What's New in v30.5 — Label-free PSF-functional reduction

I044 project

2026-07-07

Scope of the v30.5 revision

v30.5 adds exactly one passage to v30.4 (Section “Closed-form global corrections”, immediately after the PSF-family scoping paragraph introduced in v30.4). Nothing else changed: no numbers, equations, figures, tables, or validation domains were touched. The passage does two things:

Announces (without detail) that the per-instrument, per-band correction structure dissolves into a label-free PSF-functional law, deferred to a follow-up paper.
States a new operational requirement: correction coefficients are specific to the PSF-template preparation convention, so calibration and deployment must share one template pipeline.

This note records the full evidence behind both statements. Per the project decision, the reduced law itself is the main result of the follow-up paper, so the manuscript passage deliberately gives the structure but not the numbers; the numbers live here and in the internal experiment records (E055/E056).

The pilot: six real `psfgen` templates

Templates: PN, MOS1, MOS2 $\times$ energy bands 1 and 4, at a fixed central detector position $(x,y)=(330,330)$ . The decisive methodological point — discovered the hard way, see Section 3 — is that all six templates must be prepared through one pipeline. The unified pipeline used:

$401\times401$ psfgen product $\;\rightarrow\;$ rebin $4\times4$ (sum) $\;\rightarrow\;$ center crop to $31\times31$ $\;\rightarrow\;$ normalize on the $\mathtt{ecut}=15$ circular mask.

(Band-1 high-resolution products did not exist and were generated with SAS psfgen; band-4 reused the existing PSF-audit products.)

Measurement per template: the standard reference-fitter pipeline (Poisson images, profile likelihood over a $7\times7$ integer position grid, amplitude profiled by the Poisson score), $S_\mathrm{true}$ grid of 11 values from 0 to 90, backgrounds $b \in \{0.01, 0.02, 0.04, 0.08, 0.16\}$ , 1200 draws per cell, 396,000 rows, binned in $\widehat{S}$ only (never in $\mathrm{DET\_ML}$ ), residuals taken against the first-order theory, and the same five-coefficient functional forms as the manuscript’s Eqs. (mean-corr)–(sigma-corr) fitted per template with bootstrap errors.

Result: three shared constants + two single-feature laws

Unified-pipeline coefficients:

Per-template correction coefficients, unified preparation.
Template	$A_\mathrm{psf}$	peak_frac	$a_\mu$	$c_\mu$	$p_\mu$	$a_\sigma$	$c_\sigma$
M1 b1	30.86	0.0960	$0.190\pm0.048$	$-0.847\pm0.066$	$0.188\pm0.031$	$1.766\pm0.084$	$0.526\pm0.062$
M1 b4	28.85	0.0990	$0.289\pm0.043$	$-0.729\pm0.084$	$0.196\pm0.036$	$1.743\pm0.096$	$0.506\pm0.070$
M2 b1	30.69	0.0946	$0.284\pm0.051$	$-0.793\pm0.080$	$0.226\pm0.032$	$1.719\pm0.094$	$0.512\pm0.067$
M2 b4	29.13	0.0971	$0.271\pm0.053$	$-0.778\pm0.086$	$0.225\pm0.036$	$1.668\pm0.083$	$0.505\pm0.058$
PN b1	40.21	0.0704	$0.050\pm0.029$	$-0.668\pm0.052$	$0.043\pm0.024$	$1.619\pm0.085$	$0.483\pm0.058$
PN b4	35.90	0.0779	$0.098\pm0.032$	$-0.678\pm0.044$	$0.079\pm0.023$	$1.759\pm0.087$	$0.596\pm0.065$

Collapse tests (H1 = one shared value across all six templates within bootstrap errors; H2 = linear in one scalar PSF feature):

The label-free reduced model. No instrument or band identifier appears anywhere; the only inputs are two scalar functionals of the PSF template. ( $\chi^2/\mathrm{dof}$ values from the independent audit.)
Coefficient	Verdict	Reduced model	max $\|z\|$
$a_\sigma$	H1	shared $1.710$ ( $\chi^2/\mathrm{dof}=0.46$ )	1.07
$c_\sigma$	H1	shared $0.520$ ( $\chi^2/\mathrm{dof}=0.38$ )	1.16
$c_\mu$	H1	shared $-0.726$	1.84
$a_\mu$	H2	$0.877 - 0.0209\,A_\mathrm{psf}$	0.95
$p_\mu$	H2	$-0.412 + 6.40\,\mathrm{peak\_frac}$	1.02

Fifteen per-(instrument, band) factor arrays reduce to three shared constants and two one-feature linear laws. This is the result deferred to the follow-up paper.

Physically this is coherent with everything else in the record: the detection statistic itself contains no instrument or band physics — those labels enter only through the PSF template — and the beyond-Fisher residual is driven by the position-argmax mechanism, whose strength is set by PSF geometry (sharpness, effective area), not by which camera produced the photons.

The confound that almost hid this

The first pilot (E055) used band-1 templates that were native $31\times31$ psfgen products but band-4 templates from the $401\times401\rightarrow$ rebin $\rightarrow$ crop pipeline. The $\sigma$ -law coefficients then showed an apparent “band dependence”:

The apparent band dependence of the $\sigma$ -law coefficients was entirely a template-preparation artifact: it vanishes when all six templates share one pipeline.
	Confounded (E055)		Unified (E056)
Coefficient	band-1 vs band-4	split	band-1 vs band-4	split
$a_\sigma$	$1.415$ vs $1.722$	$4.3\sigma$	$1.701$ vs $1.720$	$\mathbf{0.27\sigma}$
$c_\sigma$	$0.373$ vs $0.533$	$3.2\sigma$	$0.506$ vs $0.535$	$\mathbf{0.55\sigma}$

A $4.3\sigma$ effect produced purely by the difference between a native low-resolution template and a rebinned high-resolution template of the same PSF is the direct empirical basis for the second statement added in v30.5: the absolute correction coefficients are a property of (PSF $\times$ preparation convention), not of the PSF alone. Concretely, the unified-preparation constants ( $a_\sigma=1.71$ , $c_\sigma=0.52$ ) differ from the manuscript’s production values ( $1.49$ , $0.39$ ), which were calibrated with the production template pipeline at 17 positions — both are internally valid; they must never be mixed across pipelines.

Validity boundary of the pilot, and what is being checked next

Single central detector position $(330,330)$ ; an off-axis cross-validation at two additional positions (moderate and far off-axis, 12 further templates through the same unified pipeline, testing whether the frozen central reduced model predicts the off-axis coefficients) is running as the immediate next step.
1200 draws/cell; integer $7\times7$ position grid (same approximation as all pilots in this series); a continuous-position fitter spot check remains open.
Two energy bands (1 and 4); the intermediate bands are expected to interpolate but have not been measured.

Summary