Scientific status and decision ledger

What has been demonstrated

The code implements a reciprocal staggered-edge 3D FDFD Maxwell operator with transformation-optics PML in the transverse directions and exact semi-infinite periodic mirrors in the longitudinal direction. The mirrors are converted into frequency-dependent boundary self-energies by exact period condensation and a retarded surface Green function.

The optimizer protects a full air strip, filters and projects free-form cell-density variables elsewhere, and supplies analytic gradients for fixed-frequency log-LDOS, local pole Q, and a multi-frequency Loewner pole-Q surrogate. Every accepted step is independently checked by real-axis rational continuation.

Regression status after the shifted-objective, constrained-MMA, adaptive-trust, and parallel provisional-gradient additions: 72 tests pass.

The first atom-aware objective is now implemented: centered z-projected LDOS at the normalized 780 nm transition, divided by a same-grid homogeneous- cladding LDOS. The homogeneous normalization returns exactly one on the uniform regression model, its analytic log-objective gradient passes a directional finite difference, and a bounded symmetric small-grid step raises the objective while preserving the exact air strip. See ATOM_COUPLING_OBJECTIVE.md.

Current fine-grid result (2026-08-17)

The exact y/z parity backend has now reacquired and accepted the fine-grid target pole using a 41-point full-cluster sweep, a 449-point dense local sweep, and a separately solved 28-point confirmatory grid. Periodic-lead branch edges bracket the target; the versioned sheet-local-v2 protocol keeps those non-meromorphic edge neighborhoods in the wide identity check while fitting the target pole only on its predeclared, single-sheet interval. The accepted baseline pole is

This baseline also passes all six prescribed transverse-PML perturbations plus the baseline case. The maximum complex pole displacement is 0.005713 halfwidths, the total Q-fit span is 0.7526%, the minimum possible-dielectric to PML clearance is 0.20 lambda0, every case passes its fresh spectral gate, and the protected air-strip density is exactly zero in every case. This is a PML-converged controlled-grid pole identification, not a physical or grid-converged device Q.

Two unattended common-ascent trust steps followed by one shifted constrained- MMA step have now been independently accepted. Centered z-projected atom-LDOS enhancement increased from 0.5852943111 to 0.5861772358, while independently fitted Q increased from 172.1616866 to 172.7063891. In the latest step alone, moving-pole normalized LDOS increased from 1.8839159702 to 1.8878077298; the 0.002 trust-radius proposal required no backtrack and had predicted/observed shifted-objective agreement 0.98168. Its fresh sheet-local validator passes with maximum confirmatory NRMSE 2.029e-11; air-strip density is exactly zero and reflection error is 7.43e-16.

The latest topology then passed its own six transverse-PML perturbations plus baseline. Maximum complex-pole displacement is 0.005698 halfwidths, total fitted-Q span is 0.7542%, minimum possible-dielectric/PML clearance is 0.20 lambda0, and every case passes the independent spectral gate with the exact air strip empty. The campaign is therefore PML converged on this controlled grid and the full unattended cycle is demonstrated. It is not grid converged and its fitted Q is not a physical device-Q claim.

The earlier pure atom-LDOS trial is retained in outputs_atom_cooperativity_yz_step1_rejected_q_decrease. It raised LDOS but lowered Q, exposing a missing fail-closed Q gate. The production runner now requires both quantities to improve and uses fresh local LDOS and Loewner-Q gradients to construct a bounded common-ascent direction. The current production proposal instead follows a retarded-real-axis Loewner pole, includes the device and homogeneous frequency derivatives in shifted cooperativity, solves a constrained moving-asymptote subproblem, and still requires independently evaluated fixed-atom LDOS, shifted LDOS, and Q to improve. See SHIFTED_COOPERATIVITY_ARCHITECTURE.md and OPTIMIZATION_ACCELERATION_REPORT.md.

Accepted controlled-grid result

Four independently accepted coarse Loewner steps produced:

194.98 -> 195.35 -> 196.35 -> 198.36 -> 200.33.

The Q=196.35 coarse checkpoint passes a seven-case rational PML sweep. The Q=200.33 update did not repeat that entire sweep before controlled refinement.

On the 20 x 18 x 14 controlled grid, refinement exposed overlapping modes near 1.073 and 1.079. A merged 69-frequency dataset combines a 41-point wide window with a 29-point dense local window. Seven field probes and four interleaved holdout folds give the accepted upper pole

All seven combined spectral gates pass.

What has not been demonstrated

• Grid-spacing and finite transverse/defect-domain convergence are incomplete.
• The centered z-dipole field is now solved in an exact y/z parity sector in the reflection-closed backend. Exact x reduction is not implemented.
• Total pole Q has not been decomposed into desired waveguide coupling and parasitic radiation/material loss.
• No guided-port overlap, beta factor, or input/output coupling objective is implemented.
• The driven-field energy fractions are localization diagnostics, not a rigorous dispersive quasinormal-mode volume or atom-position Purcell factor.
• Materials are nondispersive and normalized; absorption and realistic Si3N4 data are absent.
• The density field is not yet a binary, minimum-feature, etch-angle-tolerant, erosion/dilation-robust fabrication design.
• Atom trapping, Casimir-Polder forces, tweezer scattering, heating, and mechanical/thermal constraints are not in the optimizer.
• The implemented atom objective assumes a centered z-polarized transition. Trap-position/orientation uncertainty, bare coupling g, and a rigorous QNM normalization are not yet implemented.

