Fix symmetric vMF mixture handling on the hyperhemisphere

[FlorianPfaff]

Summary

• require two-component hyperspherical mixtures to actually satisfy the documented symmetric-vMF contract
• reject unequal vMF concentrations and non-antipodal component modes in identity measurement updates
• reject non-vMF mixtures in the prediction helper instead of silently evaluating them with a vMF transition formula
• recenter valid measurement mixtures with set_mode(...) rather than mutating caller-owned component means
• add focused regressions for symmetry, ownership, type safety, and unit-measurement validation

Bugs

1. Asymmetric mixtures accepted by update_identity

HyperhemisphericalGridFilter.update_identity(...) documents support for a symmetric two-component HypersphericalMixture, but main only checks that the mixture has two 0.5-weight components and then overwrites their means with z and -z.

For two vMF components, equal weights are not sufficient for antipodal symmetry: their mean directions must be antipodal and their concentrations must match. With unequal kappa, p(x) != p(-x), yet the hyperhemisphere update evaluates 2 * meas_noise.pdf(...). That makes the likelihood depend on which antipodal representative is used.

The upstream libDirectional update path also omits the equal-concentration check, while its transition-density path correctly requires equal concentrations.

Direct .mu assignment additionally mutates the caller-provided noise model and bypasses vMF unit-direction validation.

2. Non-vMF mixtures interpreted as vMF system noise

sys_noise_to_transition_density(...) checks mixture weights, means, and kappa, but not the component type. A symmetric 50/50 mixture of two Watson distributions therefore passes the condition and is then evaluated using the vMF transition formula. This silently changes the model rather than rejecting an unsupported noise family.

Fix

Mixture-based update/prediction paths now require:

• exactly two components
• 50/50 weights
• vMF components
• antipodal component mean directions
• equal concentrations

Valid measurement components are recentered via their non-mutating set_mode(...) API, which also validates that z is a unit direction.

Validation

Focused regressions cover:

• measurement-noise object is unchanged after a valid update
• unequal concentrations are rejected
• non-antipodal vMF components are rejected
• non-unit measurements are rejected rather than being written into a vMF object
• symmetric non-vMF mixtures are rejected by the prediction helper instead of being reinterpreted as vMF

GitHub Actions is the authoritative full backend/lint/integration validation.

[github-actions]

✅MegaLinter analysis: Success

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✅ REPOSITORY	checkov	yes		no		no	36.14s
✅ REPOSITORY	git_diff	yes		no		no	0.13s
✅ REPOSITORY	secretlint	yes		no		no	108.45s
✅ REPOSITORY	syft	yes		no		no	2.64s
✅ REPOSITORY	trivy-sbom	yes		no		no	2.81s
✅ YAML	prettier	11	0	0		0	0.68s
✅ YAML	v8r	11		0		0	14.63s
✅ YAML	yamllint	11		0		0	1.11s

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