2026-10-01 · codex/paper1-publication · base 8ee5d57

Paper 1 Figure Desk

Your existing paper canvas, continued in an isolated worktree. Concise source outline and reproducible figure exports.

One active figure set: the latest available plot for each topic appears in its section or appendix. Superseded versions are omitted; historical labels describe the data, not a separate archive.

Read the structure and figure audit: proposed main-text/appendix placement, individual figure verdicts, and evidence gaps. Figure IDs remain working IDs, not final numbering.

Provenance notice: live dataset and wing-mask source files changed after their historical exports. The saved plates remain intact; strict source-hash validation is flagged in the audit, not silently refreshed. The new §4 inputs match their recorded snapshots.

New work stays on codex/paper1-publication; production runs are unchanged. PDF/SVG downloads accompany every new figure.

Scope and adopted recipe

PS1-assisted astrometric and chromatic ePSF calibration of TESS full-frame images

Working outline, 2026-10-01; concise bullets, not manuscript prose.
Adopted example: S24 C2K2, tess2020120182919-s0024-2-2; science crop origin (44, 0), shape 2048 × 2048 pixels.
Replication: S20 C3K3, S22 C3K3, S24 C1K2, S23 C4K2; five independent FFIs, all four cameras.
Recipe: A3 + Gaia-XP colour; lp7s prior; no brightness-width term, fitted background, or in-loop rejection.
Final accuracy claims require five-fold held-out evaluation; all-star fits supply delivered calibrations.
Development figures illustrate methods; they do not replace the unfinished five-FFI dataset.
Historical outline; evidence and unresolved checks.

1. Introduction

Jointly constrain positions, effective response, and flux in crowded, undersampled images.
PS1 supplies a resolved contaminating scene; Gaia supplies astrometry and colour information.
Distinguish single-image calibration from time-series performance; no light-curve gains claimed.
Acknowledge established ePSF/PRF and TESS crowded-field work; colour dependence itself is not new.
Test a reproducible scene-assisted calibration and de-crowding chain across cameras.

2. PS1 reference scene

2.1 Inputs, coverage, and units

Record exposure IDs, epochs, checksums, crop, WCS, catalog selections, and per-band usable coverage.
Mapping uses the custom MOCPy polygon-point query to identify candidate PS1 skycells for each TESS grid centre.
Resolve overlapping candidates by the nearest PS1 projection centre in TESS coordinates; leave unmatched centres unassigned.
Transform each owned TESS pixel's corners through both WCS solutions; assign enclosed PS1 pixel centres its grid index.
Store the inverse PS1-to-TESS index map; F = 4 assigns quarter-pixel template cells, not native TESS pixels.
A PS1 map value of −1 means no assignment in that skycell map, not necessarily a gap in TESS coverage.
Distinguish nominal survey footprint from observed valid pixels; retain overlap/edge masks.
Convert PS1 values to common linear flux units; track flux-per-pixel and pixel-area conventions.
F1 labels a field; F = 1 and F = 4 label template sampling.
Figure 1: (a) footprint, (b) skycell ownership, (c) one skycell's PS1-to-TESS pixel assignment; distinguish stored historical geometry from final mapping.

TESS-to-PS1 skycell coverage and pixel assignment — (a) Nominal PS1 3π footprint and Sector 24 camera footprints; (b) the 986 mapped PS1 skycells covering the Camera 2, CCD 2 science crop. (c) The same fixed cutout of skycell.2483.062, showing every destination, including partially visible TESS pixels at the edges. Each PS1 pixel is coloured by its native TESS destination after grouping stored F = 4 subpixel indices; white lines trace assignment changes along PS1 pixel edges. All 43,677 PS1 pixels in this cutout are assigned to 16 native TESS pixels; there are no unmapped entries here. Legend coordinates are full-FFI, zero-based. Elsewhere, stored -1 means no assignment in this particular skycell map, not necessarily missing TESS coverage: the location may lie outside the mapped region or an overlapping skycell may own it. Historical development geometry, not a newly computed or independently validated remap.

2.2 Band synthesis

Retain separate r/i/z/y templates; combine only where required by the matching method.
D13 synthesis weights ≈ (0.254, 0.437, 0.165, 0.144); calculate with stored full precision.
Use TESS POC v2.0 response; distinguish synthesis weights from fixed D18 colour-label weights.
Specify spectral selection, response, and zero points; validate on held-out spectra.
Figure 2: bandpasses; Appendix C: colour-dependent synthesis residuals and spectral outliers.
No universal sub-percent claim; quantify very-red and emission-line limitations separately.

