# Figure 1 — Orbital aberration and remaining spatial WCS change

**Proposed caption.** Sector 20 sky-map changes after removing measured common attitude. Panels **a–c** show all 16 CCDs at the last retained exposure, `tess2020020065923` (spacecraft BTJD 1868.802), relative to `tess2019365025923` (BTJD 1848.636): measured catalogue-frame change, the physical full-velocity aberration correction, and the remaining apparent-frame change. The panels share one arrow scale in native detector pixels. CCD numbers identify each detector; placement is schematic, but detector positions and arrows are rotated consistently using each reference WCS. Nine of 81 inset probes per CCD are displayed. Panels **d–g** show the two-component vector RMS over all 324 retained probes per camera at each exposure, in millipixels (mpx). Dashed vertical lines mark the reference exposure; dotted lines mark the mapped exposure. The spacecraft-velocity correction includes both Earth's barycentric motion and TESS's Earth-relative motion; no aberration amplitude is fitted. Over 1,100 quality-selected exposures and1,296 probes, the all-camera vector RMS decreases from 60.067 to 13.652 mpx, a 94.834% reduction in summed squared amplitude **after common-attitude removal**. These are FFI-header WCS measurements with measured pointing retained as a conditioning quantity, not independent stellar accuracy or a complete pointing forecast. Remaining change includes temperature-associated distortion and other optical, attitude-convention and measurement effects. All-camera quality selection excludes camera 1-contaminated orbit 48startup; the gap is not interpolated.

## Quantity and exact denominator

For each retained exposure–probe pair, define

$$\boldsymbol M_i=\boldsymbol V_i+\boldsymbol R_i,\qquad f=1-\frac{\sum_{i=1}^{N}\lVert\boldsymbol R_i\rVert^2}{\sum_{i=1}^{N}\lVert\boldsymbol M_i\rVert^2}=0.9483417083.$$

Here $\boldsymbol M_i$ is the measured catalogue-frame WCS displacement after the fitted common-rotation projection, in native pixels (`model.npz/raw_residual`); $\boldsymbol R_i$ is the corresponding apparent-frame residual after applying full-velocity aberration and the same projection basis (`model.npz/residual`), also in native pixels. The vector $\boldsymbol V_i=\boldsymbol M_i-\boldsymbol R_i$ is the exact physical-aberration correction to these measured directions, not a regression against a reference-direction template. The index $i$ enumerates the retained vectors, and $N=1{,}100\times16\times81=1{,}425{,}600$ (2,851,200 scalar components). The dimensionless $f$ compares squared amplitudes relative to the common reference; it is neither variance about a fitted temporal mean nor a held-out predictive score. No temperature-model term enters this figure.

The plotted vectors describe **sky-map changes at fixed detector positions**. Fixed-star detector displacement has the opposite first-order sign. Orthogonal orientation transforms preserve their native-pixel vector norms; a common layout does not imply a common angular plate scale. The apparent common attitude is fitted from the header maps, so deformation components degenerate with common rotation are absorbed into that convention.

## Figure assets and provenance

- PNG: `/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/orbit/orbit_components.png`
- Vector PDF: `/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/orbit/orbit_components.pdf`
- Exact input/code hashes, display probe positions, orientation matrices, selection, epoch and numerical denominator: `/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/orbit/orbit_components_provenance.json`
- Inputs: `/astro/armin/koji/syndiff/dev_runs/wcs_focal_plane_20261002/baseline_results/inputs.npz` and `model.npz` in that directory.
- Generator: `/home/kshukawa/syndiff_pipeline/dev/.claude/worktrees/wcs-centres-20261015/paper/wcs_orbital_20261015/FIG_ORBIT_COMPONENTS.py`.

The selection is the archived Boolean `model.good`; no fit, clipping or new scientific selection is performed. The displayed exposure is chosen as the last retained exposure, not by residual amplitude. Intermediate flagged exposures are omitted from the all-camera support. PNG inspected after generation; PDF preserves vector arrows and text.

