diff --git a/CHANGELOG.md b/CHANGELOG.md
index 613f576c6..198c1ea54 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -37,6 +37,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, p. 16 `discreteDIFFUSIONstd`; Eq. 3–4, pp. 4–5; footnote 4; §7.1, pp. 18–19; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-28T13:24Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised discrete process noise on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 57–58). Page 16 prints discrete-time transformations for a chosen event interval (`discreteDRIFT`, `discreteDIFFUSION`) and, when appropriate, standardised matrices with the suffix `std`. The printed example on p. 16 is `discreteDRIFTstd`, not `discreteDIFFUSIONstd`. Footnote 4 standardises using only the relevant variance, not the total. Process noise is within-subject stochastic input, so that relevant variance is within-subject `asymDIFFUSION` `p = −q / (2 a)`, the same footnote 4 variance used for `DRIFT`. The 2017-era source forms unstandardised `discreteDIFFUSION` whenever `verbose = TRUE`, as `matrix(solve(DRIFTHATCH) %*% (expm(DRIFTHATCH Δt) − I ⊗ I) %*% rvectorize(DIFFUSION), nrow = n.latent)`. That source forms `asymDIFFUSIONstd` and `discreteDRIFTstd` in the same `verbose` block and does not form a `discreteDIFFUSIONstd` matrix. Form strictly positive `p` first, then `Q_Δt` from Equation 4, then `Q_Δt / p`. In the scalar stationary case that ratio equals `1 − exp(2 a Δt)` and does not depend on `q` once `q > 0`. Unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion; standardised discrete `DIFFUSION` is not. Zero `q` has no positive process SD and fails closed. Lasting `asymDIFFUSION` requires stable `a < 0`. A non-event clock fails closed. A non-positive event interval fails closed. `q / p = −2 a` is `DIFFUSIONstd` and does not depend on `Δt`. `Q_Δt / (trait + p + added)` uses the total, not `asymDIFFUSION`, and is not this map when `TRAITVAR` is nonzero. `TRAITVAR` is not the standardisation variance. Meredith (1993) remains unread (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 `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.
diff --git a/crates/psychometric_core/src/error.rs b/crates/psychometric_core/src/error.rs
index 4ab2695e0..e8603de39 100644
--- a/crates/psychometric_core/src/error.rs
+++ b/crates/psychometric_core/src/error.rs
@@ -710,6 +710,25 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver p. 16 `discreteDIFFUSIONstd` was requested with a
+    /// non-positive within-subject variance. Footnote 4
+    /// standardises `DIFFUSION` using only strictly positive
+    /// `asymDIFFUSION`.
+    StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance,
+    /// Driver p. 16 unstandardised `discreteDIFFUSION` `Q_Δt` was
+    /// treated as `discreteDIFFUSIONstd`. Unstandardised `Q_Δt` is
+    /// defined for growing or zero-diffusion processes;
+    /// standardised discrete `DIFFUSION` is not.
+    UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion,
+    /// Driver p. 16 `DIFFUSIONstd` `q / p = −2 a` was treated as
+    /// `discreteDIFFUSIONstd`. The continuous-diffusion ratio does
+    /// not depend on `Δt`.
+    StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion,
+    /// Driver §7.1 trait-contaminated process-noise ratio
+    /// `Q_Δt / (trait + p + added)` was treated as p. 16
+    /// `discreteDIFFUSIONstd`. Footnote 4 uses only
+    /// `asymDIFFUSION`.
+    TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1254,18 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance => {
+                "standardised discrete DIFFUSION requires strictly positive within-subject variance"
+            }
+            Self::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion => {
+                "unstandardised discrete DIFFUSION is not standardised discrete DIFFUSION"
+            }
+            Self::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion => {
+                "standardised continuous DIFFUSION is not standardised discrete DIFFUSION"
+            }
+            Self::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion => {
+                "trait-contaminated discrete DIFFUSION is not standardised discrete DIFFUSION"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2104,28 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn standardised_discrete_diffusion_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance
+                .to_string(),
+            "standardised discrete DIFFUSION requires strictly positive within-subject variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+                .to_string(),
+            "unstandardised discrete DIFFUSION is not standardised discrete DIFFUSION"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion
+                .to_string(),
+            "standardised continuous DIFFUSION is not standardised discrete DIFFUSION"
+        );
+        assert_eq!(
+            PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+                .to_string(),
+            "trait-contaminated discrete DIFFUSION is not standardised discrete DIFFUSION"
+        );
+    }
 }
diff --git a/crates/psychometric_core/src/event_time.rs b/crates/psychometric_core/src/event_time.rs
index a29bc5c18..5293e06c2 100644
--- a/crates/psychometric_core/src/event_time.rs
+++ b/crates/psychometric_core/src/event_time.rs
@@ -2501,6 +2501,144 @@ pub fn refuse_asymptotic_standardised_continuous_intercept_as_standardised_discr
     )
 }
 
+/// Exact scalar p. 16 `discreteDIFFUSIONstd` after strictly positive
+/// `asymDIFFUSION`.
+///
+/// Driver, Oud, and Voelkle (2017, p. 16; Eq. 3–4, pp. 4–5;
+/// footnote 4; Table 2, p. 12; §7.1, pp. 18–19; 2017-era ctsem
+/// `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-28T13:24Z from
+/// <https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104>)
+/// print discrete-time transformations for a chosen event interval
+/// (`discreteDIFFUSION` is the covariance of the Eq. 4 stochastic
+/// integral over that interval) and, when appropriate, standardised
+/// matrices with the suffix `std`. The printed example on p. 16 is
+/// `discreteDRIFTstd`, not `discreteDIFFUSIONstd`. Footnote 4:
+/// standardisations use only the relevant variance, not the total.
+/// Process noise is within-subject stochastic input, so that
+/// relevant variance is within-subject `asymDIFFUSION`
+/// `p = −q / (2 a)`, the same footnote 4 variance used for `DRIFT`.
+/// The 2017-era `summary.ctsemFit.R` forms unstandardised
+/// `discreteDIFFUSION` whenever `verbose = TRUE`, as
+/// `matrix(solve(DRIFTHATCH) %*% (expm(DRIFTHATCH Δt) − I ⊗ I) %*%
+/// rvectorize(DIFFUSION), nrow = n.latent)`. That source forms
+/// `asymDIFFUSIONstd` and `discreteDRIFTstd` in the same
+/// `verbose` block and does not form a `discreteDIFFUSIONstd`
+/// matrix. The scalar map here is the footnote 4 standardisation of
+/// that named discrete process noise: `Q_Δt / p`. Form strictly
+/// positive `p` first, then `Q_Δt` from Equation 4, then the
+/// ratio. In the scalar stationary case that ratio equals
+/// `1 − exp(2 a Δt)` and does not depend on `q` once `q > 0`.
+/// Unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for
+/// zero diffusion; standardised discrete `DIFFUSION` is not. Zero
+/// `q` has no positive process SD and fails closed. Lasting
+/// `asymDIFFUSION` requires stable `a < 0`. A non-event clock
+/// fails closed. A non-positive event interval fails closed. The
+/// continuous standardisation `q / p = −2 a` does not depend on
+/// `Δt` and is not this finite-interval map. Section 7.1 warns
+/// that omitting trait variance confounds between- and within-person
+/// information. `Q_Δt / (trait + p + added)` uses the total, not
+/// `asymDIFFUSION`, and is not this map when `TRAITVAR` is nonzero.
+/// `TRAITVAR` is not the standardisation variance. This is not a
+/// Kalman filter, not a matrix `expm`, not DSEM, and not ctsem
+/// estimation.
+///
+/// # Errors
+///
+/// Propagates [`recover_stationary_latent_variance`] and
+/// [`recover_discrete_process_noise`]. Returns
+/// [`PsychometricError::EventTimeRequired`] for any non-event clock,
+/// [`PsychometricError::NonPositiveInterval`] when `event_delta` is
+/// not strictly positive,
+/// [`PsychometricError::StationaryVarianceRequiresStableDrift`] when
+/// the log-rate is not strictly negative,
+/// [`PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance`]
+/// when `asymDIFFUSION` is zero, and
+/// [`PsychometricError::InvalidNumericInput`] when an input is
+/// non-finite or the diffusion is negative.
+pub fn recover_standardised_discrete_diffusion(
+    continuous_diffusion: f64,
+    log_rate: f64,
+    event_delta: f64,
+    clock: LagClock,
+) -> Result<f64, PsychometricError> {
+    let within = recover_stationary_latent_variance(continuous_diffusion, log_rate, clock)?;
+    if within == 0.0 {
+        return Err(
+            PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance,
+        );
+    }
+    let process_noise =
+        recover_discrete_process_noise(continuous_diffusion, log_rate, event_delta, clock)?;
+    Ok(process_noise / within)
+}
+
+/// Refuse treating unstandardised `discreteDIFFUSION` as p. 16
+/// `discreteDIFFUSIONstd`.
+///
+/// `Q_Δt` is defined for growing and zero-diffusion processes.
+/// Footnote 4 `discreteDIFFUSIONstd` requires strictly positive
+/// `asymDIFFUSION`. Equal numbers when `p = 1` are still distinct
+/// named quantities.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion`].
+pub fn refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion(
+    unstandardised_discrete_diffusion: f64,
+    standardised_discrete_diffusion: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (
+        unstandardised_discrete_diffusion,
+        standardised_discrete_diffusion,
+    );
+    Err(PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion)
+}
+
+/// Refuse treating p. 16 `DIFFUSIONstd` as p. 16
+/// `discreteDIFFUSIONstd`.
+///
+/// `q / p = −2 a` does not depend on the event interval.
+/// `discreteDIFFUSIONstd` does. This crate does not currently
+/// export `DIFFUSIONstd`; the refuse still names that quantity.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion`].
+pub fn refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion(
+    standardised_continuous_diffusion: f64,
+    standardised_discrete_diffusion: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (
+        standardised_continuous_diffusion,
+        standardised_discrete_diffusion,
+    );
+    Err(PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion)
+}
+
+/// Refuse treating Driver §7.1 trait-contaminated process-noise
+/// ratio as p. 16 `discreteDIFFUSIONstd`.
+///
+/// `Q_Δt / (trait + p + added)` mixes between-subject `TRAITVAR`
+/// into the process-noise ratio. Footnote 4 standardises
+/// `DIFFUSION` using only `asymDIFFUSION`.
+///
+/// # Errors
+///
+/// Always returns
+/// [`PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion`].
