feat(psychometric): recover Driver later-occasion variance of predetermined T0VAR on main

CHANGELOG.md

@@ -38,6 +38,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, §4.3, pp. 9–10; Eq. 3–4, pp. 4–5; Table 2, p. 12; p. 16; §7.2, pp. 20–21; JSS PDF re-opened 2026-08-31T09:29Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar later-occasion variance of §4.3 predetermined `T0VAR` on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register item 45). Section 4.3 treats the first time point as predetermined when no assumptions are made about the process prior to the initial time point. Free `T0VAR` `p_0` is then estimated. The process gradually transitions from the variances of the initial parameters toward those of the parameters when the model is stationary. Equation 3 writes `η(t) = exp(A Δt) η(t0) + … +` the stochastic integral. Equation 4 writes that the integral exhibits covariance `Q_Δt`. The law of total variance on the within-subject state is `e^{2 a Δt} p_0 + Q_Δt`. Trait variance and `addedTIPREDVAR` are time-invariant between-subject and do not enter that process-noise integral. The later-occasion composition is `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v`. Form the evolved free first-occasion variance first, then include the trait, then include the TI extra variance, then add. Setting `p_0 = −q / (2 a)` recovers the stationary later-occasion map. Stationary later-occasion variance uses `−q / (2 a)` in place of `p_0` and is not this map when `p_0` is free. Evolving `trait + p_0 + (B / a)² v` as if it were all state is not this map. Free `T0VAR` `p_0` is not this map. As `Δt → ∞` with stable `a < 0` the composition approaches contemporaneous stationary `T0VAR`. As `Δt → 0+` the composition approaches `trait + p_0 + (B / a)² v`. Nonzero diffusion with `a ≥ 0` is a growing process and is kept. `a ≥ 0` with a nonzero TI contribution fails closed. A non-event clock, a non-positive interval, and an overflowing product or sum fail closed. Meredith (1993) remains unread (Unpaywall historically `is_oa: false`; title *Measurement Invariance, Factor Analysis and Factorial Invariance*). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms. Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 - Removed the repository-local hourly PR-maintenance caller now covered by the central required scheduler, retired stale workflow registrations, narrowed documentation triggers, keyed PR concurrency by fixed workflow name, repository, and pull-request number without cancelling non-PR runs, and combined line/branch coverage on one sequential runner while preserving both 100% gates and diagnostics.
 
 - `event_core` adds bounded Allen interval-consistency classification, atomic path-consistency closure, contradiction/resource refusals, and an explicit dependency-error fallback without claiming unrestricted global satisfiability.

crates/psychometric_core/src/error.rs

@@ -504,6 +504,18 @@ pub enum PsychometricError {
     /// later-occasion stationary observed variance. Lagged covariance
     /// omits `Q_Δt` and `θ`.
     StationaryLaggedObservedCovarianceIsNotStationaryLaterObservedVariance,
+    /// Driver §4.3 later-occasion predetermined variance was treated
+    /// as later-occasion stationary variance. Free `T0VAR` `p_0` is
+    /// not `−q / (2 a)` when the first occasion is predetermined.
+    PredeterminedLaterLatentVarianceIsNotStationaryLaterVariance,
+    /// Driver §4.3 later-occasion predetermined variance was treated
+    /// as the free discrete evolution of `trait + p_0 + (B / a)² v`.
+    /// Trait variance and `addedTIPREDVAR` do not enter `Q_Δt`.
+    PredeterminedLaterLatentVarianceIsNotDiscreteVariance,
+    /// Driver §4.3 later-occasion predetermined variance was treated
+    /// as free first-occasion `T0VAR`. `p_0` is the start, not
+    /// `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v`.
+    PredeterminedLaterLatentVarianceIsNotInitialVariance,
     /// Driver p. 16 `CINTstd` was requested without a strictly positive
     /// `asymDIFFUSION`. Footnote 4 standardises using only the
     /// relevant variance; zero `q` has no positive process SD.
@@ -1105,6 +1117,15 @@ impl fmt::Display for PsychometricError {
             Self::StationaryLaggedObservedCovarianceIsNotStationaryLaterObservedVariance => {
                 "stationary lagged observed covariance is not the stationary later-occasion observed variance"
             }
+            Self::PredeterminedLaterLatentVarianceIsNotStationaryLaterVariance => {
+                "predetermined later-occasion latent variance is not the stationary later-occasion latent variance"
+            }
+            Self::PredeterminedLaterLatentVarianceIsNotDiscreteVariance => {
+                "predetermined later-occasion latent variance is not the free discrete latent variance"
+            }
+            Self::PredeterminedLaterLatentVarianceIsNotInitialVariance => {
+                "predetermined later-occasion latent variance is not the free first-occasion latent variance"
+            }
             Self::StandardisedContinuousInterceptRequiresPositiveStationaryVariance => {
                 "standardised continuous intercept requires strictly positive stationary within-subject variance"
             }
@@ -1852,6 +1873,23 @@ mod tests {
         );
     }
 
+    #[test]
+    fn predetermined_later_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::PredeterminedLaterLatentVarianceIsNotStationaryLaterVariance
+                .to_string(),
+            "predetermined later-occasion latent variance is not the stationary later-occasion latent variance"
+        );
+        assert_eq!(
+            PsychometricError::PredeterminedLaterLatentVarianceIsNotDiscreteVariance.to_string(),
+            "predetermined later-occasion latent variance is not the free discrete latent variance"
+        );
+        assert_eq!(
+            PsychometricError::PredeterminedLaterLatentVarianceIsNotInitialVariance.to_string(),
+            "predetermined later-occasion latent variance is not the free first-occasion latent variance"
+        );
+    }
+
     #[test]
     fn standardised_continuous_intercept_boundary_messages_are_stable() {
         assert_eq!(