**Supported conclusion:** known orbital aberration accounts for the leading spatial WCS change under the measured-attitude convention. The remaining field is coherent and requires further explanation. The figure does not establish uniquely thermal residuals, telemetry-only attitude prediction, all-camera independent centroid validation, or an absolute astrometric error bound.


# Endpoint thermal figure packet — 2026-10-15

- Generator: `FIG_ENDPOINT_THERMAL.py`; no model fitting or changed predictions.
- Exports: `/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/thermal/`.
- Every figure has PNG and vector PDF. `manifest.json` hashes the frozen input files and generator and records every cadence index, denominator, selected spatial-map exposure, and colour limit.
- All three PNGs inspected after generation. Probe array order checked against `prepare.py`: x increases across each 9-column chip, y upward through 9 rows.

## Figure A — endpoint_errors_temperature

- **Caption:** Full-day withheld distortion errors (top) and simultaneous measured Camera 3 temperatures (bottom). Columns show the first science day of orbit 47 and the final science days of orbits 47 and 48. Each endpoint was excluded from training with an additional 0.25-day buffer. Upper curves use equal-weight two-dimensional vector RMS over all 16 CCDs and 81 inset probes per CCD, after exact physical velocity aberration and the measured common attitude are removed. Blue uses the earlier three-temperature-PC predictor; orange uses the separately evaluated nested selection policy allowing instantaneous, rate and lag features. Each interval contains 49 retained exposures. Bottom curves are exposure-averaged sensor changes relative to that interval's first retained exposure; they illustrate different thermal histories and do not establish a causal component-by-component attribution.
- **Evidence boundary:** Orange is the saved `dynamic_selected` endpoint prediction, **not** the best instantaneous-only policy. Its interval RMS is 3.625, 1.099 and 1.246 millipixel, respectively. Startup is worse than the earlier model here; additional candidate lags do not guarantee better predictions. The historical instantaneous-only first-day value of 2.874 millipixel is not plotted.
- **Why this figure:** Demonstrates the endpoint asymmetry and the difference between thermal correlation and predictive completeness. Upper and lower axes use different column ranges to display structure; read numerical scales when comparing amplitudes.

## Figure B — endpoint_spatial_prediction_errors

- **Caption:** Signed x and y components of measured-minus-withheld-predicted distortion for the orange model in Figure A. For each interval, the exposure with the largest all-CCD vector RMS was selected by a fixed rule. Rows represent cameras; each panel contains four separate detector-coordinate 9×9 probe maps, ordered CCD1–4 from left to right. These are not physical focal-plane mosaics. Every panel shares the same symmetric colour scale, with no clipping (±21.854 millipixel). Selected spacecraft times are BTJD 1842.61495, 1854.84411 and 1868.57328. The maps display the actual fields underlying Figure A's error statistic, rather than residuals of an in-sample atlas calibration.
- **Evidence boundary:** These are WCS-probe displacement images, not stellar intensity residual stamps. They illustrate the worst all-CCD exposure in each interval, not every exposure entering the interval RMS. Smoothly coherent startup error and local extremes are visible. The single shared scale deliberately leaves the weaker last-day structure comparatively faint.
- **Gauge:** All-camera measured attitude and common-clean support are retained. Camera 1's contaminated orbit-48 startup has no clean common frames; that interval is omitted. The separately recovered cameras 2–4 startup solution uses a different attitude convention and is not mixed into this figure.

## Figure C — endpoint_pointing_predictions

- **Caption:** Withheld endpoint pointing predictions from fixed-guide, guide-plus-quadratic-drift and empirical velocity-response models. Upper panels show measured transverse attitude component 1 and predictions, all relative to the first measured value in that interval. Lower panels show the two-component prediction-error magnitude in arcseconds. Training excludes the entire endpoint and its 0.25-day buffer. The roll component remains measured; these are not autonomous full-attitude forecasts. The empirical velocity response need not recover unique onboard guide weights.
- **Why separate:** A small attitude-conditioned distortion error does not certify a good pointing prediction. None of the three displayed models dominates every endpoint.