+pub fn refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion(
+    trait_contaminated_discrete_diffusion: f64,
+    standardised_discrete_diffusion: f64,
+) -> Result<f64, PsychometricError> {
+    let _ = (
+        trait_contaminated_discrete_diffusion,
+        standardised_discrete_diffusion,
+    );
+    Err(PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion)
+}
+
 /// Exact scalar p. 16 `asymCINTstd` after strictly positive
 /// `asymDIFFUSION`.
 ///
@@ -6889,16 +7027,16 @@ mod tests {
         recover_standardised_asymptotic_continuous_intercept,
         recover_standardised_asymptotic_diffusion, recover_standardised_continuous_intercept,
         recover_standardised_discrete_continuous_intercept,
-        recover_standardised_initial_latent_mean, recover_standardised_initial_latent_variance,
-        recover_standardised_manifest_mean, recover_standardised_manifest_trait_variance,
-        recover_standardised_trait_variance, recover_stationary_initial_latent_mean,
-        recover_stationary_initial_latent_variance, recover_stationary_initial_observed_mean,
-        recover_stationary_initial_observed_variance, recover_stationary_lagged_latent_covariance,
-        recover_stationary_lagged_observed_covariance, recover_stationary_latent_variance,
-        recover_stationary_later_latent_variance, recover_stationary_later_observed_variance,
-        recover_time_dependent_predictor_impulse, recover_time_dependent_predictor_impulse_carry,
-        recover_trait_plus_state_lagged_covariance, recover_trait_plus_state_latent_variance,
-        recover_within_residual_event_time_log_rate,
+        recover_standardised_discrete_diffusion, recover_standardised_initial_latent_mean,
+        recover_standardised_initial_latent_variance, recover_standardised_manifest_mean,
+        recover_standardised_manifest_trait_variance, recover_standardised_trait_variance,
+        recover_stationary_initial_latent_mean, recover_stationary_initial_latent_variance,
+        recover_stationary_initial_observed_mean, recover_stationary_initial_observed_variance,
+        recover_stationary_lagged_latent_covariance, recover_stationary_lagged_observed_covariance,
+        recover_stationary_latent_variance, recover_stationary_later_latent_variance,
+        recover_stationary_later_observed_variance, recover_time_dependent_predictor_impulse,
+        recover_time_dependent_predictor_impulse_carry, recover_trait_plus_state_lagged_covariance,
+        recover_trait_plus_state_latent_variance, recover_within_residual_event_time_log_rate,
         refuse_after_extra_process_contribution_as_observed_mean,
         refuse_after_extra_process_latent_mean_as_observed_mean,
         refuse_asymptotic_continuous_intercept_as_asymptotic_time_independent_effect,
@@ -6981,6 +7119,7 @@ mod tests {
         refuse_process_noise_as_unconditional_variance,
         refuse_standardised_asymptotic_diffusion_as_standardised_initial_latent_variance,
         refuse_standardised_continuous_diffusion_as_standardised_asymptotic_diffusion,
+        refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion,
         refuse_standardised_continuous_intercept_as_standardised_asymptotic_continuous_intercept,
         refuse_standardised_continuous_intercept_as_standardised_discrete_continuous_intercept,
         refuse_standardised_initial_latent_mean_as_standardised_initial_latent_variance,
@@ -7026,6 +7165,7 @@ mod tests {
         refuse_time_independent_effect_as_time_varying_discrete_effect,
         refuse_time_independent_observed_mean_as_initial_time_dependent_observed_mean,
         refuse_time_independent_observed_mean_as_initial_time_independent_observed_mean,
+        refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion,
         refuse_trait_plus_state_lagged_covariance_as_stationary_lagged_latent_covariance,
         refuse_trait_scaled_continuous_intercept_as_standardised_continuous_intercept,
         refuse_trait_variance_as_process_noise, refuse_trait_variance_as_stationary_within_subject,
@@ -7034,6 +7174,7 @@ mod tests {
         refuse_unstandardised_asymptotic_diffusion_as_standardised_asymptotic_diffusion,
         refuse_unstandardised_continuous_intercept_as_standardised_continuous_intercept,
         refuse_unstandardised_discrete_continuous_intercept_as_standardised_discrete_continuous_intercept,
+        refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion,
         refuse_unstandardised_initial_latent_mean_as_standardised_initial_latent_mean,
         refuse_unstandardised_initial_latent_variance_as_standardised_initial_latent_variance,
         refuse_unstandardised_manifest_mean_as_standardised_manifest_mean,
@@ -16353,4 +16494,164 @@ mod tests {
             Err(PsychometricError::InvalidNumericInput)
         );
     }
+
+    #[test]
+    fn standardised_discrete_diffusion_recovers_driver_page_sixteen_after_positive_asymdiffusion() {
+        // Driver et al. (2017, p. 16 discreteDIFFUSIONstd; Eq. 4; footnote 4;
+        // 2017-era summary.ctsemFit.R discreteDIFFUSION): form strictly
+        // positive asymDIFFUSION = −q / (2 a), then Q_Δt / p. Scalar
+        // stationary ratio is 1 − exp(2 a Δt). That source does not form
+        // a discreteDIFFUSIONstd matrix.
+        let diffusion = 0.4_f64;
+        let log_rate = -0.5_f64;
+        let event_delta = 1.0_f64;
+        let recovered = recover_standardised_discrete_diffusion(
+            diffusion,
+            log_rate,
+            event_delta,
+            LagClock::EventTime,
+        )
+        .expect("discreteDIFFUSIONstd");
+        let process_noise =
+            recover_discrete_process_noise(diffusion, log_rate, event_delta, LagClock::EventTime)
+                .expect("discreteDIFFUSION");
+        let within = recover_stationary_latent_variance(diffusion, log_rate, LagClock::EventTime)
+            .expect("asymDIFFUSION");
+        assert!(within > 0.0);
+        assert!((recovered - (process_noise / within)).abs() < 1e-15);
+        let one_minus_phi_sq = 1.0 - (2.0 * log_rate * event_delta).exp();
+        assert!((recovered - one_minus_phi_sq).abs() < 1e-15);
+        let two_and_a_half =
+            recover_standardised_discrete_diffusion(diffusion, log_rate, 2.5, LagClock::EventTime)
+                .expect("discreteDIFFUSIONstd Δt=2.5");
+        assert!((two_and_a_half - (1.0 - (2.0 * log_rate * 2.5).exp())).abs() < 1e-15);
+        assert!((recovered - two_and_a_half).abs() > 1e-9);
+        let continuous_std = diffusion / within;
+        assert!((continuous_std - recovered).abs() > 1e-3);
+        let trait_variance = 1.0_f64;
+        let total = recover_trait_plus_state_latent_variance(trait_variance, within)
+            .expect("trait+state var");
+        let contaminated = process_noise / total;
+        assert!((contaminated - recovered).abs() > 1e-3);
+        assert_eq!(
+            refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion(
+                process_noise,
+                recovered
+            ),
+            Err(
+                PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+            )
+        );
+        assert_eq!(
+            refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion(
+                continuous_std,
+                recovered
+            ),
+            Err(
+                PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion
+            )
+        );
+        assert_eq!(
+            refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion(
+                contaminated,
+                recovered
+            ),
+            Err(
+                PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+            )
+        );
+    }
+
+    #[test]
+    fn standardised_discrete_diffusion_fails_closed_when_unstandardised_is_defined() {
+        let log_rate = -0.5_f64;
+        let event_delta = 1.0_f64;
+        let unstandardised_zero_q =
+            recover_discrete_process_noise(0.0, log_rate, event_delta, LagClock::EventTime)
+                .expect("Q_Δt at q=0");
+        assert!((unstandardised_zero_q - 0.0).abs() < 1e-15);
+        assert_eq!(
+            recover_standardised_discrete_diffusion(0.0, log_rate, event_delta, LagClock::EventTime),
+            Err(
+                PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance
+            )
+        );
+        let growing = recover_discrete_process_noise(0.4, 0.5, event_delta, LagClock::EventTime)
+            .expect("growing a>0");
+        assert!(growing.is_finite());
+        assert!(growing > 0.0);
+        assert_eq!(
+            recover_standardised_discrete_diffusion(0.4, 0.5, event_delta, LagClock::EventTime),
+            Err(PsychometricError::StationaryVarianceRequiresStableDrift)
+        );
+        let unit = recover_discrete_process_noise(0.4, 0.0, event_delta, LagClock::EventTime)
+            .expect("a=0");
+        assert!((unit - 0.4).abs() < 1e-15);
+        assert_eq!(
+            recover_standardised_discrete_diffusion(0.4, 0.0, event_delta, LagClock::EventTime),
+            Err(PsychometricError::StationaryVarianceRequiresStableDrift)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(
+                0.4,
+                log_rate,
+                event_delta,
+                LagClock::SystemTime
+            ),
+            Err(PsychometricError::EventTimeRequired)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(
+                0.4,
+                log_rate,
+                event_delta,
+                LagClock::AssertionTime
+            ),
+            Err(PsychometricError::EventTimeRequired)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(
+                0.4,
+                log_rate,
+                event_delta,
+                LagClock::KnowledgeCutoff
+            ),
+            Err(PsychometricError::EventTimeRequired)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(0.4, log_rate, 0.0, LagClock::EventTime),
+            Err(PsychometricError::NonPositiveInterval)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(0.4, log_rate, f64::NAN, LagClock::EventTime),
+            Err(PsychometricError::NonPositiveInterval)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(
+                -0.1,
+                log_rate,
+                event_delta,
+                LagClock::EventTime
+            ),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(
+                0.4,
+                f64::NAN,
+                event_delta,
+                LagClock::EventTime
+            ),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+        assert_eq!(
+            recover_standardised_discrete_diffusion(
+                f64::INFINITY,
+                log_rate,
+                event_delta,
+                LagClock::EventTime
+            ),
+            Err(PsychometricError::InvalidNumericInput)
+        );
+    }
 }
diff --git a/crates/psychometric_core/src/lib.rs b/crates/psychometric_core/src/lib.rs
index c081a63f6..72a56514d 100644
--- a/crates/psychometric_core/src/lib.rs
+++ b/crates/psychometric_core/src/lib.rs
@@ -261,6 +261,25 @@
 //! correlation; zero `MANIFESTTRAITVAR` fails closed; a non-event
 //! clock fails closed; `MANIFESTTRAITVAR` does not require `a < 0`;
 //! JSS PDF re-opened 2026-08-27T14:20Z),
+//! recovers the Driver p. 16 `discreteDIFFUSIONstd` as
+//! `Q_Δt / p` after strictly positive `asymDIFFUSION`
+//! `p = −q / (2 a)` (footnote 4 uses only the relevant
+//! within-subject variance; 2017-era `summary.ctsemFit.R`
+//! forms unstandardised `discreteDIFFUSION` whenever
+//! `verbose = TRUE` as `matrix(solve(DRIFTHATCH) %*%
+//! (expm(DRIFTHATCH Δt) − I ⊗ I) %*% rvectorize(DIFFUSION),
+//! nrow = n.latent)`; that source forms `asymDIFFUSIONstd`
+//! and `discreteDRIFTstd` in the same `verbose` block and
+//! does not form a `discreteDIFFUSIONstd` matrix; the scalar
+//! map is `Q_Δt / p = 1 − exp(2 a Δt)` after strictly
+//! positive `p`; unstandardised `Q_Δt` is defined for
+//! growing `a ≥ 0` and for zero diffusion and is not that
+//! map; `q / p = −2 a` is `DIFFUSIONstd` and is not that
+//! map; `Q_Δt / (trait + p + added)` uses the total and is
+//! not that map when `TRAITVAR` is nonzero; zero `q` fails
+//! closed; a non-event clock fails closed; `a ≥ 0` fails
+//! closed; a non-positive event interval fails closed;
+//! JSS PDF re-opened 2026-08-28T13:24Z),
 //! and refuses
 //! latent-mean comparison below strong invariance.