Figure 2 · Bandpasses — Exact weights and response provenance still need reconciliation.

2.3 Source removal and decomposition

Remove residual PS1 sky/background structure before smoothing; it is not the TESS exposure's background.
Without removal, PS1 background structure would spread under convolution and rebinning; excluded pixels do not enter the retained template.
Treat invalid chip-gap coverage separately, not as measured sky.
Omit selected bright-source segments from the subtraction scene; their TESS signals remain measurable.
On valid pixels: original = removed sources + excluded PS1 background + retained scene.
Bright selection is not a saturation diagnosis; merged segments and wings may remove neighbours.
Quantify neighbour preservation and excluded background in TESS-equivalent units.
Figure 3: full-skycell decomposition; supporting zoom: segmentation and nearby sources.

Figure 3 · Full-skycell decomposition — Historical scene recipe; regenerate after seam/weight fixes.

Final data needed

F3: validate neighbour preservation and regenerate the decomposition with the final weights and seam fix.

2.4 Smoothing, seams, and mapping

Distinguish PS1 response, preprocessing Gaussian, matching kernel, and TESS ePSF.
Record smoothing/support, overlap ownership, padding, and pixel-area treatment; test seams and flux accounting.
Initial F = 4 mapping uses header WCS; geometry does not depend on TESS pixel values.
Rebuild F = 4 templates on calibrated WCS before the final image; archive both mapping hashes.
Figure 4: template sampling illustration only; no differing-WCS image comparison.
Appendix A: require identical WCS, scene, masks, and matching recipe before claiming a sampling gain.

Figure 4 · Template sampling illustration — Nominal-grid illustration, not an observed F = 4 production template or an accuracy gain; both grids integrate the same PS1 scene.

Final data needed

F4: controlled sampling test at identical WCS and scene.

3. Preliminary de-crowded image

3.1 Empirical template match

Match the band-combined F = 4 scene with oversampling-aware Hotpants.
Subtract contaminating light while retaining deliberately omitted calibration stars.
Specify kernel basis, spatial variation, photometric scale, masks, and native-pixel integration.
Figure 5: data flow, including initial and calibrated-WCS template construction.

Figure 5 · Adopted data flow — Method schematic for the five-FFI recipe snapshot. The initial scene uses header WCS; the final scene is remapped on calibrated WCS. Background is prepared at image level, not fitted as a free scene term. The final refit tests stability rather than assuming it. Held-out accuracy validation is required separately and is not established by completing this chain.

3.2 Image-level background

Estimate the TESS background outside stellar masks; harmonically fill excluded regions before subtraction.
An exposed stellar wing raises the inferred background and causes over-subtraction beneath the star.
Method A: magnitude-dependent centred disks, 6–30 native pixels for T < 13; replace fixed pad 2 with pad 0.
Radii target a fitted wing level of 0.1 electrons/s; this is not a zero-leakage guarantee.
Apply extra disks to background-fit pixels only, in both background stages; shared masks and Hotpants masks stay unchanged.
Preserve separate invalid, saturation, strap, and coverage exclusions; no free background in the scene fit.
Figure 6a: wing-mask footprint and insufficient-mask comparison; Appendix A: detailed background checks.
Validate on withheld blank regions; retain signed residuals.
F1 masking tests are developmental; new cross-field background products remain provisional, not accepted final results.

