Publication outline

Working title: Inverse design of open nanophotonic cavities through differentiable mode expansions

Target: physics.optics primary, cross-listed physics.comp-ph and quant-ph. Two-column main text (~11 pages including references), self-contained supplement (~37 pages).

Main manuscript — as drafted

§	File	Content
—	00_abstract	Construction, two devices, the direction-vs-magnitude result, ringdown conditions stated in-line
1	01_introduction	Positioning against differentiable GME: real-frequency periodic slab → complex-frequency finite open cavity; four numbered contributions
2	02_method	Conventions; exact parameterized dielectric; outgoing Lippmann–Schwinger and det_reg; guided-plus-continuum Green tensor; Sommerfeld contour; Zernike–Legendre basis; assembled operator
3	03_gradient	Implicit pole derivative, cost, Hadamard boundary form, mode-identity ranking, Sobolev metric
4	04_validation	Operator gates; ringdown-adequacy table; predeclared panel table; the required run-time amendment
5	05_quan_loncar	Device I as a result: local-refinement regime, quantified; matched 24 ps gain with its ringdown condition
6	06_design23	Device II as a result: feed-pole subtraction; 105-step trajectory; geometric restructuring; blueshift and V_eff; excluded step 70
7	07_fidelity	The central result. Bias drift 0.472 → 12.31 within one trajectory; Spearman 0.911 within a fixed protocol; per-step sign agreement explicitly not claimed
8	08_discussion	Consequences for how reduced open-system models should be used; what is not established
9–11	09_methods, 10_data_code, 11_acknowledgments	Short back matter

Five figures: method schematic, Quan geometry, geometry profiles (both devices), Design23 geometry, Design23 trajectory panels, surrogate fidelity.

Supplementary Information — as drafted

Theory (S1–S13), self-contained and in one notation. S1 scope, notation, claim ledger · S2 conventions, QNM normalization, log-Q objective · S3 exact parameterized dielectric and analytic derivatives · S4 outgoing integral equation and the regularized determinant · S5 homogeneous reference Green tensor · S6 stratified reference: Fresnel recursion, Wronskian kernels, Dyson strip · S7 Sommerfeld contour, branch topology, panelized quadrature and its failure modes · S8 Zernike–Legendre aperture basis and projection · S9 symmetry reduction and finite-array assembly · S10 feed-pole extraction and residues · S11 continuation, pole search, mode identity · S12 pole and Q derivatives, reverse mode, Hadamard form, trust ladder · S13 optimizer, trust region, acceptance gates.

Evidence (S14–S19). S14 analytical convergence and gradient validation, with the audited value table · S15 FDTD protocol, ringdown audit, predeclared panel and its amendment · S16 Quan campaign in full, including the Fryett lineage caution · S17 Design23 campaign, full 33-point trajectory table, geometry metrics · S18 rejected approximations and failures, including the flat direction that the pre-repair operator scored as a 3.6× gain · S19 reproducibility and the SI-section-to-derivation-phase provenance map.

Narrative rule

The exceptional result is not "the analytical solver predicts the exact FDTD Q" — it demonstrably does not, and the paper quantifies by how much. It is that a fast, structured open-system model supplies ascent directions that an independent solver confirms at trajectory scale in two distinct physical settings, while its absolute linewidth drifts by more than an order of magnitude along the very trajectory it is driving. Every draft must protect that distinction.

Numbers

No number is typed into the LaTeX. analysis/export_values.py writes manuscript/values.tex (193 macros) and analysis/export_tables.py writes manuscript/tables/*.tex, both from JSON under results/. When the panel replaces a provisional endpoint, the JSON changes and the prose does not.