Does the F=4 template move the ePSF and WCS?

What was compared

The Paper 1 pipeline (MODEL_FREEZE D15) fits the ePSF/WCS on the F=1 Hotpants difference image, builds the F=4 per-band template from that fit, makes the final difference image, then refits on it (D14) to check nothing moved. The fit stars (T<13) are never in either template, so the template only changes the faint neighbours and background around them.

The official check waits on the D16 fit recipe. This dry run uses the chain that already exists on disk:

• Fit: the chroma-v2 A3 fit of F1 (plain fine-neighbour prior, dev f5e3605).
• F=4 image: perband_3field_20260929 … band_a3w, built with that fit's kernels and the adopted D13 band weights.
• Refit scene: the F=1 training scene with only the pixel values swapped for the F=4 image. Stars, 15×15 stamps, roles, masks and neighbour pairs are unchanged. Swapping the F=1 image back in reproduces the original scene bit for bit.
• Pedestal: the F=4 image sat a uniform +0.0176 e⁻/s above the F=1 image. It was subtracted before fitting; one run keeps it to measure its effect.

How a star's position change is measured

The WCS and the ePSF centroid can trade off against each other without moving where a star lands, so each comparison uses the effective position change

• $\Delta\mathbf{x}_i^{\rm eff}$: change in star $i$'s rendered position between two fits [TESS px; quoted in mpx].
• $B_i$: the Chebyshev WCS basis evaluated at star $i$ (21 terms per axis, fixed by the scene's source bundle).
• $\Delta\mathbf{c}$: difference of the fitted wcs_coeff vectors (42 coefficients, fitted).
• $\Delta\bar{\mathbf{m}}(\mathbf{r}_i)$: change in the ePSF's Gaussian-windowed centroid ($\sigma=1.5$ px window), interpolated from the 6×6 node grid to the star's detector position $\mathbf{r}_i$ [px].

ePSF size uses the same window: $T = I_{xx}+I_{yy}$, the sum of the windowed second moments of a node's ePSF [px²]; elongation is $e_1 = I_{xx}-I_{yy}$ and $e_2 = 2I_{xy}$.

How much do the fitted pixels change?

Comparing the two images over the 14,733 scene stars: the star cores barely change (median core-flux change −0.01 to −0.06 ppt from T7 to T13), while pixels beyond about 4 px change by a robust 0.65σ of the noise. Those changes form 2–3 px blobs, most likely faint (T>13) neighbours that the per-band template removes differently. The noise plane is identical in both images.

Template effect vs. optimisation effect

Blue bars compare F=4 with F=1 under matched training. Orange bars keep the F=1 image and change only the optimisation. The grey bar is the difference between two half-fits on different star halves (heldout harness), a loose statistical yardstick.

Loss curves

The F=4 image is fitted much better in every pairing (the data term is about 3.4 lower), consistent with cleaner faint-neighbour removal. The other-sector start (R3, R4) ends well above A3 (data term 26.2 and 22.6 against 20.3), so those fits had not converged after 5,300 steps; their paired comparison is still fair because both are at the same stage. In several runs the data term creeps upward late in training, the same drift the held-out harness found.

F=1 vs F=4 Hotpants on the same FFI

Asked alongside this check: is a first-pass F=4 Hotpants worth running? It was measured on 09-24 (template_kernel_20260924/eval/REPORT_old_vs_f1.md): Hotpants ko=2 on the adopted FFI, scored on the same frozen 2,467 stars (13 ≤ T ≤ 17).

F=4 for the reference frame, F=1 for the changes

Taking the Paper 1 WCS/ePSF from an F=4 fit of the reference frame and modelling later frames with F=1 is consistent with these results, provided the changes are measured F=1 to F=1:

• $\theta$: the fitted calibration parameters (WCS coefficients, ePSF, colour terms).
• $t_0$: the reference (adopted) frame; $t$: any other frame.
• $\theta_{F4}$, $\theta_{F1}$: fits on the F=4 and F=1 difference images, with the same recipe, stars and colour file.

Any bias from the F=1 template is then common to every frame and cancels in the bracket. The F=1↔F=4 offset on the reference frame (about 0.3 mpx, ≤0.3 ppt; table above) is the systematic to quote.

What this shows

• The template does not move the calibration. In three independent pairings, refitting on the F=4 image changes effective positions by 0.26–0.36 mpx rms, ePSF size by 0.07–0.17×10⁻³ px² and fluxes by 0.1–0.3 ppt. All pass the draft D14 tolerances; in position and ePSF size they are 20–50× below the split-half spread.
• The +0.0176 e⁻/s pedestal is minor: 0.1–0.2 ppt in flux, 0.06 mpx in position.
• The optimisation is what moves the fit. 1,500 extra steps on the same image: 1.5 mpx and −0.76×10⁻³ px². A different start: 4.1 mpx and up to 1.3 ppt. This is the D16 question (prior, schedule, convergence).
• Confidence: high for "below tolerance". The fitter is deterministic (rerun floor exactly zero), and three pairings with different starts and schedules agree within 0.1 mpx.

Limits and next steps

• F1 only, with the plain-prior A3 fit, not the D16 recipe. The official G6 check reruns make_swap_scene.py and the R1/R4 pairs on the D16 fit's per-band image; F2 and S22 are optional replications.
• The neutral-start fits had not converged; the paired comparison holds, but the absolute R3 result is not a calibration.
• Residual grids for these runs have not been added to the shared residual-grid canvas yet.
• Recording "F=4 fit = delivered calibration" in MODEL_FREEZE (D14/D15) is the user's decision; it has not been edited.

Records: README and INDEX line in /astro/armin/koji/syndiff/dev_runs/d14_refit_20260930 · scripts compare_stamps*.py, make_swap_scene.py, make_jobs.sh, compare_fits.py, make_canvas_figs.py