Figure 6a · Stellar-wing masking — Single-FFI method-development result for F1 (S24 C2K2; tess2020120182919-s0024-2-2). (a) The background-estimator input, science minus convolved template (ks_d + ks_b), in a 47 × 47 pixel cutout around a T=8.29 star selected by maximum catalogue-neighbour separation among T=8–9 candidates, not by background residual. The nearest other 7.5≤T<13 catalogue star is 22.4 px away; fainter neighbours are not excluded by this selection. The image has its local 20–22 px annulus median removed for display, not as a verified empty-sky estimate. Dashed cyan traces the actual base background-fit exclusion; yellow traces its union with the saved Method A exclusion. These contours include neighbouring masks. The central star's nominal radii are 9 px and 18 px, respectively; the Method A disk is centred at the fractional catalogue position. The displayed stamp is an observed single-star image, not the fitted average wing profile from which the radii were measured. (b) Median background estimate at scene-star positions minus nearby empty-sky medians, measured with the same harmonic-fill estimator and the current fit mask (control) or Method A's magnitude-sized exclusions; bars are robust standard errors (1.2533 × 1.4826 × MAD / √N). Bin edges and counts are recorded in the metadata. The saved background map is ks_b; each star is compared to at least five eligible reference pixels within 60 px, at least 16 px from the experiment's scene-star positions. The Method A radius table uses the worst-sector fitted stellar wing and a 0.1 e⁻ s⁻¹ edge threshold; it expands the background-fit exclusion while leaving the shared mask, Hotpants fit pixels, and scene inputs unchanged. Across this F1 frame, the median lift falls from 0.70 to 0.22 e⁻ s⁻¹ in T=7.5–9 and from 0.27 to 0.19 e⁻ s⁻¹ in T=12.5–13. A residual lift near 0.2 e⁻ s⁻¹ remains when all stars are pooled; the experiment attributes much of that floor in crowded regions to neighbour wings that single-star masks cannot remove. This is an F1-only controlled estimator comparison, not a completed multi-CCD validation or a claim that the mask eliminates all background bias.

Final data needed

F6: cross-field validation of the wing-mask/background recipe remains pending; the displayed development tests do not certify final backgrounds.

3.3 Preliminary image comparison

Compare the background-subtracted FFI with its preliminary de-crowded image at identical coordinates and display limits.
Show adjacent zooms with shared axes; white at zero, linear within ±10 electrons/s and logarithmic outside.
Historical example only: record exposure, background treatment, template, masks, and empirical matching recipe.
Reduced crowding motivates the scene fit; visual cleaning alone does not establish unbiased flux or astrometry.

Figure 6b · Historical preliminary image comparison — Historical development comparison for F1 (S24 C2K2; tess2020120182919-s0024-2-2, observed 2020-04-29). The left panel shows the archived science FFI minus its saved diff_linear/ks_b background map, which the same-run F=4 temporal-WCS bootstrap used as science input. The right panel shows that run's Hotpants hp_d signed residual after subtracting the adopted-weight, band-combined PS1 template (ko=2, bgo=0). Both panels show the identical, unbinned 256 x 256 crop at science-crop coordinates x=[1152,1408), y=[1344,1600), with matching origin and orientation. The crop was selected from Gaia scene-fit ePSF-contributor density (45 contributors; maximum on a 64-pixel scan among tiles avoiding x=[1000,1040]), not from the residual image; it lies away from the known saturation-bleed column near x=1020. Both panels use one diverging colormap and the same symmetric-log scale from -10000 to 10000 electrons s^-1: linear from -10 to +10 and logarithmic outside, with white at zero. The common symmetric limit is the next decade above the pooled 99.9th percentile of absolute intensity (minimum 100); values outside are colour-clipped. Every finite pixel is displayed regardless of mask flags; non-finite pixels are gray. This archived bootstrap is illustrative only, not the adopted five-FFI recipe and not a validation of photometric accuracy. Its README records that the adopted-weight template used a delta-form blur whose accuracy on 141 mostly seam cells was not separately quantified.

3.4 Why calibrate for time-series photometry?

Aim: recover real flux changes across epochs without confusing pointing or response changes with variability.
A clean single image is insufficient; residual neighbour light can change as stars move across detector pixels.
Jointly calibrate positions, spatial/chromatic response, and flux to support consistent subsequent light-curve extraction.
Paper 1 establishes single-image ingredients; temporal accuracy requires separate multi-epoch validation.
No standalone figure here: §3.3 shows de-crowding; §4 shows the calibrated response and remaining residuals.

4. Joint scene, WCS, and chromatic ePSF model

Current figure source: completed F1/F2 A3 + lp7s fits; saved full fits and five-fold checks.
These fits use the intended penalty but older background/mask preparation; replace inputs when final products are accepted.

4.1 Scene likelihood

Native pixel model: m_p = Σ_i f_i R_ip; define fitted flux f_i and its finite-support convention.
Account for neighbours, contributor/anchor/nuisance roles, duplicate pixels, uncertainties, masks, and robust loss.
Record provisional pre-fit exclusion v1min lists and hashes; distinguish from rejected v0/v1 lists.
Mask F2 straps; no data-dependent in-loop rejection in the adopted recipe.