## Conclusion carried by the packet

- Startup leaves coherent spatial prediction errors and distinct pointing errors even with thermal information available.
- Thermal history is explanatory context; the figures do not isolate mechanical causation or establish an invariant ePSF centre.
- All numerical curves come from the frozen October 2 endpoint products, without refitting, selecting new models, or replacing withheld results with in-sample calibration residuals.


**Sensor-label clarification, 2026-10-16:** use the exact PT1000 channel numbers. The Sector20 FITS `DESCRIPT` calls sensor2 Lens Barrel and sensor6/7 FPE Housing; the Instrument Handbook TableA.3 names sensor2 L1, leaves sensor6 generic and names sensor7 Base Plate. These source descriptions do not uniquely establish which mechanical component causes a WCS change. Sensor10 is the mosaic in both sources. Plot labels now retain numeric identifiers.


# Figure: centre conventions and orbital endpoints

**Caption — `centres_endpoints.pdf`.** Effect of a fixed elliptical-Gaussian centre convention on Sector20 camera3/CCD3 centroid-derived WCS. (a) The saved effective profile at the central detector probe in reference exposure292. (b,c) First- and last-exposure profiles of orbit47, minus that reference; their amplitudes are matched within the two-pixel fitting radius, without translating either profile. The difference panels share a colour scale. Circles mark the fitting radius. (d–g) RMS vector motion across81 detector locations, measured relative to the first usable exposure in each orbital-endpoint window. Black and orange curves use the original and Gaussian origins, respectively; blue shows the conversion itself. Physical velocity aberration is removed, and the measured common attitude is held fixed. These curves use the complete usable-cadence archive, not the earlier sparse pilot. An origin conversion does not remove the bulk startup motion. It is a coordinate-convention test, not an independent measurement of true positions or a causal thermal attribution.

- Source coverage:1167 usable exposures;81 locations; C3/CCD3 only. Gaussian fits use the saved pixel-integrated effective profiles, fixed radius2 pixels, free elliptical covariance, and zero background.
- Orbit47 first-day window RMS:11.424→11.495 millipixels;49 exposures.
- Orbit48 first-day window RMS:9.692→10.062 millipixels;38 exposures.
- Orbit47 last-day window RMS:2.064→2.777 millipixels;49 exposures.
- Orbit48 last-day window RMS:2.917→2.910 millipixels;49 exposures.
- Window metrics include the common detector translation remaining after the fixed attitude subtraction; they are not the separately tabulated shape-only metric.
- Window metrics are relative to each window's first exposure, not absolute errors or withheld-time prediction scores. Their numerical denominator differs from the thermal-model validation figures.
- Display amplitudes are adjusted only to make profile-shape differences visible. No position or ePSF is refitted for figure generation.
- First/last profile images are illustrative central-probe orbit47 exposures0 and588; the WCS curves summarize all81 probes in each window. These images do not alone represent every spatial or temporal variation.

**Caption — `centres_full_series.pdf` (supporting figure).** Evolution of the Gaussian-origin offset relative to exposure292 for three representative detector probes, using all1167 usable exposures. The x and y offsets are in native detector millipixels. The vector RMS over the complete81-probe dataset is3.478 millipixels. Constant offsets between centre conventions cancel in this time-dependent comparison. This is sensitivity to the profile-origin definition, not a validated correction to geometric positions.

- Main conclusion: the tested Gaussian convention changes millipixel structure, but does not suppress the dominant first-day motion.
- Remaining requirement: independently measured stellar positions on identical pixel support, with a common explicit centre convention; no accuracy claim follows from the conversion alone.
- Inputs and output hashes: `/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/centres/manifest.json`.
- Generator: `FIG_CENTRE_CONVENTIONS.py`; activate `syndiff`, then run the script. No new model fits or training jobs.


