Stabilize discrete-state initial probability normalization

[FlorianPfaff]

Summary

• normalize finite-state initial probability vectors after scaling by their largest entry
• preserve relative HMM and IMM priors when their direct floating-point sum would overflow
• add regressions for both discrete_forward_backward() and imm_forward_backward()

Root cause

The public discrete-state compatibility layer validated each prior entry as finite and non-negative, then summed the raw values directly:

total = float(values.sum())
return values / total

Individually finite weights can still have an infinite sum. For example, [max_float, max_float / 2] has the well-defined ratio 2:1, but its direct sum overflows to inf. Dividing by that total produces [0, 0], so valid initial HMM or IMM probabilities lose all mass and the filter fails at the first emission.

Fix

After applying the optional valid-state mask, scale the vector by its largest entry before summing. The scaled values lie in [0, 1], retain the original ratios, and normalize to finite unit mass. Existing validation for shape, numeric type, finiteness, non-negativity, and positive mass is preserved.

Validation

• reproduced the old normalization result: [max_float, max_float / 2] -> [0, 0]
• verified the scale-first result is [2/3, 1/3] with unit mass
• added end-to-end HMM and IMM regressions through the public API
• python -m py_compile passes for the modified source and new test
• branch is two commits ahead of current main and zero behind; production diff is 4 additions and 3 deletions

The full repository test and backend matrix is delegated to GitHub Actions.

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	21.63s
✅ JSON	prettier	7	0	0	0	1.32s
✅ JSON	v8r	7		0	0	3.88s
✅ MARKDOWN	markdownlint	68	0	0	0	1.94s
✅ MARKDOWN	markdown-table-formatter	68	0	0	0	0.62s
✅ PYTHON	black	1490	182	0	0	86.61s
✅ PYTHON	isort	1490	328	0	0	2.52s
✅ REPOSITORY	betterleaks	yes		no	no	2.7s
✅ REPOSITORY	checkov	yes		no	no	49.31s
✅ REPOSITORY	gitleaks	yes		no	no	13.61s
✅ REPOSITORY	git_diff	yes		no	no	0.38s
✅ REPOSITORY	secretlint	yes		no	no	59.3s
✅ REPOSITORY	syft	yes		no	no	6.39s
✅ REPOSITORY	trivy-sbom	yes		no	no	7.79s
✅ REPOSITORY	trufflehog	yes		no	no	30.88s
✅ YAML	prettier	11	0	0	0	0.66s
✅ YAML	v8r	11		0	0	9.96s
✅ YAML	yamllint	11		0	0	0.52s

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