4.2 Astrometry and gauge

Propagate Gaia positions to the observation epoch; verify observer/parallax handling before claiming it is applied.
Define the implemented WCS correction and crop-local coordinates.
Constrain the ePSF core-centroid gauge; distinguish WCS shift from effective image-centroid shift.
Figure 9: fitted WCS correction fields from available lp7s fits; not an astrometric-accuracy measurement.
Add independently measured held-out positional residuals when available across all five FFIs.

Historical fitted-WCS correction field relative to initialization — Saved lp7s full-fit Chebyshev WCS corrections for F1 (S24 C2K2) and F2 (S20 C3K3), evaluated on a 17 × 17 interior grid from 128 to 1920 pixels in each crop axis. Each vector is the fitted model position minus the same bundle's saved initial-WCS position; vector lengths are enlarged 1000× for legibility, while color and the 0.10-pixel key report true crop-local pixel displacements. The fits use the historical lp7s recipe and code pin 13a726c6. This plate describes the fitted correction field, not its astrometric accuracy; no independent held-out centroid residuals are represented.

Final data needed

Next evidence: independent held-out positional measurements; a fitted correction field is not an accuracy test.

4.3 Spatial ePSF and rendering

Interpolate spatial nodes and apply the adopted chromatic/gauge transformations.
Stored E is already pixel-integrated (pixel_integrated_v1), sampled on an O = 4 grid.
At native pixel centre (x_p, y_p), sample g = c_E + O[(x_p, y_p) − (x_i, y_i)].
Response R_ip = O² interp(E_i, g): one bilinear sample; zero outside support; no second sixteen-subpixel sum.
Keep stellar centres continuous; do not round to quarter-pixel phases.
Separate ePSF grid factor O from template sampling F, even when both equal four.
Figure 5 inset: correct sampling operator; schematic, not a measured response.
Figure 14: fitted spatial-response nodes from the available lp7s model; record support and normalization.

Figure 5 inset · Pixel rendering — Schematic geometry, not observed data. Fine lines mark the stored ePSF grid; heavy lines indicate a one-native-pixel interval. The cross is a continuous-phase query, interpolated from four grid neighbours. The stored pixel-integrated response is sampled once and multiplied by O²; it is not integrated a second time.

Figure 14 · Spatial effective-ePSF response — Nine selected nodes from the saved F1 lp7s full-fit ePSF grid. Each panel shows the effective, pixel_integrated_v1 response at the model's quarter-pixel sample pitch, using the stored response multiplied by oversampling squared (4²) as in the renderer. No second box integration is applied. The selection spans corner and interior locations of the 6×6 detector grid; titles give one-based node labels and crop-local native-pixel coordinates. A shared logarithmic scale is used; the cyan contour marks 10% of the shared display upper limit. Historical saved-fit model structure, not a measurement of held-out accuracy; the fit's background preparation is provisional in the current dataset chain.

4.4 Chromatic structure and regularization

A3: fixed Gaia-XP colour, quadratic colour shifts, and CCD-frame elongation terms.
Define colour reference, spatial normalization, 17-coefficient ordering, and non-XP fallback from metadata.
lp7s: local-polynomial weight 3 × 10⁸, 7 × 7 window; fine-neighbour weight zero.
Penalty: penalize mean-squared ePSF departures from a local-polynomial smooth model to suppress small-scale noise; validate the strength on held-out stars.
Specify prior definition and normalization; the older moment-blind recipe is superseded.
No brightness-width term in the adopted five-FFI fit.
Figure 12: A3 model responses across colour; distinguish predicted shape/shift from empirical residuals.
Figures 10/15: retain labelled older empirical colour diagnostics until their A3 replacements exist.

Figure 12 · Chromatic effective-ePSF response — Saved-fit model predictions at the same nominal crop-local position (1024, 1024) in each field. Rows show F1 and F2; columns show the reference response and signed blue-minus-reference and red-minus-reference images for Δu=−0.3 and +0.3 mag relative to the fitted Gaia-XP u colour reference. These offsets lie within the central observed Δu range in both fields. The global8 chromatic translation and fitted shape terms are evaluated using the saved coefficients and effective response generators, then passed through the pixel_integrated_v1 renderer, which scales samples by 4² without a second integration. Differences use a symmetric colour scale shared across both fields; reference images use a common linear scale. These are model predictions, not measured colour trends or an accuracy validation. The source fits use historical background preparation, marked provisional in the current dataset chain.