## Figure 5 — What do the centroids agree on?

- **Caption:** Temporal consistency of the legacy and jointly trained C3/CCD3 positions on a fixed cohort of1976 stars across590 exposures in orbit47. (a) Each star’s persistent offset is removed before taking the per-exposure median x/y differences. Gray bands identify the first and last observed days. (b,c) Per-star differences between those endpoint intervals and the orbit interior, with common colour scales; arrows show3×3-cell median vectors. Interior averages exclude the first/last two days.
- **Supports:** common temporal agreement is much tighter than individual-star agreement; spatially clustered differences remain.
- **Does not establish:** absolute accuracy, independent held-star validation, whole-CCD coverage, or orbit48 behavior. The trained region is the central1024×1024crop, and the model shares centroid-informed initialization and training images.
- **Metric:** common temporal vector RMS1.218mpx, cell-median RMS2.388mpx; these are estimator disagreements, not errors against known true positions.
- **Underlying image evidence:** retain the actual hp_d first/interior/last stellar stamps beside this figure on the webpage. The markers use the original, differing centre conventions.
- **Interpretation:** the centroids are useful for provisional ensemble trends, but cannot yet certify the smallest claimed WCS residuals.


# Same-image held-source positional pilot: method and figure notes

2026-10-15. Technical validation record, not manuscript prose. Source: SAME_IMAGE_PILOT.py in this directory. Outputs: `/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/` (100-source pilot) and `all_fold0/` (complete fold0 diagnostic).

## Contract

- One frame only: `tess2020013215923-s0020-3-3`, Sector20 Camera3 CCD3, orbit48 interior. No endpoint or multicamera validation.
- Frozen fit: `/astro/armin/koji/syndiff/dev_runs/e2e_final_recipe_20261007/run5/F2/folds_final/fits/fold0/`.
- Exact source pin: `4e248f6566f5d80f02ea7aec8d6bdfb6ff7082c2`; inspected `forward_model/crossfit/raster_oof.py`, `diagnostics/stacked_temporal_residuals.py::rasterize_packed_values`, `chain/crossfit.py::evaluate_fold` in campaign's pinned code checkout.
- Test image/noise/mask: campaign `run5/F2/nbr_final/scene_bundle.npz`, same image generation on both sides. NOT production legacy hp_d.
- Held-source contract: accepted `folds_final/eval/fold0/score.npz/held_fixed`; underlying source and whole core held, ncore>=15. Saved raster contains1720 strict held sources with finite BP-RP and positive solved flux.
- PSF/WCS parameters exclude these held sources, but raster generation re-solves source/neighbour fluxes and priors on the test scene. Thus this is conditional on photometric nuisance fitting; it is not a wholly blind pixel prediction. Shared upstream calibration remains a limitation.
- Current model reference positions are reconstructed from the fold's saved coefficients and explicit chromatic shifts by `wcs_centres/trained_compare_single.py::positions`. No model training or loss reevaluation occurs.

## Essential sampling audit

- Saved33×33 rasters live on a quarter-pixel DISPLAY grid. The actual measured values are native detector pixels bilinearly splatted to separate2×2 display cells, normalized by target solved flux.
- Fitting all finite raster cells would duplicate pixel evidence and assign false subpixel sample locations. This code instead reconstructs the exact native coordinates from source scene `cx/cy`, `x0/y0` and15×15 stamp indexing.
- Native pixels are separated by4 display cells, so their splats do not overlap. Recover each value from its occupied2×2 cells, verify within-splat equality, multiply by saved flux. Independently check recovered DATA=(MODEL+RESIDUAL) against original scene data before fitting.
- Unmeasured display holes remain NaN; they never enter the fit. Use original scene valid/noise arrays and identical finite native support for DATA and MODEL.