 
@@ -407,6 +426,8 @@ pub use event_time::recover_standardised_asymptotic_diffusion;
 pub use event_time::recover_standardised_continuous_intercept;
 /// Exact scalar p. 16 `discreteCINTstd` `A^{-1}[e^{A Δt} − I] κ / √p`.
 pub use event_time::recover_standardised_discrete_continuous_intercept;
+/// Exact scalar p. 16 `discreteDIFFUSIONstd` `Q_Δt / p` after strictly positive `asymDIFFUSION`.
+pub use event_time::recover_standardised_discrete_diffusion;
 /// Exact scalar p. 16 `T0MEANSstd` `μ_0 / √p_0`.
 pub use event_time::recover_standardised_initial_latent_mean;
 /// Exact scalar p. 16 `T0VARstd` `p_0 / p_0 = 1` after strictly positive free `T0VAR`.
@@ -620,6 +641,8 @@ pub use event_time::refuse_process_noise_as_unconditional_variance;
 pub use event_time::refuse_standardised_asymptotic_diffusion_as_standardised_initial_latent_variance;
 /// Refuse treating p. 16 `DIFFUSIONstd` as `asymDIFFUSIONstd`.
 pub use event_time::refuse_standardised_continuous_diffusion_as_standardised_asymptotic_diffusion;
+/// Refuse treating p. 16 `DIFFUSIONstd` as `discreteDIFFUSIONstd`.
+pub use event_time::refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion;
 /// Refuse treating p. 16 `CINTstd` as `asymCINTstd`.
 pub use event_time::refuse_standardised_continuous_intercept_as_standardised_asymptotic_continuous_intercept;
 /// Refuse treating p. 16 `CINTstd` as `discreteCINTstd`.
@@ -715,6 +738,8 @@ pub use event_time::refuse_time_independent_effect_as_time_varying_discrete_effe
 pub use event_time::refuse_time_independent_observed_mean_as_initial_time_dependent_observed_mean;
 /// Refuse treating process-increment `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` as the first-occasion TI-predictor observed mean.
 pub use event_time::refuse_time_independent_observed_mean_as_initial_time_independent_observed_mean;
+/// Refuse treating Driver §7.1 trait-contaminated `Q_Δt / (trait + p + added)` as `discreteDIFFUSIONstd`.
+pub use event_time::refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion;
 /// Refuse treating §4.3 trait-plus-state lagged covariance as lagged stationary `T0VAR`.
 pub use event_time::refuse_trait_plus_state_lagged_covariance_as_stationary_lagged_latent_covariance;
 /// Refuse treating `κ / √(trait + p + added)` as `CINTstd`.
@@ -733,6 +758,8 @@ pub use event_time::refuse_unstandardised_asymptotic_diffusion_as_standardised_a
 pub use event_time::refuse_unstandardised_continuous_intercept_as_standardised_continuous_intercept;
 /// Refuse treating unstandardised `discreteCINT` as `discreteCINTstd`.
 pub use event_time::refuse_unstandardised_discrete_continuous_intercept_as_standardised_discrete_continuous_intercept;
+/// Refuse treating unstandardised `discreteDIFFUSION` as `discreteDIFFUSIONstd`.
+pub use event_time::refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion;
 /// Refuse treating unstandardised `T0MEANS` as `T0MEANSstd`.
 pub use event_time::refuse_unstandardised_initial_latent_mean_as_standardised_initial_latent_mean;
 /// Refuse treating unstandardised `T0VAR` as `T0VARstd`.
diff --git a/crates/psychometric_core/tests/multilevel_event_time_recovery_contract.rs b/crates/psychometric_core/tests/multilevel_event_time_recovery_contract.rs
index 1c0027f44..cfe73103a 100644
--- a/crates/psychometric_core/tests/multilevel_event_time_recovery_contract.rs
+++ b/crates/psychometric_core/tests/multilevel_event_time_recovery_contract.rs
@@ -36,17 +36,17 @@ use psychometric_core::{
     recover_manifest_observed_variance, recover_manifest_trait_plus_state_observed_variance,
     recover_standardised_asymptotic_continuous_intercept,
     recover_standardised_asymptotic_diffusion, recover_standardised_continuous_intercept,
-    recover_standardised_discrete_continuous_intercept, recover_standardised_initial_latent_mean,
-    recover_standardised_initial_latent_variance, recover_standardised_manifest_mean,
-    recover_standardised_manifest_trait_variance, recover_standardised_manifest_variance,
-    recover_standardised_trait_variance, recover_stationary_initial_latent_mean,
-    recover_stationary_initial_latent_variance, recover_stationary_initial_observed_mean,
-    recover_stationary_initial_observed_variance, recover_stationary_lagged_latent_covariance,
-    recover_stationary_lagged_observed_covariance, recover_stationary_latent_variance,
-    recover_stationary_later_latent_variance, recover_stationary_later_observed_variance,
-    recover_time_dependent_predictor_impulse, recover_time_dependent_predictor_impulse_carry,
-    recover_trait_plus_state_lagged_covariance, recover_trait_plus_state_latent_variance,
-    recover_within_residual_event_time_log_rate,
+    recover_standardised_discrete_continuous_intercept, recover_standardised_discrete_diffusion,
+    recover_standardised_initial_latent_mean, recover_standardised_initial_latent_variance,
+    recover_standardised_manifest_mean, recover_standardised_manifest_trait_variance,
+    recover_standardised_manifest_variance, recover_standardised_trait_variance,
+    recover_stationary_initial_latent_mean, recover_stationary_initial_latent_variance,
+    recover_stationary_initial_observed_mean, recover_stationary_initial_observed_variance,
+    recover_stationary_lagged_latent_covariance, recover_stationary_lagged_observed_covariance,
+    recover_stationary_latent_variance, recover_stationary_later_latent_variance,
+    recover_stationary_later_observed_variance, recover_time_dependent_predictor_impulse,
+    recover_time_dependent_predictor_impulse_carry, recover_trait_plus_state_lagged_covariance,
+    recover_trait_plus_state_latent_variance, recover_within_residual_event_time_log_rate,
     refuse_after_extra_process_contribution_as_observed_mean,
     refuse_after_extra_process_latent_mean_as_observed_mean,
     refuse_asymptotic_continuous_intercept_as_asymptotic_time_independent_effect,
@@ -120,6 +120,7 @@ use psychometric_core::{
     refuse_observed_variance_as_standardised_manifest_variance,
     refuse_pooled_discrete_lag_across_unequal_intervals,
     refuse_process_noise_as_unconditional_variance,
+    refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion,
     refuse_standardised_initial_latent_variance_as_standardised_trait_variance,
     refuse_standardised_manifest_trait_variance_as_standardised_manifest_variance,
     refuse_standardised_trait_variance_as_standardised_manifest_trait_variance,
@@ -159,9 +160,11 @@ use psychometric_core::{
     refuse_time_independent_effect_as_time_varying_discrete_effect,
     refuse_time_independent_observed_mean_as_initial_time_dependent_observed_mean,
     refuse_time_independent_observed_mean_as_initial_time_independent_observed_mean,
+    refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion,
     refuse_trait_plus_state_lagged_covariance_as_stationary_lagged_latent_covariance,
     refuse_trait_variance_as_process_noise, refuse_trait_variance_as_stationary_within_subject,
     refuse_unmatched_time_varying_predictor_interval,
+    refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion,
     refuse_unstandardised_manifest_trait_variance_as_standardised_manifest_trait_variance,
     refuse_unstandardised_manifest_variance_as_standardised_manifest_variance,
     refuse_unstandardised_trait_variance_as_standardised_trait_variance,
@@ -6540,3 +6543,137 @@ fn manifest_variance_std_clock_path_is_runtime_opaque() {
         Err(PsychometricError::EventTimeRequired)
     );
 }
+
+#[test]
+fn standardised_discrete_diffusion_recovers_driver_page_sixteen_footnote_four() {
+    let diffusion = 0.4_f64;
+    let log_rate = -0.5_f64;
+    let event_delta = 1.0_f64;
+    let recovered = recover_standardised_discrete_diffusion(
+        diffusion,
+        log_rate,
+        event_delta,
+        LagClock::EventTime,
+    )
+    .expect("discreteDIFFUSIONstd");
+    let process_noise =
+        recover_discrete_process_noise(diffusion, log_rate, event_delta, LagClock::EventTime)
+            .expect("discreteDIFFUSION");
+    let within = recover_stationary_latent_variance(diffusion, log_rate, LagClock::EventTime)
+        .expect("asymDIFFUSION");
+    let recovered_error = (recovered - (process_noise / within)).abs();
+    assert!(
+        recovered_error < 1e-15,
+        "Driver et al. (2017, p. 16 discreteDIFFUSIONstd): RMSE {recovered_error} for Q_Δt / p"
+    );
+    assert!((recovered - (1.0 - (2.0 * log_rate * event_delta).exp())).abs() < 1e-15);
+    let two_and_a_half =
+        recover_standardised_discrete_diffusion(diffusion, log_rate, 2.5, LagClock::EventTime)
+            .expect("discreteDIFFUSIONstd Δt=2.5");
+    assert!((two_and_a_half - (1.0 - (2.0 * log_rate * 2.5).exp())).abs() < 1e-15);
+    let continuous_std = diffusion / within;
+    let continuous_error = (continuous_std - (1.0 - (2.0 * log_rate * event_delta).exp())).abs();
+    assert!(
+        recovered_error < continuous_error,
+        "Driver et al. (2017, Eq. 4): DIFFUSIONstd RMSE {continuous_error} must exceed discreteDIFFUSIONstd RMSE {recovered_error}"
+    );
+    let trait_variance = 1.0_f64;
+    let total =
+        recover_trait_plus_state_latent_variance(trait_variance, within).expect("trait+state var");
+    let contaminated = process_noise / total;
+    let contaminated_error = (contaminated - (1.0 - (2.0 * log_rate * event_delta).exp())).abs();
+    assert!(
+        recovered_error < contaminated_error,
+        "Driver et al. (2017, footnote 4 / §7.1): trait-contaminated RMSE {contaminated_error} must exceed discreteDIFFUSIONstd RMSE {recovered_error}"
+    );
+    let unstandardised_error = (process_noise - (1.0 - (2.0 * log_rate * event_delta).exp())).abs();
+    assert!(
+        recovered_error < unstandardised_error,
+        "Driver et al. (2017, Eq. 4): unstandardised Q_Δt RMSE {unstandardised_error} must exceed discreteDIFFUSIONstd RMSE {recovered_error}"
+    );
+    assert_eq!(
+        refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion(
+            process_noise,
+            recovered
+        ),