Figure 10 · Chromatic residual stacks — F1 — Historical model #14, in-sample. Any embedded “adopted” label refers to that older experiment; regenerate for A3 heldouts.

Figure 10 · Chromatic residual stacks — F2 — Replication of the older #14 experiment, not independent validation of the current A3 recipe.

Figure 15 · Displacement versus colour — F1 — Older #14 fit; baseline and corrected panels use different vertical ranges. Not final A3 accuracy.

Figure 15 · Displacement versus colour — F2 — Replication for the older model; retain the role split and null checks as development evidence.

Final data needed

Next replacement: empirical A3 colour-residual stacks and displacement diagnostics; model response predictions are shown separately.

4.5 Validation

Run to stated convergence criteria; retain learning curves and parameter-drift checks.
Five fixed folds: held-out stars/scoring pixels must not train the shared calibration.
Document leakage controls for blends, colour mapping, preprocessing, and hyperparameter selection.
Compare baselines on identical samples; show N, bin edges, scatter, units, and uncertainty definitions.
Figure 11: held-out data/model/residual stamps; common signed scales; selection independent of residual quality.
Pixel-validation plate: current lp7s five-fold scores and learning curves; show remaining overfitting, not just gains.
Photometric consistency: retain the older held-out flux plot; replace with matched lp7s/XP measurements when available.
Gaia-XP predicts comparison flux, not exact truth; separate response, variability, and flux-support effects.

Figure 11 · Observed, model and residual held-out stamps — Observed stamps, fitted models and observed-minus-model residuals for four real held-out stars from F1 and F2 (S24 C2K2 and S20 C3K3). All stars are T=10–11 and were selected without visual curation: within each field, the examples are the eligible held-out stars nearest fixed CCD-local positions (512,512) and (1536,1536), with at least 20 valid grid samples inside 1.5 native pixels. Residual values did not enter selection; the residual RMS of each selected star is recorded in metadata. The fit for each star was trained on the other four spatial folds; this held-out label applies to the star/pixels, while shared calibration parameters were trained elsewhere. The raster stores model and residual divided by that star's re-solved flux; observed is reconstructed as model + residual, not a simulation. Values are native-pixel flux divided by fitted total stellar flux, resampled by the raster renderer onto the quarter-pixel grid to preserve subpixel positions; the grid cells are not quarter-pixel flux measurements. Intensity and residual use separate shared scales across rows; grey cells are unsampled or invalid/masked. The color scales are clipped at the 99.7th percentile for intensity and 99.5th percentile of absolute residual. Each stamp spans 8.25 native pixels on a 0.25-pixel grid. This is an older A3 recipe (soft 7×7 local-polynomial prior, λ=3×10⁸, no fitted local-background or width term) evaluated with the older scene background; it is not final-recipe validation.

Figure 17 · K=5 held-out performance and learning curves — Left: the ratio of median per-star mean core χ² for lp7s to the no-prior fit, calculated separately within the same source-ID intersection for lp7s and no-prior (positive fitted flux and at least 15 valid core pixels in both fits), then summarized by the median across five folds; whiskers span the minimum to maximum fold ratio. Values below one favor lp7s for this metric. Right: per-fold held-out core χ² learning curves for T=10–13, each point being the median of the T=10–11, 11–12 and 12–13 bin medians and normalized to the leak-free step-0 initialization; faint lines are individual folds and thick lines are field medians over the step range shared by all five folds; thin lines retain each fold's full run. P5 passes in 0/10 lp7s fold fits; the gate requires all T=8–13 bins to pass both the final-window slope and end/min tests. Worst T=10–13 end/min ratios are 1.16 (F1) and 1.12 (F2). The no-prior reference itself overfits, so ratios describe this matched historical comparison rather than absolute calibration accuracy. Both arms use the older scene background and omit fitted local-background/width terms; shared calibration is trained on four folds while the scored fold is held out. This is not final-recipe validation and does not imply astrometric accuracy.

Figure 17 · Provisional held-out photometric consistency — Latest available held-out plate, but an older recipe. Separate zero-point-removed consistency from absolute calibration; final common-fold evaluation remains needed.

