Source
engines/majumdar_lab/package/multilayer_autonomous_optimizer/fryett_q_series_phase4/STATUS_PHASE4.md · assembled 2026-07-29 15:57 UTC.
Phase 4 status¶
Completed¶
- Complete normalized real-Zernike modes through arbitrary total disk degree.
- Normalized Legendre modes through arbitrary thickness degree.
- Exact thickness selection rule and spectrally convergent disk projection.
- Vectorization over all three field components and every physical hole.
- Exact numerical reduction to the Phase-3 constant mode at degree zero.
- Higher-order outgoing cavity determinant and complex simple-pole tracker.
- A runner for the first coupled truncation sequence.
- A panelized beta contour added after the global tangent rule failed its first pole-convergence test.
What the first table can establish¶
- Whether a simple numerical root can be followed as basis and quadrature orders are raised.
- Which truncation axis immediately dominates movement of that root.
- Whether reciprocity and residual errors remain small during tracking.
It cannot yet establish the Fryett Q. The table begins with only the nearest hole pairs, low polynomial degree, and modest momentum/contour orders.
First branch-labelled results¶
All entries below are the same lower-half-plane branch, labelled by null-vector overlap. They are diagnostics, not the Fryett result.
| Axis | Truncation | Provisional Q |
|---|---|---|
| segmented beta contour | order 8 | 11.8087 |
| segmented beta contour | order 10 | 12.7131 |
| segmented beta contour | order 12 | 12.7897 |
| hole basis | Zernike 0, z 0 | 11.8087 |
| hole basis | Zernike 1, z 0 | 11.2401 |
| hole basis | Zernike 1, z 1 | 11.2249 |
| transverse momentum | order 12 | 11.8087 |
| transverse momentum | order 14 | 11.0022 |
| transverse momentum | order 16 | 11.7884 |
| transverse momentum | order 20 | 13.6093 |
| physical holes | 12 total | 11.8087 |
| physical holes | 14 total | 10.3108 |
| physical holes | 16 total | 12.0109 |
| physical holes | 20 total | 9.9080 |
The longitudinal contour is beginning to stabilize: orders 10 and 12 differ in Q by about 0.6%. The first in-plane hole modes shift Q by about 5%, while the first thickness mode changes it by only 0.14%. The transverse-momentum and physical-hole axes are plainly not converged.
Next step after this checkpoint¶
Replace the transverse tangent-map quadrature by a fixed-cutoff, fixed-panel rule analogous to the repaired beta contour. Converge its cutoff and panel order first; then add the remaining mirror holes and repeat every axis around a higher common baseline. Only then should the comparison with the reported Q be unpinned.