Initialize hyperhemispherical particle filter on valid manifold points

[FlorianPfaff]

Summary

• initialize HyperhemisphericalParticleFilter with deterministic unit vectors at the upper-hemisphere north pole instead of uninitialized memory
• add regression coverage that requires every initial particle to have unit norm and lie on the upper hemisphere

Bug

HyperhemisphericalParticleFilter.__init__() constructed its initial HyperhemisphericalDiracDistribution from empty((n_particles, dim + 1)). On NumPy/PyTorch this can expose arbitrary allocator contents; on backends that zero-fill empty, it produces zero vectors. Neither is a valid deterministic point set on the unit hyperhemisphere, so a freshly constructed filter can start with off-manifold or non-finite particle locations before a caller assigns a prior.

The neighboring HypersphericalParticleFilter already avoids this by initializing with valid sphere points.

Fix

Initialize all particles at the north pole [0, ..., 0, 1]. This is deterministic, has unit norm, and is in the upper hemisphere for every supported dimension.

Validation

• focused regression checks particle norms, upper-hemisphere membership, and the north-pole coordinate
• branch is based directly on current main and changes only the filter constructor plus its existing test module
• modified source passes Python syntax compilation locally
• full backend/test validation is delegated to GitHub Actions because this environment cannot clone the repository over the network

[github-actions]

✅MegaLinter analysis: Success

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✅ MARKDOWN	markdownlint	68	0	0		0	1.74s
✅ MARKDOWN	markdown-table-formatter	68	0	0		0	0.35s
✅ PYTHON	black	1983	10	0		0	45.75s
✅ PYTHON	isort	1983	20	0		0	2.16s
✅ REPOSITORY	betterleaks	yes		no		no	1.16s
✅ REPOSITORY	checkov	yes		no		no	27.45s
✅ REPOSITORY	git_diff	yes		no		no	0.18s
✅ REPOSITORY	secretlint	yes		no		no	77.36s
✅ REPOSITORY	syft	yes		no		no	2.43s
✅ REPOSITORY	trivy-sbom	yes		no		no	1.58s
✅ YAML	prettier	11	0	0		0	0.75s
✅ YAML	v8r	11		0		0	13.48s
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[FlorianPfaff]

Correction: the earlier triage note was based on stale/mismatched PR metadata. This PR is the valid-manifold initialization fix for HyperhemisphericalParticleFilter, not the hemisphere particle-count change. Reopening it and evaluating it on its own merits/CI.

[FlorianPfaff]

Closing as superseded by #5345, which fixes the same HyperhemisphericalParticleFilter initialization bug and additionally covers HyperhemisphereCartProdParticleFilter with regression tests. Keeping the broader fix avoids duplicate changes.