fix(profile): fade each peak to zero at its support edge

[drthyang]

Problem

synthesizePattern summed each peak inside a hard ±20·FWHM window, and leBailExtract inside ±12·FWHM. The edge moves with every width and position parameter. When a data point crossed it, y jumped by the pseudo-Voigt's Lorentzian tail. A central difference divided that jump by 2h, so the column spiked ∝ 1/h at one point.

On the Mn₃Ga 30 K example (Example 3, claude/example-magnetic), the profW column at the engine's step gave JᵀJ = 218, 91 % of it from one data point, instead of 8.7.

Fix

supportTaper fades each peak to exactly 0 over the outer 20 % of its support with a C² quintic. It depends only on dist/half, so it moves smoothly with Γ and the centre.

• The binary-search window is unchanged. Points in the flat 80 % are bit-identical.
• The fade removes 0.18 % of a Lorentzian's area; the 1.6 % beyond 20 Γ was never modelled.
• Gaussian and TOF tails are already below 1e-7 of the peak there. TOF's old jump was at most ~2e-9 of the peak, so TOF moves only at roundoff.
• Le Bail gets the same fade. The cell check refines its FWHM by finite differences, and a crossing there had moved yCalc by 7e-4 of the peak.
• Cost: ~7 % per synthesis (7.2 vs 6.75 ms at 20k points × 5k pseudo-Voigt peaks).

Example 3 replay (old → fixed)

	old	fixed
profW JᵀJ at the engine step	218.4 (90.6 % from point #1273)	8.730, flat for h = 1e-2…1e-6
profW esd	0.071	1.16
profU / profV esd	1.60 / 1.59	3.40 / 4.66
final χ² → after continuing	6366.1 → 6357.7	6366.1 → 6357.5

The last row is a separate issue this PR does not fix. The final fit stops early on a flat U/V/W–moment valley, with or without the spike.

Tests

All four new tests fail on the old code.

• peakWindow.test.ts puts a data point exactly on the strongest peak's edge. The profW JᵀJ must agree across h = 1e-3…1e-7·|W|. With the hard cutoff it was up to 7·10⁶× too large.
• profile.test.ts requires the finite-difference width derivative to match the analytic ∂pV/∂Γ at every step. It also checks that a peak is exactly 0 at its edge, and that ascending, descending and unordered grids agree.
• leBail.test.ts requires Le Bail to stay continuous in the width across an edge crossing.
• nextParameters.test.ts changed its "converged model promises no real wR gain" case. It now converges scale + background on noisy data first. Its starting values alone left wR at 18 %, and the profile group's predicted gain there (0.0053 vs a 0.005 limit) depended on the tails. Converged: wR 0.8 %, largest predicted gain 2e-5, limit tightened to 1e-3.

Golden shifts

All are GaNb₄Se₈ synchrotron data with a TCH pseudo-Voigt. Every other golden moved only at roundoff.

• Rietveld wR: 10.3484 → 10.3475 %
• Staged: wR 5.718 → 5.721 %, W 5.040 → 4.997
• GSAS-II benchmark, fixed atoms: 18.31 → 18.33 % (single pV) and 23.44 → 23.33 % (TCH+FCJ)

Verification

• vitest run with data/ present: 1495 passed, 46 skipped (the same env-gated skips as main).
• tsc -b --noEmit and eslint . are clean.

🤖 Generated with Claude Code