## Estimator, exclusions, controls

- Primary: independently fit elliptical Gaussian amplitude, centre, two widths, shear and constant background to native DATA and MODEL; inverse-variance weights identical; fixed radius3px around the current saved effective render origin. Report DATA-centre minus MODEL-centre. Both sides fit the same non-Gaussian image approximation; neither side is absolute truth.
- Sensitivity: radius2 constant background, radius3 planar background. Report full accepted samples and a separate common-successful-source population. Bound-limited/nonconverged fits excluded and counts retained; support minimum12 native pixels (15 for plane).
- Model is the full summed scene prediction, including neighbours. Isolation control uses frozen catalogue geometry: nearest source>3px and nearest neighbour with at least10% nominal target brightness>5px. Catalogue search extends8px. This is a control, not proof of isolation; residual unlisted faint neighbours may remain.
- Mask control: fully retained nominal aperture vs all accepted. All data/model support is identical per pair. No clipping on measured residuals.
- Exact Gaussian known-shift controls use each source's actual support, phase and mask. They test optimizer/sign implementation, not astronomical model accuracy.
- Noise proxy: one seeded noisy Gaussian per source using the original noise scaled to model peak, fixed widths0.8/0.7px and shear0.1. Refit with identical estimator. This is a conditional synthetic noise comparison, not a measured error floor; it excludes real non-Gaussian shape, uncertain backgrounds, blends and upstream model uncertainty. Do not subtract its RMS in quadrature and call the remainder instrumental error.
- No standard training residual-grid regeneration: no new training/fixed-scene rendering took place. All native reconstructed images and existing model residuals are retained.

## Artifacts / API

- `positions.csv`: IDs, saved model position, Tmag/colours, neighbour flags, radius/background policy, count/support fraction, convergence, DATA/MODEL centres, signed differences and Jacobian condition diagnostics.
- `summary.csv`: policy/population counts, median,90th percentile, vector RMS and mean signed residuals.
- `matched_sensitivity.csv`: same-source policy comparison, avoiding selection-induced differences.
- `binned_signed.csv`: spatial-cell, Tmag and colour counts, signed medians and vector residual summaries.
- `recovery_audit.csv`: per-source native reconstruction errors.
- `controls.csv`, `noise_controls.csv`: exact-shift and noise proxy results.
- `native_stamps.npz`: all native DATA/MODEL/RESIDUAL/support arrays and IDs; binary products stay on /astro.
- `audit.json`: paths, source pin, frame, selection and failure details, pre-plot compute duration.
- `position_diagnostics.png`: six panels (position/magnitude/colour/neighbours, signed-cell median, noise proxy).
- `spatial_stacks.png`: all selected sources' per-cell DATA/MODEL/residual median stacks in native stamp coordinates. No subpixel recentering; both sides share identical stack operation. Per-source model-peak normalization, residual scale ±3%.
- `stamps_*.png`: representative individual measured native DATA/MODEL/residuals, shared per-star peak normalization and residual scale ±5%; mask contour shown. All sources remain in NPZ even when gallery is sampled.

Commands (activate syndiff first):

```
OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python SAME_IMAGE_PILOT.py --limit 100
OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python SAME_IMAGE_PILOT.py --limit 0 --gallery-limit 24 --output /astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/all_fold0
```

## Preliminary100-source checkpoint

- Compute6seconds before plots;98 primary accepted pairs. Median5.41mpx,90th percentile12.15mpx, vector RMS10.51mpx. Isolation subset70 sources, median5.51mpx. These numbers describe estimator residual on selected stars, not accuracy of WCS.
- Native DATA recovery maximum relative discrepancy8.33e-8; exact Gaussian control maximum centre error5.60e-12px.
- Inspected position diagnostic and all five pilot stamp pages. Some crowded/masked examples and a long residual tail are visible; source isolation does not remove every outlier.
- Final all-fold result below supersedes this selected-sample summary for population statements.

## Claim boundary / caption outline

Suggested caption: “Same-image position consistency for sources excluded from a frozen fold0 PSF/WCS fit. Independently fitted native-pixel Gaussian centres of observed and summed-model stamps are compared on identical masks and weights. Panels show signed/spatial, brightness/colour and isolation dependence; companion panels show the underlying native data, model and residual images. Photometric nuisance fluxes were solved on the test scene. This tests conditional model–image consistency in one exposure, not absolute astrometric truth or time-transfer.”

Conclusion: this diagnostic closes the different-image and source-holdout gaps of the earlier legacy-versus-trained comparison for one static frame, with explicit conditional flux fitting. It does not close epoch holdout, multicamera coverage, independent centroid definition or physical-truth validation.

