  (per-tick proper-time rate, cited [s500])
    ⚠ Rev29 FENCES: ω₀ is a declared input; the dial is not asserted to BE
      physical zitterbewegung; no measured electron property is claimed.

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VERDICT (type; no tier moves, no public observable moves):
  'ELECTRON = TWO-DIAMETER WIDTH OF TIME CIRCLES' — TYPE-ADMISSIBLE,
  as the exact closure arithmetic of the certified spinor dial:
    · one circle = two diameter-steps (half-turns);
    · the certified T²=−1 forces closure only at FOUR diameter-steps
      = TWO full time circles (720°) — the electron-type envelope is
      literally two circles wide in the constructed clock;
    · the one-circle (plain, P²=+1) reading is ELIMINATED by print.
  NOT CLAIMED: physical zitter identity (Rev29 fence); live-56 equality
  (D1011-class); any measured width of the physical electron.

ASSERTS: 18/18 passed
s1088 END
