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[NEW FEATURE] Fourth-order moments #697

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@martinkilbinger

Implement fourth-order moments for PSF diagnostics (PSFHOME-style; useful for PSF-leakage systematics in DES/HSC).

Current state. No higher-order-moment code exists on develop. PR #698 (branch moment4) implemented this in psfex_interp.py (_get_psfshapes / _get_starshapes): whiten the pixel grid with the inverse-sqrt second-moment matrix, compute the centered p+q=4 moments, store the spin-2 combinations M40 − M04 and 2(M13 + M31) as M_4_{PSF,STAR}_{1,2}. That branch is now ~435 commits behind develop and predates the HSM column-grammar refactor.

Plan. Implement as a follow-up on top of #812 (sky-coords HSM), which rewrites the same two functions. Measuring in sky coordinates removes the pixel→sky rotation the old code would need. Deliverables:

  • spin-2 fourth-moment combinations (port the fourth-order moments #698 math onto the sky-coords frame; the whitening matrix must be built from the sky-frame moments),
  • galsim's spin-0 moments_rho4 (already computed by FindAdaptiveMom, currently discarded),
  • tests for both.

#698 is kept open as reference for the original implementation; the new work supersedes it.

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