## Final complete-fold result

- All1720 saved strict-held fold0 sources tested; primary radius3 constant-background1689 accepted,31 bound-limited or nonconverged. Compute126.5seconds before figures, one BLAS/OMP thread. No retraining.
- Direct audit against the frozen fold's `held_pixel_mask.npy`: zero fitting-support violations across all1720 native masks, including the effective-origin radius3 support. No mask intersection was needed, no results changed. Reproducible assertions now enforce this in the script. `all_fold0/held_support_audit.json` records the independent check.
- Native recovery maximum relative discrepancy1.095e-7; exact Gaussian shift controls maximum error9.20e-11px.

|Primary population|Accepted pairs|Median [mpx]|90th percentile [mpx]|Vector RMS [mpx]|
|---|---:|---:|---:|---:|
|All accepted|1689|5.263|11.635|26.791|
|Isolation control|1126|5.503|11.421|8.529|
|Full aperture support|1502|5.219|11.227|10.752|

- Long tails matter:16 accepted residuals>40mpx,14>50mpx,5>100mpx. Four of14>50mpx still pass the catalogue-isolation criterion. All five>100mpx fail isolation; three have incomplete aperture support. No sigma clipping or residual-dependent rejection was used.
- Largest accepted displacement987mpx: neighbour separation0.683px and79.3% aperture support; the single-Gaussian approximation is unsuitable in this strongly blended/masked case. The five largest residuals are shown explicitly in `outlier_stamps.png/pdf` with DATA/MODEL Gaussian markers. They remain in the all-accepted RMS.
- Common successful-source sensitivity population1295: radius2 constant, radius3 constant, radius3 plane respectively have median5.249/5.182/5.159mpx and RMS8.428/10.843/7.982mpx. This matched population is smaller than the full primary set; do not claim its lower RMS as an improvement on identical1720-source coverage.
- Same1689 accepted-source Gaussian noise proxy: median1.033mpx, RMS1.872mpx. Real-image residuals are broader than this simple synthetic-noise control. This does not uniquely identify WCS error, since real shape, background, blending and model uncertainty were omitted from the proxy.
- Spatial cells have122–243 accepted sources. Their signed coordinate medians range roughly−2.0 to+1.3mpx; these are coherent estimator residuals in one exposure, not independent accuracy estimates or significance detections. Full cell/colour/magnitude counts and signed summaries are in binned_signed.csv.

![Six-panel positional diagnostic](/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/all_fold0/position_diagnostics.png)
![Underlying all-source spatial stacks](/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/all_fold0/spatial_stacks.png)
![Largest residuals, retained in reported RMS](/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/all_fold0/outlier_stamps.png)
![Representative sources, page1](/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/all_fold0/stamps_00.png)
![Representative sources, page2](/astro/armin/koji/syndiff/dev_runs/wcs_paper_package_20261015/figure_outline/same_image/all_fold0/stamps_01.png)

PDF exports share those basenames. Six-panel scatter plots show every accepted tail on logarithmic displacement axes; histogram explicitly states16 data values>40mpx omitted from its displayed range. Spatial-stack residual scale is±0.3% of model peak (updated from the initial±3% diagnostic); individual residual stamps use±5%. Representative gallery selects24 evenly spaced source-list entries independent of residual; worst-five gallery is explicitly residual-selected.

Final caption bullets:

- Same underlying image generation, native pixel coordinates, per-pair support and noise; no oversampled display holes treated as observed pixels.
- Strict held-source and held-pixel audit; frozen shape/WCS with photometric nuisance fluxes re-solved on test scene.
-1720 tested,1689 accepted; typical5.26mpx estimator difference with visible long tails, not5mpx astrometric accuracy.
- Show counts, masks, crowded worst cases, signed-cell residuals and matched-sample radius/background checks.
- One fold, one orbit48 interior exposure; endpoint, cross-orbit, multicamera, independent calibration and absolute-truth tests remain open.

Conclusion: the same-image held-source pilot is now executed and traceable. It establishes several-millipixel typical native-Gaussian model–data disagreement plus a consequential blended/masked tail. It closes specific image-generation and source/pixel-holdout confounds of the prior comparison, but cannot certify accurate physical WCS or explain temporal motion.