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engines/design23_v1/package/design23_recentered_optimizer/fryett_q_series_phase5/STATUS_PHASE5.md · assembled 2026-07-29 15:57 UTC.

Phase 5 status

Implemented

  • Fixed-width dimensionless transverse-momentum panels.
  • Independent panel-order and cutoff convergence axes.
  • A nesting audit proving cutoff growth preserves all interior nodes.
  • Vectorized two-dimensional homogeneous Green contraction.
  • Direct equivalence check against the original Phase-2 nested loop.

Required numerical sequence

  1. Track the twelve-hole constant-mode branch while raising panel order at a fixed transverse cutoff.
  2. Hold the accepted order and panel width fixed while adding outer panels.
  3. Repeat at the first Zernike--Legendre hole truncation if the constant-mode branch stabilizes.
  4. Add mirror holes up to the full candidate Fryett geometry.

No Q from this phase is accepted until both transverse axes pass.

Numerical outcome

For the twelve-hole broad branch, fixed-panel order is stable by orders 9--10 to 0.025% in Q. Increasing the dimensionless cutoff from 4 to 10 moves Q from 12.12 to 12.30; the remaining tail effect is below 1% beyond cutoff 5 but is not strictly monotone.

The complete legacy reconstruction contains 90 holes. Its constant-hole basis has several resolved lower-half-plane branches. The largest Q found in the scanned band is approximately 352 at

omega/omega_ref = 1.02144988 - 0.00145109 i.

Refining that branch gives Q values between about 354 and 376 over the tested transverse orders and cutoffs. This is a genuine finite-cavity resonance but is still almost three orders of magnitude below the reported Q near 100,000.

Most importantly, enlarging the full-geometry hole basis from constant modes to first-order in-plane Zernike modes moves the same branch from Q = 351.96 to Q = 98.78. The null-vector overlap remains 0.9999997 and the pole residual is small, so this is a truncation failure rather than branch loss.

Next required step

Raise the full-geometry hole basis through Zernike degrees 2, 3, and beyond, with corresponding waveguide cross-section degrees. The present Q must not be compared quantitatively with the paper until that sequence stabilizes.