feat(psychometric): recover 2017-era commented asymTOTALVAR as p + trait/a² 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 2017-era commented-out `asymTOTALVAR` as `-q / (2 a) + trait / a²` on current main after `0ce16e8` dropped the pre-consolidation code (register items 106–107). 2017-era ctsem `summary.ctsemFit.R` comments `asymTOTALVAR <- asymDIFFUSION` then, when `TRAITVAR != 0`, `asymTOTALVAR <- asymDIFFUSION + asymTRAITVAR` with `asymTRAITVAR <- solve(DRIFT) %*% TRAITVAR %*% t(solve(DRIFT))`. Driver, Oud, and Voelkle (2017, Eq. 1, p. 4; Eq. 4, p. 5; Table 2, p. 12; §4.3, p. 9; JSS PDF re-opened 2026-08-31T03:10Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) write `dη = (Aη + ξ + Bz + Mx) dt + G dW`. The Lyapunov within-subject variance is `asymDIFFUSION` `-q / (2 a)`. At a stable equilibrium a random intercept in `CINT` units has process-mean variance `trait / a²`. Form `1 / a` first, then square, then multiply by `trait`, then add `asymDIFFUSION`. This crate does not currently export `recover_asymptotic_trait_variance`; form `trait / a²` inline. Table 2/3 do not name `asymTOTALVAR`; the commented-out 2017-era matrix licenses this two-term slice. A zero trait and a zero diffusion is exactly zero even if `a ≥ 0`. `a ≥ 0` with a nonzero trait or diffusion fails closed. A zero trait keeps `asymDIFFUSION`. A zero diffusion keeps `trait / a²`. `trait + p` is §4.3 trait-plus-state and is not this map: Table 2 `TRAITVAR` is already in process units, while `solve(DRIFT)` converts random-intercept units. `trait / a²` is `asymTRAITVAR` and equals this total when `q = 0` and remains a distinct named quantity. `-q / (2 a)` is `asymDIFFUSION` and equals this total when `trait = 0` and remains a distinct named quantity. Stationary `T0VAR` `trait + p + (B / a)² v` keeps `TRAITVAR` in process units and is not this map. The later commented `addedTIPREDVAR` addend is not this two-term slice. A non-event clock fails closed. Meredith (1993) remains unread (web search 2026-08-31T03:10Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 - `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.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `MANIFESTTRAITVAR`; §7.1, p. 19; p. 16 `MANIFESTTRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-27T14:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest-trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 83–84). Table 2 names `MANIFESTTRAITVAR` `Ψ_τ` the additional time-invariant variance-covariance on the measurement level and sets it `NULL` when there is no manifest trait. Equation 5 writes `Γ ~ N(τ, Ψ)` and names that covariance the manifest traits. Section 7.1 names manifest traits stable individual differences in indicator levels, distinct from process-level `TRAITVAR` `φ_ξ`. Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `MANIFESTTRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named indicator-level correlation is `MANIFESTTRAITVAR`, not process-level `TRAITVAR` and not residual `MANIFESTVAR` `θ`. The 2017-era source forms `MANIFESTTRAITVARstd` only when `MANIFESTTRAITVAR != 0`, as `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(c(ridging), n.manifest)`. The default `ridging = FALSE` adds 0, not `0.0001`; that ridge is a numerical hack and is not this exact map. The scalar correlation is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR`. Form strictly positive `ψ` first, then `1 / √ψ`, then `(1 / √ψ) ψ (1 / √ψ)`. Unstandardised `MANIFESTTRAITVAR` is defined for a zero trait; standardised `MANIFESTTRAITVAR` is not. Zero `MANIFESTTRAITVAR` skips forming `MANIFESTTRAITVARstd` in the 2017-era source and fails closed here. Indicator-level trait variance is an event-time structural quantity, so a non-event clock fails closed. `MANIFESTTRAITVAR` does not require stable `a < 0`. Distinct positive `ψ` recover the same 1. `trait / trait = 1` is `TRAITVARstd` and recovers the same number and remains a distinct named quantity. `θ` is `MANIFESTVAR` and is measurement error, not this correlation. Meredith (1993) remains unread (web search 2026-08-27T14:20Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/psychometric_core/src/error.rs

@@ -710,6 +710,23 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// 2017-era commented-out `asymTOTALVAR` was requested for a
+    /// non-stable drift. The two-term map `-q / (2 a) + trait / a²`
+    /// requires `a < 0` whenever a contribution is nonzero.
+    AsymptoticTotalVarianceRequiresStableDrift,
+    /// Driver §4.3 trait-plus-state variance was treated as 2017-era
+    /// `asymTOTALVAR`. `trait + p` keeps `TRAITVAR` in process units;
+    /// the commented total uses `solve(DRIFT)` and is `p + trait / a²`.
+    TraitPlusStateVarianceIsNotAsymptoticTotalVariance,
+    /// Driver p. 16 `asymDIFFUSION` was treated as 2017-era
+    /// `asymTOTALVAR`. `-q / (2 a)` is the within-subject Lyapunov
+    /// variance, not the two-term total that adds `trait / a²`.
+    AsymptoticDiffusionIsNotAsymptoticTotalVariance,
+    /// 2017-era `asymTRAITVAR` was treated as 2017-era
+    /// `asymTOTALVAR`. `trait / a²` is the random-intercept
+    /// contribution, not the two-term total that adds
+    /// `asymDIFFUSION`.
+    AsymptoticTraitVarianceIsNotAsymptoticTotalVariance,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1252,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::AsymptoticTotalVarianceRequiresStableDrift => {
+                "asymptotic total variance requires a stable negative drift"
+            }
+            Self::TraitPlusStateVarianceIsNotAsymptoticTotalVariance => {
+                "trait-plus-state variance is not asymptotic total variance"
+            }
+            Self::AsymptoticDiffusionIsNotAsymptoticTotalVariance => {
+                "asymptotic diffusion is not asymptotic total variance"
+            }
+            Self::AsymptoticTraitVarianceIsNotAsymptoticTotalVariance => {
+                "asymptotic trait variance is not asymptotic total variance"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2102,24 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn asymptotic_total_variance_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::AsymptoticTotalVarianceRequiresStableDrift.to_string(),
+            "asymptotic total variance requires a stable negative drift"
+        );
+        assert_eq!(
+            PsychometricError::TraitPlusStateVarianceIsNotAsymptoticTotalVariance.to_string(),
+            "trait-plus-state variance is not asymptotic total variance"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticDiffusionIsNotAsymptoticTotalVariance.to_string(),
+            "asymptotic diffusion is not asymptotic total variance"
+        );
+        assert_eq!(
+            PsychometricError::AsymptoticTraitVarianceIsNotAsymptoticTotalVariance.to_string(),
+            "asymptotic trait variance is not asymptotic total variance"
+        );
+    }
 }