[Paullo9]

Requested by Paul · project thread

Part of #8

Stacked on #59 (issue-8-pooled-sum-peaks): both PRs add a FitPolicy field with a tolerant decoder in QuantificationPolicy.swift, and #50 touches it too. Merge #59 first; this PR's base is that branch.

What

The default continuum cuts its Bernstein segments at the Al K edge (1.5596 keV) with a jump between two adjacent channels. A detector cannot record a jump: every channel is the incoming spectrum convolved with the resolution (about 75 eV FWHM at 1.56 keV for 128 eV at Mn K-alpha). On top of that, the Al K-beta line sits at the edge energy itself.

FitPolicy.continuumEdgeStep = .broadened (opt-in) weights each segment by the detector's Gaussian step at its edges, w_s = Phi((E - a)/sigma_a) - Phi((E - b)/sigma_b). Sigma comes from the line-width law at the edge, at the line model's resolution, so it follows the axis refinement. Each polynomial continues past its edge at its end value. The weights telescope to 1 and stay non-negative, so the continuum stays non-negative.

• .sharp stays the default and is the earlier form, value for value.
• The default policy's canonical JSON is unchanged byte for byte: the key is written only when it is not the default.
• A stored policy without the key decodes to .sharp.
• exSpy's background is a plain polynomial with no edge, so no parity path is involved.

Diagnosis

Cause: the sharp step at the edge channel, plus the order-5 segment above the edge, which cannot follow the absorption recovery just above the edge. Cheap experiment first: broaden the step and refit. The step part would be refuted if broadening left the misfit unchanged. It halves it.

Pure-Al wedge, public dataset: Snelson, Collins, MacArthur (2026), University of Leeds, doi 10.5518/1826, CC BY 4.0. Titan 200 kV, Super-X, 214 793 px, 3e5 Al K-alpha counts, same refined axis.

continuum	model drop minus data drop across 1.559/1.564 keV	data minus model, 1.53-1.65 keV	model / data - 1, 1.65-2.2 keV	chi2/n, 0.8-2.6 keV
sharp (default)	351 counts	+1677	+39.1 %	6.63
broadened	42	+907	+19.1 %	3.10
broadened, Poisson ML		+850	+8.2 %	2.52
no edge split		+3097	+49.1 %	12.0

Raising the order of the segment above the edge (9, 9) does not help on this spectrum (+20 %). What remains in 1.53-1.65 keV is data above the model on the high side of the Al K lines; the tied Al K-beta weight (EPQ 0.0132) at the edge is the next candidate.

Synthetic, noise-free (generated in the test, no measured file in the repo). Al film with a resolution-broadened edge, 3e5 Al K-alpha, weak Si K-alpha of 2000 counts:

continuum	Si net vs planted
sharp	-38.7 %
broadened	-25.4 %
broadened, orders (9, 9) (measured, not shipped)	-8.0 %

The public AlMgSi demo (sim_edx.py v2.0, noise-free pools ×100, true axis) plants an unbroadened step. Broadening still helps there, because Al K-beta sits on the split.

pool	Si sharp	Si broadened	Si sharp + sum peaks	Si broadened + sum peaks	Mg sharp	Mg broadened
recipe A (1217 px)	-17.2 %	-16.2 %	-6.2 %	-3.5 %	-32.0 %	-29.8 %
all matrix (2897 px)	-18.8 %	-17.9 %	-6.4 %	-3.6 %	-31.8 %	-29.7 %
precipitate end-on	-3.2 %	-3.2 %	-3.0 %	-3.0 %	-1.2 %	-1.2 %

Si planted counts include Si K-beta and the internal-fluorescence peak.

Why opt-in, not the default

Switching the default moves five registered synthetic results:

• testWeakLineRecoveryRegisteredSelection, whose numbers appear in every footer;
• the FitRange P1 and P3 Ti pins;
• the proposer null-variance pins;
• one detection-rate draw;
• the seeded flatness test.

The cause is the same in all five: their generators plant an unbroadened step, so they measure a sharp truth. Making .broadened the default means first moving those generators to a convolved continuum and re-measuring the results. That stays open on #8, together with the order of the segment above the edge.

Tests

• New: ContinuumEdgeBroadeningTests.
  • Red on main: on the broadened-edge spectrum the default (sharp) fit reads Si -38.7 % and misses the edge channel by 5.5 %.
  • Broadened against sharp, on pure Al and with weak Si.
  • .sharp gives the same columns as the unbroadened form.
  • The weights sum to 1, with one edge and with two close edges.
  • The policy default, the footer line, round-trip decoding, and an old stored policy.
• Gate: swift test -c release --parallel --num-workers 1 -j 1 --skip SpectroKitParityTests, 290 tests green (on the merge with feat!: the pooled fit models sum peaks when the strongest line's self pair is significant #59). Goldens do not move (the default is unchanged), so the parity target was not run.
• Numerics review done (one reviewer). It found that the product form over-counts between two close edges; fixed with the telescoping difference and a two-edge test. It also asked for byte-stable default JSON; done.
• validation: "none": one standard, one detector, synthetic truth.

🤖 Generated with Claude Code