Integrate unresolved ARTS2D resonances into detector bins

[joglekara]

Builds on #142 (merged). Fixes #134.

What changed

• Exposes reusable ARTS2D numerator and dielectric terms on arbitrary wavelength nodes while caching the EDF sinogram.
• Finds every sign-changing zero of Re(epsilon) on a fine fixed scan, differentiates roots implicitly, and tan-maps disjoint coarse-panel neighborhoods through the local complex-linearized resonance.
• Integrates the full collisionless spectrum directly into calibrated detector-bin edges using exact Gaussian-CDF bin probabilities. No collision model or dielectric epsilon floor is introduced.
• Separates root_scan_panels (4096) from integration_panels (256), raises static root capacity to 16, and returns fatal fixed-shape diagnostics instead of partial results.
• Applies rectangular iawfilter attenuation to the continuous source spectrum with exact integration breakpoints; iawoff remains a detector-space visualization mask.
• Replaces index-space spectral/angular blur and peak restoration with physical-coordinate, unit-area bin responses. Nonuniform angular axes use the exact dense operator; uniform fine spectral grids use the identical memory-linear Toeplitz/FFT operator.
• Preserves calibrated detector edges through data reduction, including ragged final groups, and avoids a second spectral blur/binning pass downstream.

Direct quadrature versus local correction

On the corrected 22-degree Maxwellian benchmark, the unresolved root is at 474.199678891 nm with 3.49399e-4 nm HWHM. The adaptive detector-area reference is 0.6525638697.

Method	Detector L1 error	Gradient L2 error	Warm value	Warm value+gradient
Full root-aware quadrature	0.0393-0.0399%	0.0569-0.1035%	3.721 ms	3.805 ms
First-order local correction	0.0138-0.3162%	15.5-210.5%	3.722 ms	2.622 ms

The local method gives no forward speedup and its faster backward pass is numerically wrong, so it is recorded as a rejected benchmark rather than exposed to fitting.

Root-scan and convergence evidence

The representative 449-670 nm spectrum has eight roots, including a pair only 0.096012 nm apart. Across 39 scan phases, 2048 panels missed that pair in six phases; 4096 and 8192 found all eight every time. Warm one-geometry scan timing was 23.5/32.2/55.8 ms, so 4096 is the smallest tested phase-stable default.

For the physical narrow-line regression, 64-to-128 and 64-to-256 integration refinement changed detector values by at most 4.94e-5 and gradients by at most 2.64e-4. Fine-grid phase variation was 2.10e-6 for values and 2.06e-5 for gradients, well below the 1% target.

Validation

• 186 passed, 5 skipped on both Linux CPU and project GPU for rebased head 6917ec4d: https://github.com/ergodicio/tsadar/actions/runs/33335580949
• Full-range adversarial-phase regression requires all eight roots and finite nonzero reverse-mode drift gradients.
• Close multiple roots, close notch breakpoints, nonuniform detector bins, exact area/centroid preservation, constant spectra, JIT/vmap, aperture topology, and no-double-IRF paths are covered.
• The ARTS1D golden snapshot was refreshed because it encoded the removed index-space shift and peak restoration; independent physical-coordinate IRF tests provide the correctness reference.

[joglekara]

Manual validation on current head 3cc7296 is green: both Linux CPU and project GPU jobs completed the full suite (186 passed, 5 skipped). Run: https://github.com/ergodicio/tsadar/actions/runs/33329223046

This was dispatched manually because the workflow only auto-triggers for PRs based on main, while #143 is intentionally stacked on #142. The first dispatch exposed a test-only GPU allocation problem from using reverse-mode Jacobians for one scalar input and hundreds of outputs; the regression now uses forward mode for the full detector Jacobian and independently checks a scalar reverse-mode loss gradient.