Final data needed

Next replacement: final-background inputs and matched held-out flux/XP validation. Existing five-fold development results remain usable with their stated limitations.

5. Final de-crowded image and measurements

5.1 Calibrated remapping

Export fitted WCS; rebuild F = 4 per-band templates; verify seams, weights, coverage, and scaling.
Preliminary/final differences include remapping and scale changes, not only kernels.
Isolate kernel effects using Hotpants, achromatic, and chromatic controls on identical remapped templates.

5.2 Band-resolved kernels

Fit a least-squares line through nonlinear A3 responses at 25 training-colour quantiles (2–98%).
E_b = P₀ + δ_b P₁; normalize ΣP₀ = 1 and ΣP₁ = 0.
P₁ is a fitted colour slope, not necessarily a derivative; P₀ is a fitted intercept.
Derive matching K_b from E_b and the pre-smoothed PS1 response; K_b ≠ E_b.
Apply spatial weights at source positions before convolution; integrate the F = 4 template onto native pixels.
Verify reconstruction, normalization, ringing, colour extrapolation, and boundaries.
Figure 20: response/kernel bases at a recorded node; signed colour components and calibrated axes.

Figure 20 · Response and matching-kernel bases — Development A3 basis at spatial node (row, column) = (2, 2), crop position (819.2, 819.2) pixels. Central ±4-native-pixel view at four samples per native pixel; full stored arrays are 63² for P and 127² for K. Each panel has its own symmetric scale; no normalization to the displayed crop. P₀/P₁ are the normalized intercept/colour slope of a least-squares response fit; K₀/K₁ include deconvolution of the pre-smoothed PS1 response. Intercepts are dimensionless grid weights; slopes are per unit of the XP-mapped colour coordinate (mag). Signed lobes are retained. Legacy fixed colour-label weights are recorded in metadata; this is not a validation of the final synthesis recipe.

Final data needed

F20: final kernels and reconstruction checks.

5.3 Image-level evidence

Figure 18: preselected real-image region; identical coordinates, shared masks, signed scales.
Figure 16: controlled residual scores versus colour/position; consistent noise propagation.
Separate full-chain and kernel-only gains; show failure regions alongside improvements.
Compare cameras only with identical recipes, not mixed development runs.

Figure 18 · Matched real-image comparison — Development F1 run: a fixed 256² region centred on the CCD, selected without inspecting residual quality. All finite pixels are shown at the same signed ±3 electrons s⁻¹ scale; grey contours mark the common exclusion mask (union of nonzero method masks), not removed data. Deliberately retained bright stars saturate the display and are not subtraction failures. Panel a→d changes the full chain; b/c/d share calibrated mapping and templates but have separately fitted matching scales. This run used brightness-width and background terms and has known seam/weight caveats; it is not the final paper recipe.

Figure 16 · Colour-split residual stacks — Historical A3 whole-CCD dry run, not final held-out evidence. These images accompany the population scores below.

Figure 16 · Residual scores versus colour — Same development comparison; recipe, masks and samples must be controlled before attributing gains to chromatic kernels.

Final data needed

F16 / F18: final controlled scores and matching cutouts.

5.4 Refit stability

Refit with identical initialization and warm continuation; compare effective position, flux, and shape.
Report every gate separately; small WCS drift does not establish complete stability.
Development G6: position/flux stable, effective-width tolerance fails; brightness/background terms differ from the adopted recipe.
Supplement G6: signed changes and tolerance bands; repeat with adopted recipe before claiming stability.

Supplement G6 · Refit stability is not a blanket pass — Development refit minus calibration. Blue: refit with the original initialization; orange: warm continuation. Shaded bands mark recorded D14 tolerances (2 mpx, 1 ppt, 0.2 × 10⁻³ pixel²); flux points are bin medians, not individual-star errors. Effective position includes WCS and ePSF centroid. T_eff is the Gaussian-windowed second-moment trace plus the recorded brightness-width correction at fixed charge. The width check fails for both refits. This older fit includes brightness/background terms excluded from the adopted recipe; repeat all gates on the final dataset.

Final data needed

G6: repeat every stability gate with the adopted recipe.