+        Err(PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion)
+    );
+    assert_eq!(
+        refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion(
+            continuous_std,
+            recovered
+        ),
+        Err(PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion)
+    );
+    assert_eq!(
+        refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion(
+            contaminated,
+            recovered
+        ),
+        Err(
+            PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+        )
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.4, -0.5, 1.0, LagClock::SystemTime),
+        Err(PsychometricError::EventTimeRequired)
+    );
+}
+
+#[test]
+fn standardised_discrete_diffusion_refuses_non_event_clocks_and_does_not_keep_growing_or_zero_diffusion()
+ {
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.4, -0.5, 1.0, LagClock::AssertionTime),
+        Err(PsychometricError::EventTimeRequired)
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.4, -0.5, 1.0, LagClock::KnowledgeCutoff),
+        Err(PsychometricError::EventTimeRequired)
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.4, -0.5, 0.0, LagClock::EventTime),
+        Err(PsychometricError::NonPositiveInterval)
+    );
+    let growing =
+        recover_discrete_process_noise(0.4, 0.5, 1.0, LagClock::EventTime).expect("growing a>0");
+    assert!(growing.is_finite() && growing > 0.0);
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.4, 0.5, 1.0, LagClock::EventTime),
+        Err(PsychometricError::StationaryVarianceRequiresStableDrift)
+    );
+    let zero_q =
+        recover_discrete_process_noise(0.0, -0.5, 1.0, LagClock::EventTime).expect("Q_Δt at q=0");
+    assert!((zero_q - 0.0).abs() < 1e-15);
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.0, -0.5, 1.0, LagClock::EventTime),
+        Err(PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance)
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(-0.4, -0.5, 1.0, LagClock::EventTime),
+        Err(PsychometricError::InvalidNumericInput)
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(f64::NAN, -0.5, 1.0, LagClock::EventTime),
+        Err(PsychometricError::InvalidNumericInput)
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(f64::INFINITY, -0.5, 1.0, LagClock::EventTime),
+        Err(PsychometricError::InvalidNumericInput)
+    );
+}
+
+#[test]
+fn discrete_diffusion_std_clock_path_is_runtime_opaque() {
+    let clocks = [
+        LagClock::SystemTime,
+        LagClock::DocumentTime,
+        LagClock::AssertionTime,
+    ];
+    let non_event_index = std::process::id() as usize % clocks.len();
+    let non_event = clocks[non_event_index];
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.4, -0.5, 1.0, non_event),
+        Err(PsychometricError::EventTimeRequired)
+    );
+}
diff --git a/crates/psychometric_core/tests/scientific_claim_boundary_contract.rs b/crates/psychometric_core/tests/scientific_claim_boundary_contract.rs
index 6ccf7f38b..29f7a72a8 100644
--- a/crates/psychometric_core/tests/scientific_claim_boundary_contract.rs
+++ b/crates/psychometric_core/tests/scientific_claim_boundary_contract.rs
@@ -31,17 +31,17 @@ use psychometric_core::{
     recover_manifest_observed_variance, recover_manifest_trait_plus_state_observed_variance,
     recover_standardised_asymptotic_continuous_intercept,
     recover_standardised_asymptotic_diffusion, recover_standardised_continuous_intercept,
-    recover_standardised_discrete_continuous_intercept, recover_standardised_initial_latent_mean,
-    recover_standardised_initial_latent_variance, recover_standardised_manifest_mean,
-    recover_standardised_manifest_trait_variance, recover_standardised_manifest_variance,
-    recover_standardised_trait_variance, recover_stationary_initial_latent_mean,
-    recover_stationary_initial_latent_variance, recover_stationary_initial_observed_mean,
-    recover_stationary_initial_observed_variance, recover_stationary_lagged_latent_covariance,
-    recover_stationary_lagged_observed_covariance, recover_stationary_latent_variance,
-    recover_stationary_later_latent_variance, recover_stationary_later_observed_variance,
-    recover_time_dependent_predictor_impulse, recover_time_dependent_predictor_impulse_carry,
-    recover_trait_plus_state_lagged_covariance, recover_trait_plus_state_latent_variance,
-    recover_within_residual_event_time_log_rate,
+    recover_standardised_discrete_continuous_intercept, recover_standardised_discrete_diffusion,
+    recover_standardised_initial_latent_mean, recover_standardised_initial_latent_variance,
+    recover_standardised_manifest_mean, recover_standardised_manifest_trait_variance,
+    recover_standardised_manifest_variance, recover_standardised_trait_variance,
+    recover_stationary_initial_latent_mean, recover_stationary_initial_latent_variance,
+    recover_stationary_initial_observed_mean, recover_stationary_initial_observed_variance,
+    recover_stationary_lagged_latent_covariance, recover_stationary_lagged_observed_covariance,
+    recover_stationary_latent_variance, recover_stationary_later_latent_variance,
+    recover_stationary_later_observed_variance, recover_time_dependent_predictor_impulse,
+    recover_time_dependent_predictor_impulse_carry, recover_trait_plus_state_lagged_covariance,
+    recover_trait_plus_state_latent_variance, recover_within_residual_event_time_log_rate,
     refuse_after_extra_process_contribution_as_observed_mean,
     refuse_after_extra_process_latent_mean_as_observed_mean,
     refuse_asymptotic_continuous_intercept_as_asymptotic_time_independent_effect,
@@ -121,6 +121,7 @@ use psychometric_core::{
     refuse_process_noise_as_unconditional_variance,
     refuse_standardised_asymptotic_diffusion_as_standardised_initial_latent_variance,
     refuse_standardised_continuous_diffusion_as_standardised_asymptotic_diffusion,
+    refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion,
     refuse_standardised_continuous_intercept_as_standardised_asymptotic_continuous_intercept,
     refuse_standardised_continuous_intercept_as_standardised_discrete_continuous_intercept,
     refuse_standardised_initial_latent_mean_as_standardised_initial_latent_variance,
@@ -167,6 +168,7 @@ use psychometric_core::{
     refuse_time_independent_effect_as_time_varying_discrete_effect,
     refuse_time_independent_observed_mean_as_initial_time_dependent_observed_mean,
     refuse_time_independent_observed_mean_as_initial_time_independent_observed_mean,
+    refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion,
     refuse_trait_plus_state_lagged_covariance_as_stationary_lagged_latent_covariance,
     refuse_trait_scaled_continuous_intercept_as_standardised_continuous_intercept,
     refuse_trait_variance_as_process_noise, refuse_trait_variance_as_stationary_within_subject,
@@ -174,6 +176,7 @@ use psychometric_core::{
     refuse_unstandardised_asymptotic_diffusion_as_standardised_asymptotic_diffusion,
     refuse_unstandardised_continuous_intercept_as_standardised_continuous_intercept,
     refuse_unstandardised_discrete_continuous_intercept_as_standardised_discrete_continuous_intercept,
+    refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion,
     refuse_unstandardised_initial_latent_mean_as_standardised_initial_latent_mean,
     refuse_unstandardised_initial_latent_variance_as_standardised_initial_latent_variance,
     refuse_unstandardised_manifest_mean_as_standardised_manifest_mean,
@@ -3782,3 +3785,86 @@ fn standardised_manifest_variance_is_not_unstandardised_traitstd_or_observed_var
         )
     );
 }
+
+#[test]
+fn standardised_discrete_diffusion_is_not_unstandardised_or_trait_contaminated() {
+    let diffusion = 0.4_f64;
+    let log_rate = -0.5_f64;
+    let event_delta = 1.0_f64;
+    let recovered = recover_standardised_discrete_diffusion(
+        diffusion,
+        log_rate,
+        event_delta,
+        LagClock::EventTime,
+    )
+    .expect("discreteDIFFUSIONstd");
+    let process_noise =
+        recover_discrete_process_noise(diffusion, log_rate, event_delta, LagClock::EventTime)
+            .expect("discreteDIFFUSION");
+    let within = recover_stationary_latent_variance(diffusion, log_rate, LagClock::EventTime)
+        .expect("asymDIFFUSION");
+    assert!(
+        (recovered - (process_noise / within)).abs() < 1e-15,
+        "Driver et al. (2017, p. 16 / footnote 4): scalar discreteDIFFUSIONstd is Q_Δt / asymDIFFUSION"
+    );
+    assert!((recovered - (1.0 - (2.0 * log_rate * event_delta).exp())).abs() < 1e-15);
+    let continuous_std = diffusion / within;
+    assert!(
+        (continuous_std - recovered).abs() > 1e-3,
+        "Driver et al. (2017, Eq. 4): −2 a is not Q_Δt / p"
+    );
+    let trait_variance = 1.0_f64;
+    let total =
+        recover_trait_plus_state_latent_variance(trait_variance, within).expect("trait+state var");
+    let contaminated = process_noise / total;
+    assert!(
+        (contaminated - recovered).abs() > 1e-3,
+        "Driver et al. (2017, footnote 4 / §7.1): TRAITVAR contaminates the process-noise ratio"
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(0.0, log_rate, event_delta, LagClock::EventTime),
+        Err(
+            psychometric_core::PsychometricError::StandardisedDiscreteDiffusionRequiresPositiveWithinSubjectVariance
+        )
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(diffusion, 0.5, event_delta, LagClock::EventTime),
+        Err(psychometric_core::PsychometricError::StationaryVarianceRequiresStableDrift)
+    );
+    assert_eq!(
+        recover_standardised_discrete_diffusion(
+            diffusion,
+            log_rate,
+            event_delta,
+            LagClock::DocumentTime
+        ),
+        Err(psychometric_core::PsychometricError::EventTimeRequired)
+    );
+    assert_eq!(
+        refuse_unstandardised_discrete_diffusion_as_standardised_discrete_diffusion(
+            process_noise,
+            recovered
+        ),
+        Err(
+            psychometric_core::PsychometricError::UnstandardisedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+        )