Why the current validation is elaborate

A scalar response around the refined resonance is not reliably one-pole. Changing AAA order moved the apparent upper Q from roughly 750 to 2000. A single Lorentzian also disagreed. The accepted estimate therefore requires:

• wide and dense-local frequency windows;
• seven different linear field outputs sharing the same physical poles;
• interleaved frequency holdouts;
• pole, response, and Q stability;
• an independent Fano-linewidth estimate; and
• a SIMO Loewner realization.

This complexity is not cosmetic. It prevents the optimizer from switching between overlapping modes or fitting analytic background curvature as a high-Q pole.

Known rejected result

An earlier compact-domain topology appeared to reach Q=24,867 and showed good pole/linewidth agreement. It failed because the design region overlapped the y-PML, a floating-point boundary comparison broke reflection symmetry, and PML perturbations changed Q to 25--56 or moved the pole into the upper half plane. This established that linewidth agreement alone is insufficient.

Fine-grid handoff

The original full-domain transfer remains at outputs_refined_fine_workstation64_checkpoint/run_data.npz. Geometry-only transfer to the exact y/z backend is stored at outputs_refined_fine_yz_symmetry_checkpoint/run_data.npz; the qualified spectral and PML evidence are in outputs_fine_yz_symmetry_combined_sheetlocal_dense449_confirm28 and outputs_fine_yz_symmetry_combined_pml_sheetlocal_v2. The first accepted common-ascent checkpoint is outputs_atom_cooperativity_yz_step1/run_data.npz with adjacent configuration, metrics, restart spectra, geometry, and field diagnostics. The latest demonstrated unattended checkpoint and its checkpoint-bound spectral/PML evidence are under outputs_shifted_mma_demo/step_0001, with campaign state at outputs_shifted_mma_demo/campaign_state.json.

Exact transverse-symmetry backend

The original solver used all 68,640 electromagnetic unknowns even when its 960 topology variables and gradients were projected over eight x/y/z reflections. An opt-in reflection-closed backend now solves the exact y/z parity sector of the centered z dipole: 16,960 field unknowns and a 424-vector lead surface plane. Small-grid full-versus-reduced comparisons agree to 1.2e-14 in the field and 1.5e-14 in the raw gradient. The fine boundary identities pass, the air strip remains exactly zero, and the cladding-to-PML clearances are unchanged. One fine-frequency solve measured 6.09 s and 0.677 GiB, compared with about 280.05 s and 17.685 GiB for the prior full solve.

No pole or Q was transferred across this boundary change. The eventual fresh 41-point wide, 449-point local, and independent 28-point confirmatory sweep finds and spectrally accepts

The old 113-point merged-window failure was traced to periodic-lead square-root branch edges, not solve noise. The branch-aware sheet-local protocol passes, the baseline PML gate passes, and the first common-ascent topology step passes fresh spectral validation. See SYMMETRY_ACCELERATION.md for the formulation and complete evidence.

Criteria for moving to the next research phase

The optimizer can now run a multi-step campaign unattended on this controlled grid. Every topology update remains fail-closed at fresh checkpoint-bound wide/local/confirmatory spectral gates and must improve fixed-atom LDOS, moving-pole LDOS, and fitted Q while remaining inside the atom-detuning and pole-motion limits. Full seven-case transverse-PML campaigns now follow the explicit adaptive-pml-v1 cadence: intervals grow through 1, 2, 3, 5, and at most 8 only after repeated tightly converged results, while large pole, Q, or cumulative topology motion forces an early campaign. Intermediate checkpoints are spectrally accepted, not PML converged. Any scheduled or triggered PML failure remains a scientific stop condition. The controller is restartable, carries adaptive trust radii, locks against concurrent runs, and preserves rejected/partial evidence and every cadence decision.

The production domain-expansion path moves each defect/lead interface outward by two complete mirror periods while keeping the transverse grid and slab thickness fixed. This exposes 1,152 additional x-direction design voxels at modest field-solve cost and preserves the mirror phase. The resulting 64 x 26 x 22 checkpoint remains a topology transfer only until its fresh 41/449/28-point spectral bootstrap and checkpoint-bound transverse-PML gate pass; no smaller-domain pole or Q is carried into that decision.

In parallel with a controlled-grid optimization campaign, obtain a second controlled grid/domain point and a credible convergence trend. That evidence is required before any physical Q claim. Guided-mode port projections, atom-position/orientation robustness, and fabrication robustness remain later research phases.