feat(psychometric): recover Driver p.16 TIPREDVARstd after positive TIPREDVAR

[seonghobae]

Stacked on #210 (MANIFESTVARstd). Next licensed 2017-era summary.ctsemFit.R std after the measurement-side matrices is TIPREDVARstd (predictor covariance; not addedTIPREDVAR).

Driver, Oud, and Voelkle (2017, Table 2, p. 12 TIPREDVAR; p. 16 suffix std; footnote 4; JSS PDF re-opened 2026-08-23T22:53Z) name TIPREDVAR the variance/covariance of time-independent predictors. The 2017-era source forms TIPREDVARstd whenever verbose = TRUE and n.TIpred > 0:

TIPREDVARdiag <- diag(diag(TIPREDVAR), n.TIpred) + diag(c(ridging), n.TIpred)
TIPREDVARstd <- solve(sqrt(TIPREDVARdiag)) %&% TIPREDVAR

OpenMx %&% is t(A) %*% B %*% A. Unlike TRAITVARstd, the 2017-era source does add diag(c(ridging), n.TIpred). The default ridging = FALSE adds 0, not 0.0001; that ridge is a numerical hack and is not this exact map. The 2017-era source assigns dimnames(TIPREDVARstd) to TIpredNames; that assignment matches the n.TIpred × n.TIpred matrix and is this map. Scalar map after strictly positive TIPREDVAR is v / v = 1.

Recovery

• recover_standardised_time_independent_predictor_variance(v, clock) forms strictly positive v, then 1/√v, then the quadratic.
• Distinct positive v recover the same 1 (to_bits equal).
• Zero TIPREDVAR fails closed. Unlike TRAITVAR / MANIFESTTRAITVAR, the 2017-era source does not skip forming TIPREDVARstd when v = 0; solve(sqrt(0)) fails.
• Non-event clock fails closed.
• TIPREDVAR does not require a < 0.

Claim boundary

• Unstandardised TIPREDVAR is not TIPREDVARstd.
• MANIFESTVARstd is not TIPREDVARstd even when both equal 1 (measurement error vs predictor covariance).
• Section 7.2 addedTIPREDVAR (B / a)² v is extra process variance, not TIPREDVARstd.

Meredith (1993) and Mislevy (1991) remain closed (Unpaywall re-checked this cycle: 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]

Maintainer Verification — exact head cc281b57af46b0f6af497a33b837e20954d44428

• Scope: fail-closed numerical edge coverage for event-time psychometric recovery; no production migration or dependency change.
• Local toolchain: Rust 1.97.1; branch coverage used nightly-2026-08-01.
• Verification: cargo fmt --all -- --check; workspace check/test; clippy; nextest; doctests; rustdoc; cargo deny check; Python quality coverage; workspace/docstring/documentation contracts — PASS.
• Coverage: authored LCOV 4906/4906 (100%); branch 1842/1842 (100%).
• Exact-head hosted state: this head was pushed normally after revalidating the prior remote head; no hosted check run had been published at comment time, so hosted evidence is not claimed as passed.
• Review state: PR remains Draft and has no qualifying approval; no merge or bypass is authorized.
• Decision: WAIT_AND_REMEDIATE until exact-head hosted checks and independent review are available.