+    );
+    assert_eq!(
+        refuse_standardised_continuous_diffusion_as_standardised_discrete_diffusion(
+            continuous_std,
+            recovered
+        ),
+        Err(
+            psychometric_core::PsychometricError::StandardisedContinuousDiffusionIsNotStandardisedDiscreteDiffusion
+        )
+    );
+    assert_eq!(
+        refuse_trait_contaminated_discrete_diffusion_as_standardised_discrete_diffusion(
+            contaminated,
+            recovered
+        ),
+        Err(
+            psychometric_core::PsychometricError::TraitContaminatedDiscreteDiffusionIsNotStandardisedDiscreteDiffusion
+        )
+    );
+}
diff --git a/docs/adr/0005-posterior-esem-dsem.md b/docs/adr/0005-posterior-esem-dsem.md
index ee1e6cf0d..0e43f5c95 100644
--- a/docs/adr/0005-posterior-esem-dsem.md
+++ b/docs/adr/0005-posterior-esem-dsem.md
@@ -1,8 +1,8 @@
 # ADR 0005 — Posterior-aware ESEM/DSEM and structural interpretation
 
 **Decision status:** Accepted
-**Implementation maturity:** partial — construct classification, valid log-ratio/logistic-normal indicator gates, CPU `f64` OLS and posterior-draw loading point-estimate averaging, Rubin `T_m = Ū_m + (1+1/m) B_m` on draw-level OLS loadings, cluster-mean within/between OLS with the CWC contextual effect and Kish ESS WLS, event-time discrete lag-1 and exact scalar local log-rate, exact scalar forward map and unequal-interval remapping, exact scalar discrete effect of a constant predictor, first-order discrete effect of a time-varying predictor with matched sampling and constancy intervals (Voelkle et al., 2012, Eq. 14), exact scalar discrete process noise (Driver, Oud, & Voelkle, 2017, Eq. 3), exact scalar lagged latent covariance and unconditional latent variance (Driver et al., 2017, Eq. 3–4), exact scalar stationary within-subject variance (Driver et al., 2017, Eq. 4 as `Δt → ∞`; §4.3; p. 16 `asymDIFFUSION`), exact scalar trait-plus-state variance and lagged covariance (Driver et al., 2017, §4.3 `TRAITVAR`; not process noise and not `asymDIFFUSION`), exact scalar observed-indicator variance and lagged observed covariance (Driver et al., 2017, Eq. 5, p. 5; Table 2, p. 12; `λ² Var(η) + θ` when `MANIFESTTRAITVAR` is zero, else `λ² Var(η) + θ + ψ`; lagged `λ² cov(η_t, η_{t-1}) + ψ`; `MANIFESTVAR` is `Θ`, not `Var(y)`; `Θ` does not enter lagged observed covariance; `MANIFESTTRAITVAR` is not `MANIFESTVAR`; observed-indicator mean is `τ + λ μ` (`MANIFESTMEANS` is `τ`, not `E(y)`; `CINT` is not `MANIFESTMEANS`; `T0MEANS` is not `E(y)`; Equation 1 is the SDE; not a Kalman filter), exact scalar discrete latent mean `exp(a Δt) μ_0 + (exp(a Δt) − 1)/a κ` (Driver et al., 2017, Eq. 3; `T0MEANS` is not `μ_t`; `CINT` is not the discrete increment), exact scalar evolved observed-indicator mean `τ + λ μ_t` (Driver et al., 2017, Eq. 5 of that Eq. 3 map; the first-occasion map `τ + λ μ_0` is not `E(y_t)`), exact scalar contemporaneous `TDPREDEFFECT` impulse `m x` (Driver et al., 2017, Eq. 3 fourth summand; Table 2 `TDPREDEFFECT` is `M`, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14; the §7.2 level-change form is not that impulse), exact scalar observed mean of that contemporaneous impulse `τ + λ(μ_t + m x)` (Driver et al., 2017, Eq. 5 of that Eq. 3 composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar time-independent `TIPREDEFFECT` increment `A^{-1}[e^{A Δt} − I] B z` (Driver et al., 2017, Eq. 3 second summand; Table 2 `TIPREDEFFECT` is `B`, not `κ`, not `M`, and not Voelkle Eq. 14; `B` is not that discrete increment), exact scalar observed mean of that increment `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` (Driver et al., 2017, Eq. 5 of that Eq. 3 printed addend after the `T0MEANS` carry and the `CINT` increment; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar within-interval `TDPREDEFFECT` carry `e^{A(t−u)} M x` for `t0 < u < t` (Driver et al., 2017, Eq. 1–2 Green-function integral of Eq. 2; §7.2 dissipation; not the contemporaneous Dirac, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14), exact scalar observed mean of that carry `τ + λ(μ_t + e^{a(t−u)} m x)` (Driver et al., 2017, Eq. 5 of that carried latent mean; `τ + λ μ_t` is not that observed mean), exact scalar first-occasion `T0TIPREDEFFECT` shift `t0_b z` and Eq. 3 first-summand carry `e^{A Δt} t0_b z` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; `T0TIPREDEFFECT` is not `TIPREDEFFECT` `B`; `t0_b z` is not `A^{-1}[e^{A Δt} − I] B z`; `e^{A Δt} t0_b z` is not `t0_b z`), exact scalar observed mean of that first-occasion carry `τ + λ(μ_t + e^{a Δt} t0_b z)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean), exact scalar first-occasion `T0TDPREDEFFECT` shift `t0_m x0` and Eq. 3 first-summand carry `e^{A Δt} t0_m x0` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; JSS PDF re-opened 2026-08-20T19:10Z; `T0TDPREDEFFECT` is not `TDPREDEFFECT` `M`; `t0_m x0` is not `M x`; `e^{A Δt} t0_m x0` is not `t0_m x0`; `e^{A Δt} t0_m x0` is not `e^{A(t−u)} M x` for `t0 < u < t`; `t0_m x0` is not `t0_b z`; an impulse at `u ≤ t0` that used `M` is already in `η(t0)` as `TDPREDEFFECT`, not as `T0TDPREDEFFECT`), exact scalar observed mean of that first-occasion TD carry `τ + λ(μ_t + e^{a Δt} t0_m x0)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand TD composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean; `τ + λ(μ_t + e^{a Δt} t0_b z)` is not that observed mean), exact scalar §7.2 level-change `CINT` `κ = −a m x` (Driver et al., 2017, §7.2, pp. 20–21; `a < 0` so `−κ / a = m x`; not the dissipating Dirac, not a free `CINT`, not `TIPREDEFFECT`, and not the extra near-zero-drift latent process also named in §7.2), exact scalar Eq. 3 increment of that setting `(1 − e^{a Δt}) m x` (not `m x`, not `κ`, and not `TIPREDEFFECT`), exact scalar §7.2 extra near-zero-drift latent process contribution `a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a)` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-20T23:10Z; identification `TDPREDEFFECT` on the extra process is 1; extra `DRIFT` printed as `−0.000001`; precisely 0 causes computational problems; `ε = a` is `a_{ηξ} x Δt e^{a Δt}`; not `κ = −a m x`, not `(1 − e^{a Δt}) m x`, and not the dissipating Dirac `m x`; `ε ≥ 0` fails closed), exact scalar observed mean of that extra-process contribution `τ + λ(μ_t + a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a))` (Driver et al., 2017, Eq. 5, p. 5; §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:12Z; the extra process has `LAMBDA` 0 and is not an observed indicator; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; the contribution is not `E(y_t)`; the evolved-plus-contribution latent mean is not `E(y_t)`), exact scalar after-t0 extra-process contribution `a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a)` for `t0 < u < t` and Eq. 5 observed mean `τ + λ(μ_t + a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a))` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:32Z; `T0TDPREDEFFECT` uses `Δt` for both the evolution and the extra drive; `TDPREDEFFECT` after `t0` uses `t − u`; `e^{a(t−u)} m x` is a Dirac on the original process, not this `DRIFT` drive), exact scalar §7.2 `asymTIPREDEFFECT` `-B z / a` (Driver et al., 2017, §7.2, pp. 20–21; JSS PDF opened 2026-08-21T13:08Z; expected total change in process means given a time-independent predictor; `a < 0`; not the coefficient `B`, not `A^{-1}[e^{A Δt} − I] B z`, not `CINT`, and not `M x`; `a ≥ 0` fails closed), exact scalar §7.2 `addedTIPREDVAR` `(B / a)² v` (Driver et al., 2017, §7.2, pp. 20–21; stable between-subject variance accounted for by a time-independent predictor; not `TRAITVAR`, not `asymDIFFUSION`, and not `-B z / a`), exact scalar Table 2 `asymCINT` `-κ / a` (Driver et al., 2017, Table 2, p. 12; Eq. 3 as `Δt → ∞`; `a < 0`; not `κ`, not `A^{-1}[e^{A Δt} − I] κ`, not `T0MEANS`, and not `-B z / a`; `a ≥ 0` fails closed), exact scalar p. 16 stationary `T0MEANS` `-κ / a + −B z / a` (Driver et al., 2017, p. 16; constrained first-occasion mean using `T0MEANSbase` / `T0MEANSfree`; not free `T0MEANS`, not `asymCINT` alone, not `asymTIPREDEFFECT` alone, and not the finite-interval discrete latent mean), exact scalar Eq. 5 of that constrained mean `τ + λ(−κ / a + −B z / a)` (Driver et al., 2017, §4.3, pp. 9–10; Eq. 5, p. 5; JSS PDF re-opened 2026-08-21T20:07Z; form the stationary latent mean first, then `τ + λ` of that mean; `τ + λ μ_0` is not that observed mean; `τ + λ(−κ / a)` is not that observed mean when `B z ≠ 0`; `τ + λ μ_t` is not that observed mean; `MANIFESTMEANS` is not `E(y_0)`; the constrained latent mean is not `E(y_0)`), exact scalar §4.3 / p. 16 stationary `T0VAR` `trait + −q / (2 a) + (B / a)² v` (Driver et al., 2017, §4.3, pp. 9–10; p. 16; JSS PDF re-opened 2026-08-22T03:07Z; not free `T0VAR`, not `asymDIFFUSION` alone, not `TRAITVAR` alone, not `addedTIPREDVAR` alone, and not the finite-interval discrete latent variance. Eq. 5 of that constrained variance is `λ²(trait + −q / (2 a) + (B / a)² v) + θ + ψ` (JSS PDF re-opened 2026-08-22T03:20Z; form the stationary latent variance first, then `λ² p + θ + ψ`; `λ² p_0` is not that observed variance; `λ²(−q / (2 a)) + θ` is not that observed variance when `TRAITVAR` or `addedTIPREDVAR` is nonzero; `MANIFESTVAR` is not `Var(y_0)`; the constrained latent variance is not `Var(y_0)`), exact scalar lagged covariance of that constrained process `trait + e^{a Δt}(−q / (2 a)) + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T19:13Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; contemporaneous `T0VAR` is not that lagged map; decaying the constrained total as if it were all state is not that lagged map), exact scalar Eq. 5 of that lagged covariance `λ²(trait + e^{a Δt}(−q / (2 a)) + (B / a)² v) + ψ` (`Θ` does not enter; contemporaneous `Var(y_0)` is not that lagged observed covariance; the lagged latent covariance is not that observed covariance), exact scalar later-occasion variance of that constrained process `trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T23:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; under stationarity that composition equals contemporaneous `T0VAR`; evolving the constrained total as if it were all state is not that later map; the lagged covariance omits `Q_Δt` and is not that later map; `Q_Δt` is not that later map), exact scalar Eq. 5 of that later-occasion variance `λ²(trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v) + θ + ψ` (the lagged observed covariance omits `Q_Δt` and `θ`; `MANIFESTVAR` is not that later observed variance; the later-occasion latent variance is not that observed variance)), exact scalar later-occasion variance of §4.3 predetermined `T0VAR` `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T05:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; free `T0VAR` `p_0` is not that later map; setting `p_0 = −q / (2 a)` recovers the stationary later-occasion map; stationary later variance uses `−q / (2 a)` in place of `p_0` and is not that later map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that later 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. Eq. 5 of that predetermined later-occasion variance is `λ²(trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that later observed variance; the predetermined later-occasion latent variance is not that observed variance; stationary later observed variance is not that observed variance when `p_0` is free)), exact scalar lagged covariance of §4.3 predetermined `T0VAR` `trait + e^{a Δt} p_0 + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T09:04Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; free `T0VAR` `p_0` is not that lagged map; setting `p_0 = −q / (2 a)` recovers the stationary lagged map; stationary lagged covariance uses `−q / (2 a)` in place of `p_0` and is not that lagged map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that lagged map; later-occasion variance includes `Q_Δt` and is not that lagged map. Eq. 5 of that predetermined lagged covariance is `λ²(trait + e^{a Δt} p_0 + (B / a)² v) + ψ` (`MANIFESTVAR` does not enter; the predetermined lagged latent covariance is not that observed covariance; predetermined later observed variance includes `Q_Δt` and `θ` and is not that lagged observed covariance; stationary lagged observed covariance is not that observed covariance when `p_0` is free)), exact scalar first-occasion variance of §4.3 predetermined `T0VAR` `trait + p_0 + (B / a)² v` (free `p_0` is not that map; stationary first-occasion variance uses `−q / (2 a)` in place of `p_0` and is not that map when `p_0` is free; lagged covariance decays the state and is not that map; later-occasion variance includes `Q_Δt` and is not that map), exact scalar Eq. 5 of that predetermined first-occasion variance `λ²(trait + p_0 + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that first-occasion observed variance; the predetermined first-occasion latent variance is not that observed variance; stationary first-occasion observed variance is not that observed variance when `p_0` is free; predetermined later observed variance includes `Q_Δt` and is not that first-occasion observed variance; later-start lagged covariance of predetermined `T0VAR` is `trait + e^{a s}(e^{2 a u} p_0 + Q_u) + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 4; JSS PDF re-opened 2026-08-23T10:27Z; first-occasion lagged omits `e^{a s} Q_u`; later-occasion variance does not lag; stationary lagged uses `−q / (2 a)`; decaying the later total is not that map; Eq. 5 of that later-start lagged covariance is `λ²` of it plus `ψ`; `Θ` does not enter; first-occasion lagged observed omits `e^{a s} Q_u`; later observed variance includes `Q_u` and `θ`; later-start later-occasion variance of predetermined `T0VAR` is `trait + e^{2 a s}(e^{2 a u} p_0 + Q_u) + Q_s + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 3–4 Chapman–Kolmogorov `Q_{u+s} = e^{2 a s} Q_u + Q_s`; JSS PDF re-opened 2026-08-23T11:05Z; later-occasion variance at `u` omits `Q_s`; later-start lagged covariance omits `Q_s`; stationary later uses `−q / (2 a)`; evolving the later total as if it were all state is not that map; ignoring `startoffset` omits `e^{2 a s} Q_u`; Eq. 5 of that later-start later-occasion variance is `λ²` of it plus `θ + ψ`; `MANIFESTVAR` is not that observed variance; p. 16 `discreteDRIFTstd` is `e^{a Δt}` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; footnote 4; §7.1; JSS PDF re-opened 2026-08-23T11:40Z; unstandardised `e^{a Δt}` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDRIFTstd`; the trait-plus-state autocorrelation uses `TRAITVAR` and is not `discreteDRIFTstd`; p. 16 `discreteDIFFUSIONstd` is `Q_Δt / (−q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-23T13:06Z; unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDIFFUSIONstd`; the continuous standardisation `−2 a` is not `discreteDIFFUSIONstd`; `Q_Δt / (trait + p + added)` uses `TRAITVAR` and is not `discreteDIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DIFFUSIONstd` is `q / (−q / (2 a)) = −2 a` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-23T13:20Z; unstandardised `q` is defined for growing `a ≥ 0` and for zero diffusion and is not `DIFFUSIONstd`; the discrete standardisation `Q_Δt / (−q / (2 a))` depends on `Δt` and is not `DIFFUSIONstd`; `q / (trait + p + added)` uses `TRAITVAR` and is not `DIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DRIFTstd` is the continuous auto-effect after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 1; footnote 4; JSS PDF re-opened 2026-08-23T13:28Z); unstandardised `a` is defined for growing `a ≥ 0` and for zero diffusion and is not `DRIFTstd`; the discrete standardisation `e^{a Δt}` depends on the event interval and is not `DRIFTstd`; `a p / (trait + p + added)` uses `TRAITVAR` and is not `DRIFTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `asymTIPREDEFFECTstd` is `(-B / a) · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T14:25Z; unstandardised `-B / a` is defined for a zero coefficient and for zero predictor variance and is not `asymTIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `asymTIPREDEFFECTstd`; `(-B / a) · √v / √(trait + p + added)` uses `TRAITVAR` and is not `asymTIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `TIPREDEFFECTstd` is `B · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T16:21Z; unstandardised `B` is defined for a zero coefficient and for zero predictor variance and is not `TIPREDEFFECTstd`; the asymptotic standardisation `(-B / a) · √v / √p` is the total change and is not `TIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `TIPREDEFFECTstd`; `B · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); Table 3 `T0TIPREDEFFECTstd` is `t0_b · √v / √p_0` after strictly positive free `T0VAR` `p_0` and strictly positive predictor variance `v` (Driver et al., 2017, Table 3, p. 13; p. 16; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T17:20Z; the affected variance is free `T0VAR`, not `asymDIFFUSION`; unstandardised `t0_b` is defined for a zero coefficient and for zero predictor variance and is not `T0TIPREDEFFECTstd`; `TIPREDEFFECTstd` `B · √v / √(-q / (2 a))` is the continuous coefficient and is not `T0TIPREDEFFECTstd`; `asymTIPREDEFFECTstd` `(-B / a) · √v / √p` is the total change and is not `T0TIPREDEFFECTstd`; `t0_b · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); 2017-era `addedT0TIPREDVAR` is `t0_b² v` (Driver et al., 2017, Table 3, p. 13; p. 16; §7.2; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T18:20Z; `T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` immediately after `T0TIPREDEFFECTstd`; form `t0_b` first, then square, then multiply by `v`; a zero coefficient or zero predictor variance is exactly zero; free `T0TIPREDEFFECT` does not require `a < 0`; `(B / a)² v` is `addedTIPREDVAR` and is not this first-occasion map; `t0_b · √v / √p_0` is `T0TIPREDEFFECTstd` and is not this variance; free `T0VAR` is not this extra TI variance; `TRAITVAR` is not this extra TI variance; Equation 5 of 2017-era `addedT0TIPREDVAR` is `λ² t0_b² v` (Driver et al., 2017, Eq. 5, p. 5; Table 3, p. 13; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T19:10Z; form `t0_b² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; `t0_b² v` is the latent extra, not the observed extra; `λ² p_0 + θ` is first-occasion observed variance, not this extra; `λ² (B / a)² v` is Eq. 5 of `addedTIPREDVAR`, not this first-occasion observed extra; `MANIFESTVAR` `θ` is not this extra; Equation 5 of §7.2 `addedTIPREDVAR` is `λ² (B / a)² v`; form `(B / a)² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; lasting asymptotic extra requires `a < 0`; `(B / a)² v` is the latent extra, not the observed extra; `λ² t0_b² v` is first-occasion extra observed TI variance, not this extra; `λ² p + θ` is stationary observed variance, not this extra; `MANIFESTVAR` `θ` is not this extra; p. 16 `TDPREDEFFECTstd` is `m · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` and strictly positive time-dependent predictor variance; unstandardised `M` is not `TDPREDEFFECTstd`; `TIPREDEFFECTstd` is not `TDPREDEFFECTstd` even when `M = B`; intercept-style `A^{-1}[e^{A Δt} − I] M · √v / √p` is not `TDPREDEFFECTstd`; `m · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TDPREDEFFECTstd`; Table 3 / p. 16 `T0TDPREDEFFECTstd` is `t0_m · √v / √p_0` after strictly positive free `T0VAR` and strictly positive TD predictor variance; unstandardised `t0_m` is not `T0TDPREDEFFECTstd`; `TDPREDEFFECTstd` uses `asymDIFFUSION` and is not `T0TDPREDEFFECTstd`; `T0TIPREDEFFECTstd` is not `T0TDPREDEFFECTstd` even when `t0_m = t0_b`; `t0_m · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TDPREDEFFECTstd`; free `T0VAR` does not require `a < 0`; p. 16 `T0VARstd` is `p_0 / p_0 = 1` after strictly positive free `T0VAR` (`solve(sqrt(diag(T0VAR))) %&% T0VAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; default ridge is 0); unstandardised `T0VAR` is not `T0VARstd`; `T0TDPREDEFFECTstd` is not `T0VARstd`; `addedT0TIPREDVAR` is not `T0VARstd`; p. 16 `TRAITVARstd` is `trait / trait = 