feat(psychometric): recover Eq. 5 of Driver later-occasion predetermined T0VAR on main

[seonghobae]

Summary

psychometric_core recovers Equation 5 of later-occasion §4.3 predetermined T0VAR independently on current main (register item 46). Driver, Oud, and Voelkle (2017, Eq. 5, p. 5; 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 2026-08-31T09:55Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) write y_i(t) = Γ + Λ η_i(t) + ζ_i(t) with ζ ~ N(0, Θ) and Γ ~ N(τ, Ψ).

This is an independent companion of still-unmerged 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 Unpublished #363 recover_predetermined_later_latent_variance is not imported; the later latent is formed INLINE from on-main recover_discrete_latent_variance, recover_trait_plus_state_latent_variance, and recover_asymptotic_time_independent_predictor_variance, then recover_manifest_trait_plus_state_observed_variance. Stationary later-occasion observed variance is already on main as recover_stationary_later_observed_variance.

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 3–4 evolve that state as e^{2 a Δt} p_0 + Q_Δt. Trait variance and addedTIPREDVAR are time-invariant between-subject and do not enter Q_Δt. The later-occasion latent composition is trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v. Equation 5 of that composition is λ²(trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v) + θ + ψ.

• A zero loading is exactly θ + ψ.
• Setting p_0 = −q / (2 a) recovers the stationary later-occasion observed variance.
• Stationary later observed variance uses −q / (2 a) in place of free p_0 and is not this map when p_0 is free.
• MANIFESTVAR θ is not Var(y_t).
• The predetermined later-occasion latent variance is not Var(y_t).
• Nonzero diffusion with a ≥ 0 is a growing process and is kept (unlike the stationary later-occasion map, which fails closed on a ≥ 0).

Fail-closed EventTime-only clocks, non-positive Δt, and invalid numeric input. Three refuse helpers: refuse_predetermined_later_latent_variance_as_observed_variance, refuse_measurement_error_as_predetermined_later_observed_variance, refuse_stationary_later_observed_variance_as_predetermined_later_observed_variance.

Meredith (1993) remains unread (Unpaywall 2026-08-31T09:50Z: 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 2026-08-31T09:50Z: is_oa: false; title Randomization-Based Inference about Latent Variables from Complex Samples). 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_later_observed_variance(λ, trait, p_0, q, B, v, a, Δt, θ, ψ, clock) as λ²(trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v) + θ + ψ on origin/main, forming the later latent INLINE from on-main recoveries, with three refuse helpers, three error variants, CHANGELOG, ADR 0005 timestamp, CLAUDE.md, research notes item 46 timestamp, and crate/contract tests. Independent of #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_later_observed (3 passed; 186 filtered)
• cargo test -p psychometric_core --test multilevel_event_time_recovery_contract predetermined_later_observed (2 passed)
• cargo test -p psychometric_core --test scientific_claim_boundary_contract predetermined_later_observed (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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