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

[seonghobae]

Summary

psychometric_core recovers the 2017-era active asymptotes=TRUE DIFFUSION rewrite as the scalar −2 a · q on current main.

This is an independent companion of still-unmerged PR #349 (CINT <- -DRIFT %*% CINT as −a · κ) and PR #355 (TIPREDEFFECT <- -DRIFT %*% TIPREDEFFECT as −a · B). It branches from origin/main 1bc02f58, does not wait for those drafts, and is not stacked on them. cran/ctsem 2.5.0 summary.ctsemFit.R has three active asymptotes=TRUE rewrites: CINT (L213), DIFFUSION (L230), TIPREDEFFECT (L378–379). DIFFUSION was not on main and not in any open PR.

cran/ctsem 2.5.0 forms DRIFTHATCH <- (DRIFT %x% I) + (I %x% DRIFT) 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. Driver, Oud, and Voelkle (2017, Table 2, p. 12; Eq. 4, p. 5; p. 16; JSS PDF re-opened 2026-08-31T07:40Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) name DIFFUSION the continuous process-noise covariance. For one latent the Kronecker sum is 2 a, so the scalar map is −2 a · q. Form 2 a first, then negate, then multiply by q. When asymptotes=TRUE the stored DIFFUSION is the asymptotic parameterization Table 2 / p. 16 names asymDIFFUSION p = −q / (2 a); multiplying by -DRIFTHATCH converts that stored value back to original q. −2 a · (−q / (2 a)) = q. The companion active rewrites CINT <- -DRIFT %*% CINT and TIPREDEFFECT <- -DRIFT %*% TIPREDEFFECT use -DRIFT, not -DRIFTHATCH, on different matrices and are not this process-noise map.

A zero diffusion is exactly zero even if a ≥ 0. a ≥ 0 with a nonzero diffusion fails closed. A negative diffusion fails closed. Numeric: a = −0.25, q = 0.4 recovers 0.2, distinct from unstandardised DIFFUSION (0.4), from asymDIFFUSION −q / (2 a) (0.8), from the finite-interval discreteDIFFUSION at Δt = 1 (≈ 0.3148), and from DIFFUSIONstd q / p = −2 a (0.5). Stored p = 0.8 recovers original q 0.4. The rate is not a = −0.5, so −2 a · q ≠ q. Unstandardised q is not this rewrite. asymDIFFUSION is not this rewrite. Finite-interval Q_Δt is not this rewrite. DIFFUSIONstd is not this rewrite. A non-event clock fails closed.

Meredith (1993) remains unread (Unpaywall historically is_oa: false; Springer content/pdf is an HTML stub). 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.

Plan

Fail-closed scalar recover_asymptotes_true_continuous_diffusion(continuous_diffusion, log_rate, clock) as −2 a · q on origin/main, with four refuse helpers (unstandardised q, asymDIFFUSION, discreteDIFFUSION, DIFFUSIONstd), five error variants, register items 110–111, CHANGELOG, ADR 0005, and crate/contract tests. Independent of #349 and #355.

Verification

• cargo fmt --all
• cargo clippy -p psychometric_core --all-targets -- -D warnings
• cargo test -p psychometric_core --lib (193)
• cargo test -p psychometric_core --test multilevel_event_time_recovery_contract (110)
• cargo test -p psychometric_core --test scientific_claim_boundary_contract (53)
• RUSTDOCFLAGS='-D warnings' cargo doc -p psychometric_core --no-deps

Register items 110–111.

Opened by: Grok Build (xAI) on behalf of Seongho Bae.

Do not merge without independent non-author APPROVE + exact-head required-check success. Do not convert from draft. Do not self-approve.

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