feat(core): own reusable covariance standardization

[seonghobae]

Superseded

Closed unmerged in favor of #1722. Both PRs implement issue #1720 from the same protected-main base, but #1722 removes the undocumented binary64 tolerances and correlation clamping present on this branch. Before closing this lane, #1722 also preserved this PR's unique external public-contract evidence: the exact fast_mlsirm.covariance_standardization@1.0.0 identity, scalar scale-invariance and fail-closed admission, known matrix recovery, multiplicative scale invariance, and malformed-input coverage. The numerical heuristics from this branch are intentionally not carried forward.

Closes #1720 only through the surviving #1722 lane; this PR itself is not merged and supplies no predecessor-head gate evidence.

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Closes #1720.

Canonical-owner repair

TEPP #475 currently places scalar covariance standardization inside psychometric_core::event_time, although the arithmetic is reusable static psychometric computation. This PR moves the canonical numerical ownership to mlsirm-core; TEPP retains event-time admission and temporal composition through an adapter after a released version exists.

No TEPP type, clock, state equation, provider API, database contract, or product-specific model name is imported here.

TDD lineage

• RED 738d3e5e7aa63b75f664fd17d9f422441bfa65e6: external crate tests require a versioned covariance_standardization public contract before the module exists. They require scalar scale invariance, known matrix recovery, multiplicative scale invariance, and typed fail-closed malformed inputs.
• GREEN e2ec9e8766b3dec46f4d4db9665b34849c3baf2e + 6d7fcc264036aa9e2b89d07292bed1403c6cd129: implement and expose the domain-neutral Rust kernel.
• Research/ownership trace f811b42631abed273d767841696887832f5159e2.

The hosted exact-current-head jobs remain landing authority; the source-level RED commit is preserved lineage, not a claim that hosted CI executed on that failing commit.

Numerical contract

fast_mlsirm.covariance_standardization@1.0.0 exposes:

• standardize_variance(v) for finite v > 0, evaluating (v / sqrt(v)) / sqrt(v) rather than hard-coding 1;
• standardize_covariance_matrix(Σ, n) for row-major symmetric covariance input, implementing D^{-1/2} Σ D^{-1/2};
• typed failures for invalid shape, non-finite values, non-positive variance, material asymmetry, impossible pairwise covariance and non-finite output;
• sequential division by marginal standard deviations so a finite correlation is not rejected merely because multiplying two large standard deviations would overflow;
• exact-symmetric output and a documented pairwise-bound check without overstating that this routine proves full PSD.

External tests span f64::MIN_POSITIVE through f64::MAX, a known 2x2 result, 1e100 scale invariance and malformed numeric inputs.

Research boundary

Driver, Oud, & Voelkle (2017), DOI 10.18637/jss.v077.i05, and the associated ctsem standardization path provide the motivating TEPP use case. The generic covariance-to-correlation identity is owned here; ctsem names and EventTime semantics are deliberately excluded.

Downstream migration gate

TEPP must not consume this PR head as a production dependency. After this contract is merged and released/versioned, TEPP can replace #475's duplicate static arithmetic with an EventTime adapter and parity tests against the preserved TIPREDVARstd fixtures. Until then #475 remains non-production migration evidence.

Protected base at creation: main@45627700c26c29bca150896a9519a9b7426acb56.
Exact head at creation: f811b42631abed273d767841696887832f5159e2.

No self-approval, protection bypass, or predecessor-head evidence transfer.

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