feat(psychometric): recover Driver p.16 MANIFESTTRAITVARstd after positive Ψ_τ

[seonghobae]

Stacked on #207 (TRAITVARstd). Next licensed 2017-era summary.ctsemFit.R std after the trait matrices is MANIFESTTRAITVARstd.

Driver, Oud, and Voelkle (2017, Table 2, p. 12 MANIFESTTRAITVAR Ψ_τ; §7.1, p. 19; p. 16 suffix std; footnote 4; JSS PDF re-opened 2026-08-23T22:28Z) name manifest traits stable individual differences in indicator levels, distinct from process-level TRAITVAR. The 2017-era source forms MANIFESTTRAITVARstd only when MANIFESTTRAITVAR != 0:

MANIFESTTRAITVARdiag <- diag(diag(MANIFESTTRAITVAR), n.manifest) + diag(c(ridging), n.manifest)
MANIFESTTRAITVARstd <- solve(sqrt(MANIFESTTRAITVARdiag)) %&% MANIFESTTRAITVAR

OpenMx %&% is t(A) %*% B %*% A. Unlike TRAITVARstd, the 2017-era source does add diag(c(ridging)). The default ridging = FALSE adds 0, not 0.0001; that ridge is a numerical hack and is not this exact map. Scalar map after strictly positive MANIFESTTRAITVAR is ψ / ψ = 1.

Recovery

• recover_standardised_manifest_trait_variance(ψ, clock) forms strictly positive ψ, then 1/√ψ, then the quadratic.
• Distinct positive ψ recover the same 1 (to_bits equal).
• Zero MANIFESTTRAITVAR fails closed (2017-era source skips forming MANIFESTTRAITVARstd).
• Non-event clock fails closed.
• MANIFESTTRAITVAR does not require a < 0.

Claim boundary

• Unstandardised MANIFESTTRAITVAR is not MANIFESTTRAITVARstd.
• TRAITVARstd is not MANIFESTTRAITVARstd even when both equal 1 (process-level vs indicator-level).
• MANIFESTVAR θ is not MANIFESTTRAITVARstd.

Meredith (1993) and Mislevy (1991) remain closed (Unpaywall 2026-08-23T22:21Z: is_oa: false, 0 locations).

Do not merge without an independent APPROVE plus exact-head required-check success. Do not self-approve. Do not request Copilot.

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[seonghobae]

Folded into the consolidation vehicle #231; this draft stays open until the vehicle merges, then closes as superseded-by-consolidation.

[seonghobae]

Superseded by consolidation: this slice's Driver et al. (2017) standardization recovery landed on protected main through the integration vehicles (#231/#232), and its contract coverage is carried by the reconciled suites (multilevel_event_time_recovery_contract, rubin_and_mean_gate_contract) with test-signature repair tracked in #234. The stacked-draft form is retired to keep the delivery queue at review-ready work only; no capability is lost — the exact-head provenance remains in the vehicle PR descriptions and CHANGELOG.