1` after strictly positive `TRAITVAR` (`solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; no ridge addend); unstandardised `TRAITVAR` is not `TRAITVARstd`; `T0VARstd` is not `TRAITVARstd` even when both equal 1; `addedT0TIPREDVAR` is not `TRAITVARstd`; p. 16 `MANIFESTTRAITVARstd` is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR` (`solve(sqrt(diag(MANIFESTTRAITVAR))) %&% MANIFESTTRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0); unstandardised `MANIFESTTRAITVAR` is not `MANIFESTTRAITVARstd`; `TRAITVARstd` is not `MANIFESTTRAITVARstd` even when both equal 1; `MANIFESTVAR` is not `MANIFESTTRAITVARstd`; p. 16 `MANIFESTVARstd` is `θ / θ = 1` after strictly positive `MANIFESTVAR` (`solve(sqrt(diag(MANIFESTVAR))) %&% MANIFESTVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; 2017-era `dimnames` assignment to `latentNames` is a source bug); unstandardised `MANIFESTVAR` is not `MANIFESTVARstd`; `MANIFESTTRAITVARstd` is not `MANIFESTVARstd` even when both equal 1; Equation 5 `Var(y)` is not `MANIFESTVARstd`; p. 16 `TIPREDVARstd` is `v / v = 1` after strictly positive `TIPREDVAR` (`solve(sqrt(diag(TIPREDVAR))) %&% TIPREDVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `TIpredNames`); unstandardised `TIPREDVAR` is not `TIPREDVARstd`; `MANIFESTVARstd` is not `TIPREDVARstd` even when both equal 1; §7.2 `addedTIPREDVAR` is not `TIPREDVARstd`; p. 16 `asymDIFFUSIONstd` is `p / p = 1` after strictly positive `asymDIFFUSION` (`solve(sqrt(diag(asymDIFFUSION))) %&% asymDIFFUSION`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `latentNames`); unstandardised `asymDIFFUSION` is not `asymDIFFUSIONstd`; `TIPREDVARstd` is not `asymDIFFUSIONstd` even when both equal 1; `DIFFUSIONstd` `−2 a` is not `asymDIFFUSIONstd`; p. 16 `discreteCINTstd` is `A^{-1}[e^{A Δt} − I] κ / √p` after strictly positive `asymDIFFUSION`; unstandardised `discreteCINT` is not `discreteCINTstd`; `κ / √p` is not `discreteCINTstd`; `(-κ / a) / √p` is not `discreteCINTstd`; `asymCINTstd` is `(-κ / a) / √p` after strictly positive `asymDIFFUSION`; unstandardised `asymCINT` is not `asymCINTstd`; `κ / √p` is not `asymCINTstd`; `discreteCINTstd` is not `asymCINTstd`; `T0MEANSstd` is `μ_0 / √p_0` after strictly positive free `T0VAR`; unstandardised `T0MEANS` is not `T0MEANSstd`; `T0VARstd` is not `T0MEANSstd`; `μ_0 / √asymDIFFUSION` is not `T0MEANSstd`; `MANIFESTMEANSstd` is `τ / √θ` after strictly positive `MANIFESTVAR`; unstandardised `MANIFESTMEANS` is not `MANIFESTMEANSstd`; `MANIFESTVARstd` is not `MANIFESTMEANSstd`; `τ / √(λ² Var(η) + θ)` is not `MANIFESTMEANSstd`;))))), CWC-then-event-time residual lag, irregular already-centered residual log-rate, and strong/strict-gated two-group OLS latent-mean difference are implemented on the stacked psychometric PR and are not implemented-main until exact-head checks, review, and protected-main integration complete; full ESEM/set-ESEM, formative composites, DSEM, and matrix continuous-time dynamics remain accepted-target
-**Implementation maturity:** partial — construct classification, valid log-ratio/logistic-normal indicator gates, CPU `f64` OLS and posterior-draw loading point-estimate averaging, Rubin `T_m = Ū_m + (1+1/m) B_m` on draw-level OLS loadings, cluster-mean within/between OLS with the CWC contextual effect and Kish ESS WLS, event-time discrete lag-1 and exact scalar local log-rate, exact scalar forward map and unequal-interval remapping, exact scalar discrete effect of a constant predictor, first-order discrete effect of a time-varying predictor with matched sampling and constancy intervals (Voelkle et al., 2012, Eq. 14), exact scalar discrete process noise (Driver, Oud, & Voelkle, 2017, Eq. 3), exact scalar lagged latent covariance and unconditional latent variance (Driver et al., 2017, Eq. 3–4), exact scalar stationary within-subject variance (Driver et al., 2017, Eq. 4 as `Δt → ∞`; §4.3; p. 16 `asymDIFFUSION`), exact scalar trait-plus-state variance and lagged covariance (Driver et al., 2017, §4.3 `TRAITVAR`; not process noise and not `asymDIFFUSION`), exact scalar observed-indicator variance and lagged observed covariance (Driver et al., 2017, Eq. 5, p. 5; Table 2, p. 12; `λ² Var(η) + θ` when `MANIFESTTRAITVAR` is zero, else `λ² Var(η) + θ + ψ`; lagged `λ² cov(η_t, η_{t-1}) + ψ`; `MANIFESTVAR` is `Θ`, not `Var(y)`; `Θ` does not enter lagged observed covariance; `MANIFESTTRAITVAR` is not `MANIFESTVAR`; observed-indicator mean is `τ + λ μ` (`MANIFESTMEANS` is `τ`, not `E(y)`; `CINT` is not `MANIFESTMEANS`; `T0MEANS` is not `E(y)`; Equation 1 is the SDE; not a Kalman filter), exact scalar discrete latent mean `exp(a Δt) μ_0 + (exp(a Δt) − 1)/a κ` (Driver et al., 2017, Eq. 3; `T0MEANS` is not `μ_t`; `CINT` is not the discrete increment), exact scalar evolved observed-indicator mean `τ + λ μ_t` (Driver et al., 2017, Eq. 5 of that Eq. 3 map; the first-occasion map `τ + λ μ_0` is not `E(y_t)`), exact scalar contemporaneous `TDPREDEFFECT` impulse `m x` (Driver et al., 2017, Eq. 3 fourth summand; Table 2 `TDPREDEFFECT` is `M`, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14; the §7.2 level-change form is not that impulse), exact scalar observed mean of that contemporaneous impulse `τ + λ(μ_t + m x)` (Driver et al., 2017, Eq. 5 of that Eq. 3 composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar time-independent `TIPREDEFFECT` increment `A^{-1}[e^{A Δt} − I] B z` (Driver et al., 2017, Eq. 3 second summand; Table 2 `TIPREDEFFECT` is `B`, not `κ`, not `M`, and not Voelkle Eq. 14; `B` is not that discrete increment), exact scalar observed mean of that increment `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` (Driver et al., 2017, Eq. 5 of that Eq. 3 printed addend after the `T0MEANS` carry and the `CINT` increment; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar within-interval `TDPREDEFFECT` carry `e^{A(t−u)} M x` for `t0 < u < t` (Driver et al., 2017, Eq. 1–2 Green-function integral of Eq. 2; §7.2 dissipation; not the contemporaneous Dirac, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14), exact scalar observed mean of that carry `τ + λ(μ_t + e^{a(t−u)} m x)` (Driver et al., 2017, Eq. 5 of that carried latent mean; `τ + λ μ_t` is not that observed mean), exact scalar first-occasion `T0TIPREDEFFECT` shift `t0_b z` and Eq. 3 first-summand carry `e^{A Δt} t0_b z` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; `T0TIPREDEFFECT` is not `TIPREDEFFECT` `B`; `t0_b z` is not `A^{-1}[e^{A Δt} − I] B z`; `e^{A Δt} t0_b z` is not `t0_b z`), exact scalar observed mean of that first-occasion carry `τ + λ(μ_t + e^{a Δt} t0_b z)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean), exact scalar first-occasion `T0TDPREDEFFECT` shift `t0_m x0` and Eq. 3 first-summand carry `e^{A Δt} t0_m x0` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; JSS PDF re-opened 2026-08-20T19:10Z; `T0TDPREDEFFECT` is not `TDPREDEFFECT` `M`; `t0_m x0` is not `M x`; `e^{A Δt} t0_m x0` is not `t0_m x0`; `e^{A Δt} t0_m x0` is not `e^{A(t−u)} M x` for `t0 < u < t`; `t0_m x0` is not `t0_b z`; an impulse at `u ≤ t0` that used `M` is already in `η(t0)` as `TDPREDEFFECT`, not as `T0TDPREDEFFECT`), exact scalar observed mean of that first-occasion TD carry `τ + λ(μ_t + e^{a Δt} t0_m x0)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand TD composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean; `τ + λ(μ_t + e^{a Δt} t0_b z)` is not that observed mean), exact scalar §7.2 level-change `CINT` `κ = −a m x` (Driver et al., 2017, §7.2, pp. 20–21; `a < 0` so `−κ / a = m x`; not the dissipating Dirac, not a free `CINT`, not `TIPREDEFFECT`, and not the extra near-zero-drift latent process also named in §7.2), exact scalar Eq. 3 increment of that setting `(1 − e^{a Δt}) m x` (not `m x`, not `κ`, and not `TIPREDEFFECT`), exact scalar §7.2 extra near-zero-drift latent process contribution `a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a)` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-20T23:10Z; identification `TDPREDEFFECT` on the extra process is 1; extra `DRIFT` printed as `−0.000001`; precisely 0 causes computational problems; `ε = a` is `a_{ηξ} x Δt e^{a Δt}`; not `κ = −a m x`, not `(1 − e^{a Δt}) m x`, and not the dissipating Dirac `m x`; `ε ≥ 0` fails closed), exact scalar observed mean of that extra-process contribution `τ + λ(μ_t + a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a))` (Driver et al., 2017, Eq. 5, p. 5; §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:12Z; the extra process has `LAMBDA` 0 and is not an observed indicator; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; the contribution is not `E(y_t)`; the evolved-plus-contribution latent mean is not `E(y_t)`), exact scalar after-t0 extra-process contribution `a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a)` for `t0 < u < t` and Eq. 5 observed mean `τ + λ(μ_t + a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a))` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:32Z; `T0TDPREDEFFECT` uses `Δt` for both the evolution and the extra drive; `TDPREDEFFECT` after `t0` uses `t − u`; `e^{a(t−u)} m x` is a Dirac on the original process, not this `DRIFT` drive), exact scalar §7.2 `asymTIPREDEFFECT` `-B z / a` (Driver et al., 2017, §7.2, pp. 20–21; JSS PDF opened 2026-08-21T13:08Z; expected total change in process means given a time-independent predictor; `a < 0`; not the coefficient `B`, not `A^{-1}[e^{A Δt} − I] B z`, not `CINT`, and not `M x`; `a ≥ 0` fails closed), exact scalar §7.2 `addedTIPREDVAR` `(B / a)² v` (Driver et al., 2017, §7.2, pp. 20–21; stable between-subject variance accounted for by a time-independent predictor; not `TRAITVAR`, not `asymDIFFUSION`, and not `-B z / a`), exact scalar Table 2 `asymCINT` `-κ / a` (Driver et al., 2017, Table 2, p. 12; Eq. 3 as `Δt → ∞`; `a < 0`; not `κ`, not `A^{-1}[e^{A Δt} − I] κ`, not `T0MEANS`, and not `-B z / a`; `a ≥ 0` fails closed), exact scalar p. 16 stationary `T0MEANS` `-κ / a + −B z / a` (Driver et al., 2017, p. 16; constrained first-occasion mean using `T0MEANSbase` / `T0MEANSfree`; not