feat(psychometric): recover Driver lagged covariance of predetermined T0VAR on main

[seonghobae]

Summary

psychometric_core recovers the lagged covariance of §4.3 predetermined T0VAR independently on current main (register item 47). Driver, Oud, and Voelkle (2017, Eq. 3–4, pp. 4–5; §4.3, pp. 9–10; Table 2, p. 12; p. 16; §7.2, pp. 20–21; JSS PDF re-opened 2026-08-31T10:02Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) treat the first time point as predetermined when no assumptions are made about the process prior to T0.

This is an independent companion of still-unmerged PR #365 (item 46, Eq. 5 of predetermined later observed), PR #363 (item 45, predetermined later latent), PR #310 (discreteDRIFTstd), PR #357 (asymptotes=TRUE DIFFUSION rewrite), PR #355 / #352 (asymptotes=TRUE TIPREDEFFECT rewrite), and PR #349 (asymptotes=TRUE CINT rewrite). It branches from origin/main 1bc02f58, does not wait for those drafts, and is not stacked on them. Unpublished #363 recover_predetermined_later_latent_variance and unpublished #365 observed maps are not imported; the lagged composition is formed INLINE from on-main recover_trait_plus_state_lagged_covariance and recover_asymptotic_time_independent_predictor_variance. Stationary lagged covariance is already on main as recover_stationary_lagged_latent_covariance.

Section 4.3 treats the first time point as predetermined when no assumptions are made about the process prior to T0: free first-occasion variance p_0 is estimated. Equation 3 writes η(t) = exp(A Δt) η(t0) + …. Equation 4 writes cov(η_t, η_{t-1}) = A_Δt cov(η_{t-1}). Trait variance and addedTIPREDVAR are time-invariant between-subject and do not decay with e^{a Δt}. The lagged composition is trait + e^{a Δt} p_0 + (B / a)² v.

• Setting p_0 = −q / (2 a) recovers the stationary lagged map.
• Stationary lagged covariance uses −q / (2 a) in place of free p_0 and is not this map when p_0 is free.
• Later-occasion variance includes Q_Δt and is not this lagged map (formed INLINE from on-main recoveries).
• Evolving trait + p_0 + (B / a)² v as if it were all state is not this map.
• Free p_0 is not this map.
• A zero-diffusion carry with a ≥ 0 is e^{a Δt} p_0 and is kept.
• Nonzero TI extra still requires a < 0.

Fail-closed EventTime-only clocks, non-positive Δt, and invalid numeric input. Three refuse helpers: refuse_stationary_lagged_latent_covariance_as_predetermined_lagged_latent_covariance, refuse_predetermined_later_latent_variance_as_predetermined_lagged_latent_covariance, refuse_decayed_predetermined_total_as_predetermined_lagged_latent_covariance.

Meredith (1993) remains unread (Unpaywall 2026-08-31T10:02Z: is_oa: false; title Measurement Invariance, Factor Analysis and Factorial Invariance; Springer content/pdf historically an HTML stub). Mislevy (1991, Psychometrika, 56, 177–196, DOI 10.1007/bf02294457) remains unread (Unpaywall 2026-08-31T10:02Z: is_oa: false). The 1988 ETS RR of the same title is OA-flagged by Unpaywall (10.1002/j.2330-8516.1988.tb00310.x) but Wiley pdfdirect returned Cloudflare 403; it is not the 1991 journal article. Still not a Kalman filter, not a matrix expm, not ESEM estimation, not DSEM, and not ctsem estimation.

Plan

Fail-closed scalar recover_predetermined_lagged_latent_covariance(trait, p_0, B, v, a, Δt, clock) as trait + e^{a Δt} p_0 + (B / a)² v on origin/main, forming the lagged composition INLINE from on-main recoveries, with three refuse helpers, three error variants, CHANGELOG, ADR 0005 timestamp, CLAUDE.md, research notes item 47 timestamp, and crate/contract tests. Independent of #365, #363, #310, #357, #355, #352, and #349.

Verification

• cargo clippy -p psychometric_core --all-targets -- -D warnings (clean)
• cargo test -p psychometric_core --lib predetermined_lagged_latent (3 passed; 186 filtered)
• cargo test -p psychometric_core --test multilevel_event_time_recovery_contract predetermined_lagged_latent (2 passed)
• cargo test -p psychometric_core --test scientific_claim_boundary_contract predetermined_lagged_latent (1 passed)
• cargo test -p psychometric_core --lib stationary_later_variance_boundary_messages (1 passed)

Do not rustfmt lib.rs (reorders types after functions).

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. Do not request Copilot.

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