5.5 Photometry and targeted de-crowding

Specify fitted parameters, neighbour handling, flux support, and uncertainty propagation.
Omit a chosen target from the subtraction scene while retaining neighbours; verify segment accounting.
Figure 19: target retained/subtracted, marked neighbours, catalog identifiers.
Figure 21: extraction residuals and flux/uncertainty checks on independently selected targets.
Validate uncertainties with injection/recovery or scoped repeat observations; a single frame is insufficient.

Final data needed

F19 / F21: actual independently selected target-extraction products.

6. Discussion and conclusions

State measured calibration/de-crowding results only; distinguish method scope from performance evidence.
Discuss colour extrapolation, missing XP, variability, epoch mismatch, saturation, seams, blends, and finite support.
Colour slopes alone cannot identify response-curve errors; label interpretations as hypotheses.
Release pinned code/configuration, input/output hashes, exclusions, folds, figure tables, and build commands.
Future work: temporal calibration and light curves, not demonstrated here.

Appendix A. Sampling and background masks

Controlled F = 1/F = 4 test with fixed WCS, scene, masks, noise, and matching.
Synthetic illustration is not an observed sampling gain.
Compare insufficient versus magnitude-sized masks on identical data; show background lift beneath masked stars.
Separate isolated-star improvement from residual neighbour-wing contamination; no blanket background-fix claim.
Retain the older full-frame background decomposition as labelled historical context.

Figure 6 · Background decomposition — Legacy F1 background products, not the adopted harmonic run. Top row shares a linear intensity scale; d/f share a signed scale, while e has its own expanded scale to reveal the background change. Native 2048² images are displayed as 8×8 area means; no smoothing or offset is applied to the science arrays. B₂−B₁ is a change between saved background estimates, not a convergence proof. Saturated display values are clipped at the colour-bar extensions.

Figure 8 · Synthetic sampling comparison — Illustrative reconstruction, not observed performance. This example does not establish F = 4 superiority.

Appendix B. Model selection and numerical checks

Compare A3 and simpler colour models using held-out evidence; label exploratory history.
Historical spatial/colour flux trends are supporting single-image diagnostics, not demonstrated light-curve performance.
Include convergence/prior, centroid gauge, pixel phase, support, and kernel reconstruction tests.
Report measured computational cost and environment, not extrapolated performance.

Figure 7 · Spatial and colour structure — In-sample development comparison of 10,493 common stars, 8 ≤ T_XP < 13. Δm = fitted magnitude − T_XP after a separate median zero point per method. The inherited sample excludes |Δm| > 0.5 mag in any compared model; it is not an unbiased accuracy sample. Map cells require N ≥ 10; fixed ±40 mmag limits. Curves show medians; shading is the 16–84 percentile scatter, not confidence intervals; colour bins require N ≥ 30.

Spatial ePSF · Initial and fitted nodes — Older 6 × 6 in-sample node comparison; supporting context for Figure 14, not held-out improvement.

Model selection · Candidate terms and optical-axis scan — Historical #14 selection diagnostics; a selection set is not the final evaluation set.

Model checks · Trained ablations and checkpoint drift — Older model and recipe; embedded adoption labels are historical. Repeat controlled ablations for the final recipe.

Numerical checks · Gauge and normalization — Historical fitting-sensitivity tests, not acceptance of the current calibration.

A3 development · Comparison with model #14 — Warm-started, in-sample development comparison; not unbiased confirmation of A3.

A3 development · Multiple-FFI diagnostics — Older eleven-FFI campaign, distinct from the adopted five-FFI dataset; not a replacement for final cross-camera validation.

A3 development · Coefficient fields — Coefficients have heterogeneous units; interpret through their induced response, not colour amplitude alone.

A3 development · Remaining width structure — A known residual width discrepancy; retain this negative evidence until the final-recipe test replaces it.

Appendix C. Band-synthesis verification

Publish exact synthesis/colour-label weights separately; record responses, zero points, spectra, and holdout selection.
Show errors versus colour/type, including very-red and emission-line limitations.
Separate response/catalog uncertainty from measured camera-dependent trends.

Band synthesis · Spectral and colour residuals — Latest available spectral diagnostic; specify training versus held-out spectra and the supported colour/extinction domain. No universal sub-percent claim.

Band synthesis · Response-curve comparison — Historical image/catalog comparisons; a colour trend alone does not establish its physical cause.

Band synthesis · Weight-change diagnostics — Historical comparison: lower residual scores coexist with remaining colour/aperture discrepancies. Not a blanket photometric improvement.