feat(psychometric): restore Driver p.16 DIFFUSIONstd q/p=−2a on main

CHANGELOG.md

@@ -40,6 +40,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 - `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, p. 16 `DIFFUSIONstd`; Eq. 4, p. 5; Table 2, p. 12; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-09-01T19:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised continuous diffusion on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 59–60). Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `DIFFUSIONstd`. Footnote 4 standardises using only the relevant variance, not the total. Table 2 names `DIFFUSION` `Q` the lower-triangular `n.latent × n.latent` Cholesky of diffusion variance/covariance. Process noise is within-subject stochastic input, so that relevant variance is within-subject `asymDIFFUSION` `p = −q / (2 a)`. The 2017-era source forms unstandardised `DIFFUSION` as `mxEval(DIFFUSION, mxobj, compute=TRUE)` and forms `asymDIFFUSIONstd` when `verbose = TRUE`. That source does not form a `DIFFUSIONstd` matrix; the scalar map is the footnote 4 standardisation of that named continuous diffusion: `q / p` after strictly positive `p`. Form strictly positive `p` first, then divide `q` by `p`. In the scalar stationary case that ratio equals `−2 a` and does not depend on `q` once `q > 0`. Unstandardised `q` is defined for growing `a ≥ 0` and for a zero process; standardised `DIFFUSION` is not. Zero `q` has no positive process SD and fails closed. Lasting `p` requires stable `a < 0`. A non-event clock fails closed. `Q_Δt / p` is `discreteDIFFUSIONstd` and depends on the event interval. `p / p = 1` is `asymDIFFUSIONstd` and recovers the same number when `a = −0.5` and remains a distinct named quantity. `q / (trait + p + added)` uses the total and is not this map when `TRAITVAR` is nonzero. Meredith (1993) remains unread (Unpaywall 2026-08-26T17:20Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; Unpaywall `is_oa: false`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 - `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.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TRAITVAR`; §7.1, pp. 18–19; p. 16 `TRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-26T17:45Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 81–82). Table 2 names `TRAITVAR` `φ_ξ` the latent trait variance/covariance and sets it `NULL` when there is no trait. Section 7.1 names traits the stable between-subject differences (unit-level unobserved heterogeneity). Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `TRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named between-subject correlation is `TRAITVAR`, not free first-occasion `T0VAR` and not process-dynamics `asymDIFFUSION`. The 2017-era source forms `TRAITVARstd` only when `TRAITVAR != 0`, as `solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `T0VARstd`, that formation uses `diag(diag(TRAITVAR))` and does not add `diag(c(ridging))`. The ridge is a `T0VAR` numerical hack and is not this exact map. The scalar correlation is `trait / trait = 1` after strictly positive `TRAITVAR`. Form strictly positive `trait` first, then `1 / √trait`, then `(1 / √trait) trait (1 / √trait)`. Unstandardised `TRAITVAR` is defined for a zero trait; standardised `TRAITVAR` is not. Zero `TRAITVAR` skips forming `TRAITVARstd` in the 2017-era source and fails closed here. Between-subject variance is an event-time structural quantity, so a non-event clock fails closed. `TRAITVAR` does not require stable `a < 0`. Distinct positive `trait` recover the same 1. `p_0 / p_0 = 1` is `T0VARstd` and recovers the same number and remains a distinct named quantity. `t0_b² v` is `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this correlation. Meredith (1993) remains unread (Unpaywall 2026-08-26T17:20Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; Unpaywall `is_oa: false`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/psychometric_core/src/error.rs

@@ -605,6 +605,23 @@ pub enum PsychometricError {
     /// `asymDIFFUSIONstd`. The continuous-diffusion ratio is not
     /// the correlation form of `asymDIFFUSION`.
     StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion,
+    /// Driver p. 16 `DIFFUSIONstd` was requested without a strictly
+    /// positive `asymDIFFUSION`. Footnote 4 standardises using only
+    /// the relevant variance; zero `q` has no positive process SD.
+    StandardisedContinuousDiffusionRequiresPositiveStationaryVariance,
+    /// Driver Table 2 unstandardised `DIFFUSION` `q` was treated as
+    /// `DIFFUSIONstd`. Unstandardised diffusion is defined for
+    /// growing `a ≥ 0` and for zero diffusion; standardised
+    /// `DIFFUSION` is not.
+    UnstandardisedContinuousDiffusionIsNotStandardisedContinuousDiffusion,
+    /// Driver p. 16 `discreteDIFFUSIONstd` `Q_Δt / p` was treated
+    /// as `DIFFUSIONstd`. The discrete map depends on the event
+    /// interval; the continuous ratio does not.
+    DiscreteStandardisedDiffusionIsNotStandardisedContinuousDiffusion,
+    /// Driver §7.1 total `q / (trait + p + added)` was treated as
+    /// p. 16 `DIFFUSIONstd`. Footnote 4 uses only within-subject
+    /// `asymDIFFUSION`, not the total.
+    TotalVarianceScaledDiffusionIsNotStandardisedContinuousDiffusion,
     /// Driver p. 16 `TIPREDVARstd` was treated as p. 16
     /// `asymDIFFUSIONstd`. Equal numbers of 1 after a strictly
     /// positive relevant variance are still distinct named
@@ -1168,6 +1185,18 @@ impl fmt::Display for PsychometricError {
             Self::StandardisedContinuousDiffusionIsNotStandardisedAsymptoticDiffusion => {
                 "standardised continuous diffusion is not standardised asymptotic diffusion"
             }
+            Self::StandardisedContinuousDiffusionRequiresPositiveStationaryVariance => {
+                "standardised continuous diffusion requires strictly positive stationary within-subject variance"
+            }
+            Self::UnstandardisedContinuousDiffusionIsNotStandardisedContinuousDiffusion => {
+                "unstandardised continuous diffusion is not standardised continuous diffusion"
+            }
+            Self::DiscreteStandardisedDiffusionIsNotStandardisedContinuousDiffusion => {
+                "discrete standardised diffusion is not standardised continuous diffusion"
+            }
+            Self::TotalVarianceScaledDiffusionIsNotStandardisedContinuousDiffusion => {
+                "total-variance scaled diffusion is not standardised continuous diffusion"
+            }
             Self::StandardisedTimeIndependentPredictorVarianceIsNotStandardisedAsymptoticDiffusion => {
                 "standardised time-independent predictor variance is not standardised asymptotic diffusion"
             }
@@ -1979,6 +2008,30 @@ mod tests {
         );
     }
 
+    #[test]
+    fn standardised_continuous_diffusion_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedContinuousDiffusionRequiresPositiveStationaryVariance
+                .to_string(),
+            "standardised continuous diffusion requires strictly positive stationary within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedContinuousDiffusionIsNotStandardisedContinuousDiffusion
+                .to_string(),
+            "unstandardised continuous diffusion is not standardised continuous diffusion"
+        );
+        assert_eq!(
+            PsychometricError::DiscreteStandardisedDiffusionIsNotStandardisedContinuousDiffusion
+                .to_string(),
+            "discrete standardised diffusion is not standardised continuous diffusion"
+        );
+        assert_eq!(
+            PsychometricError::TotalVarianceScaledDiffusionIsNotStandardisedContinuousDiffusion
+                .to_string(),
+            "total-variance scaled diffusion is not standardised continuous diffusion"
+        );
+    }
+
     #[test]
     fn standardised_trait_variance_boundary_messages_are_stable() {
         assert_eq!(