feat(psychometric): recover Eq. 5 of 2017-era active asymptotes=TRUE DIFFUSION rewrite on main

[seonghobae]

Summary

psychometric_core recovers Equation 5 of the 2017-era active asymptotes=TRUE DIFFUSION rewrite as the scalar λ² (−2 a · q) with θ = 0 and ψ = 0 on current main after 0ce16e8 dropped the pre-consolidation code.

This is an independent successor of queued latent asymptotes=TRUE DIFFUSION rewrite −2 a · q (#357). It does not depend on unpublished crates and is not stacked on that PR. Do not import unpublished #357 helpers. cran/ctsem 2.5.0 summary.ctsemFit.R forms DRIFTHATCH <- (DRIFT %x% I) + (I %x% DRIFT) and then if(asymptotes==TRUE) DIFFUSION <- matrix(-DRIFTHATCH %*% OpenMx::rvectorize(DIFFUSION), nrow=n.latent, ncol=n.latent) immediately after mxEval(DIFFUSION, mxobj, compute=TRUE) and puts that rewrite in the active outlist. For one latent the Kronecker sum is 2 a, so the scalar rewrite is −2 a · q. Driver, Oud, and Voelkle (2017, Eq. 5, p. 5; Table 2, p. 12; Eq. 4, p. 5; p. 16; JSS PDF re-opened 2026-08-31T09:50Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) write y_i(t) = τ + Λ η_i(t) + ε_i(t) with ε ~ N(0, Θ) and τ_i ~ N(μ_τ, Ψ_τ). Form 2 a first, then negate, then multiply by q, then (λ extra) λ. Do not form λ² first.

A zero loading or zero extra is exactly zero. A zero diffusion is exactly zero even if a ≥ 0. a ≥ 0 with a nonzero diffusion fails closed. Numeric: a = −0.25, q = 0.4, λ = 2 recovers rewrite extra 0.2 and Eq. 5 0.8. Unstandardised λ² q = 1.6 is not that map. λ² p of stored asymDIFFUSION p = 0.8 is 3.2 and is not that map. The latent rewrite −2 a · q is not Var(y). MANIFESTVAR θ is not this extra. A non-event clock fails closed.

Meredith (1993) remains unread (Springer content/pdf is an HTML stub; Unpaywall historically is_oa: false). Mislevy (1991, Psychometrika, 56, 177–196, DOI 10.1007/bf02294457) remains unread on the same terms. Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation.

Verification

• cargo fmt of changed files except lib.rs (never rustfmt lib.rs; it reorders types after functions)
• cargo clippy -p psychometric_core --all-targets -- -D warnings
• cargo test -p psychometric_core --lib (190 passed)
• cargo test -p psychometric_core --test multilevel_event_time_recovery_contract (110 passed)
• cargo test -p psychometric_core --test scientific_claim_boundary_contract (53 passed)
• RUSTDOCFLAGS='-D warnings' cargo doc -p psychometric_core --no-deps

Do not self-approve. Do not request Copilot. Independent non-author review is required. Do not merge without independent non-author APPROVE + exact-head required-check success. Queued/pending/skipped/cancelled/stale/predecessor-head is non-passing.

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