free `T0MEANS`, not `asymCINT` alone, not `asymTIPREDEFFECT` alone, and not the finite-interval discrete latent mean), exact scalar Eq. 5 of that constrained mean `τ + λ(−κ / a + −B z / a)` (Driver et al., 2017, §4.3, pp. 9–10; Eq. 5, p. 5; JSS PDF re-opened 2026-08-21T20:07Z; form the stationary latent mean first, then `τ + λ` of that mean; `τ + λ μ_0` is not that observed mean; `τ + λ(−κ / a)` is not that observed mean when `B z ≠ 0`; `τ + λ μ_t` is not that observed mean; `MANIFESTMEANS` is not `E(y_0)`; the constrained latent mean is not `E(y_0)`), exact scalar §4.3 / p. 16 stationary `T0VAR` `trait + −q / (2 a) + (B / a)² v` (Driver et al., 2017, §4.3, pp. 9–10; p. 16; JSS PDF re-opened 2026-08-22T03:07Z; not free `T0VAR`, not `asymDIFFUSION` alone, not `TRAITVAR` alone, not `addedTIPREDVAR` alone, and not the finite-interval discrete latent variance. Eq. 5 of that constrained variance is `λ²(trait + −q / (2 a) + (B / a)² v) + θ + ψ` (JSS PDF re-opened 2026-08-22T03:20Z; form the stationary latent variance first, then `λ² p + θ + ψ`; `λ² p_0` is not that observed variance; `λ²(−q / (2 a)) + θ` is not that observed variance when `TRAITVAR` or `addedTIPREDVAR` is nonzero; `MANIFESTVAR` is not `Var(y_0)`; the constrained latent variance is not `Var(y_0)`), exact scalar lagged covariance of that constrained process `trait + e^{a Δt}(−q / (2 a)) + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T19:13Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; contemporaneous `T0VAR` is not that lagged map; decaying the constrained total as if it were all state is not that lagged map), exact scalar Eq. 5 of that lagged covariance `λ²(trait + e^{a Δt}(−q / (2 a)) + (B / a)² v) + ψ` (`Θ` does not enter; contemporaneous `Var(y_0)` is not that lagged observed covariance; the lagged latent covariance is not that observed covariance), exact scalar later-occasion variance of that constrained process `trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T23:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; under stationarity that composition equals contemporaneous `T0VAR`; evolving the constrained total as if it were all state is not that later map; the lagged covariance omits `Q_Δt` and is not that later map; `Q_Δt` is not that later map), exact scalar Eq. 5 of that later-occasion variance `λ²(trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v) + θ + ψ` (the lagged observed covariance omits `Q_Δt` and `θ`; `MANIFESTVAR` is not that later observed variance; the later-occasion latent variance is not that observed variance)), exact scalar later-occasion variance of §4.3 predetermined `T0VAR` `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T05:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; free `T0VAR` `p_0` is not that later map; setting `p_0 = −q / (2 a)` recovers the stationary later-occasion map; stationary later variance uses `−q / (2 a)` in place of `p_0` and is not that later map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that later 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. Eq. 5 of that predetermined later-occasion variance is `λ²(trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that later observed variance; the predetermined later-occasion latent variance is not that observed variance; stationary later observed variance is not that observed variance when `p_0` is free)), exact scalar lagged covariance of §4.3 predetermined `T0VAR` `trait + e^{a Δt} p_0 + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T09:04Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; free `T0VAR` `p_0` is not that lagged map; setting `p_0 = −q / (2 a)` recovers the stationary lagged map; stationary lagged covariance uses `−q / (2 a)` in place of `p_0` and is not that lagged map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that lagged map; later-occasion variance includes `Q_Δt` and is not that lagged map. Eq. 5 of that predetermined lagged covariance is `λ²(trait + e^{a Δt} p_0 + (B / a)² v) + ψ` (`MANIFESTVAR` does not enter; the predetermined lagged latent covariance is not that observed covariance; predetermined later observed variance includes `Q_Δt` and `θ` and is not that lagged observed covariance; stationary lagged observed covariance is not that observed covariance when `p_0` is free)), exact scalar first-occasion variance of §4.3 predetermined `T0VAR` `trait + p_0 + (B / a)² v` (free `p_0` is not that map; stationary first-occasion variance uses `−q / (2 a)` in place of `p_0` and is not that map when `p_0` is free; lagged covariance decays the state and is not that map; later-occasion variance includes `Q_Δt` and is not that map), exact scalar Eq. 5 of that predetermined first-occasion variance `λ²(trait + p_0 + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that first-occasion observed variance; the predetermined first-occasion latent variance is not that observed variance; stationary first-occasion observed variance is not that observed variance when `p_0` is free; predetermined later observed variance includes `Q_Δt` and is not that first-occasion observed variance; later-start lagged covariance of predetermined `T0VAR` is `trait + e^{a s}(e^{2 a u} p_0 + Q_u) + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 4; JSS PDF re-opened 2026-08-23T10:27Z; first-occasion lagged omits `e^{a s} Q_u`; later-occasion variance does not lag; stationary lagged uses `−q / (2 a)`; decaying the later total is not that map; Eq. 5 of that later-start lagged covariance is `λ²` of it plus `ψ`; `Θ` does not enter; first-occasion lagged observed omits `e^{a s} Q_u`; later observed variance includes `Q_u` and `θ`; later-start later-occasion variance of predetermined `T0VAR` is `trait + e^{2 a s}(e^{2 a u} p_0 + Q_u) + Q_s + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 3–4 Chapman–Kolmogorov `Q_{u+s} = e^{2 a s} Q_u + Q_s`; JSS PDF re-opened 2026-08-23T11:05Z; later-occasion variance at `u` omits `Q_s`; later-start lagged covariance omits `Q_s`; stationary later uses `−q / (2 a)`; evolving the later total as if it were all state is not that map; ignoring `startoffset` omits `e^{2 a s} Q_u`; Eq. 5 of that later-start later-occasion variance is `λ²` of it plus `θ + ψ`; `MANIFESTVAR` is not that observed variance; p. 16 `discreteDRIFTstd` is `e^{a Δt}` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; footnote 4; §7.1; JSS PDF re-opened 2026-08-23T11:40Z; unstandardised `e^{a Δt}` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDRIFTstd`; the trait-plus-state autocorrelation uses `TRAITVAR` and is not `discreteDRIFTstd`; p. 16 `discreteDIFFUSIONstd` is `Q_Δt / (−q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-23T13:06Z; unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDIFFUSIONstd`; the continuous standardisation `−2 a` is not `discreteDIFFUSIONstd`; `Q_Δt / (trait + p + added)` uses `TRAITVAR` and is not `discreteDIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DIFFUSIONstd` is `q / (−q / (2 a)) = −2 a` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-23T13:20Z; unstandardised `q` is defined for growing `a ≥ 0` and for zero diffusion and is not `DIFFUSIONstd`; the discrete standardisation `Q_Δt / (−q / (2 a))` depends on `Δt` and is not `DIFFUSIONstd`; `q / (trait + p + added)` uses `TRAITVAR` and is not `DIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DRIFTstd` is the continuous auto-effect after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 1; footnote 4; JSS PDF re-opened 2026-08-23T13:28Z); unstandardised `a` is defined for growing `a ≥ 0` and for zero diffusion and is not `DRIFTstd`; the discrete standardisation `e^{a Δt}` depends on the event interval and is not `DRIFTstd`; `a p / (trait + p + added)` uses `TRAITVAR` and is not `DRIFTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `asymTIPREDEFFECTstd` is `(-B / a) · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T14:25Z; unstandardised `-B / a` is defined for a zero coefficient and for zero predictor variance and is not `asymTIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `asymTIPREDEFFECTstd`; `(-B / a) · √v / √(trait + p + added)` uses `TRAITVAR` and is not `asymTIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `TIPREDEFFECTstd` is `B · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T16:21Z; unstandardised `B` is defined for a zero coefficient and for zero predictor variance and is not `TIPREDEFFECTstd`; the asymptotic standardisation `(-B / a) · √v / √p` is the total change and is not `TIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `TIPREDEFFECTstd`; `B · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); Table 3 `T0TIPREDEFFECTstd` is `t0_b · √v / √p_0` after strictly positive free `T0VAR` `p_0` and strictly positive predictor variance `v` (Driver et al., 2017, Table 3, p. 13; p. 16; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T17:20Z; the affected variance is free `T0VAR`, not `asymDIFFUSION`; unstandardised `t0_b` is defined for a zero coefficient and for zero predictor variance and is not `T0TIPREDEFFECTstd`; `TIPREDEFFECTstd` `B · √v / √(-q / (2 a))` is the continuous coefficient and is not `T0TIPREDEFFECTstd`; `asymTIPREDEFFECTstd` `(-B / a) · √v / √p` is the total change and is not `T0TIPREDEFFECTstd`; `t0_b · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); 2017-era `addedT0TIPREDVAR` is `t0_b² v` (Driver et al., 2017, Table 3, p. 13; p. 16; §7.2; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T18:20Z; `T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` immediately after `T0TIPREDEFFECTstd`; form `t0_b` first, then square, then multiply by `v`; a zero coefficient or zero predictor variance is exactly zero; free `T0TIPREDEFFECT` does not require `a < 0`; `(B / a)² v` is `addedTIPREDVAR` and is not this first-occasion map; `t0_b · √v / √p_0` is `T0TIPREDEFFECTstd` and is not this variance; free `T0VAR` is not this extra TI variance; `TRAITVAR` is not this extra TI variance; Equation 5 of 2017-era `addedT0TIPREDVAR` is `λ² t0_b² v` (Driver et al., 2017, Eq. 5, p. 5; Table 3, p. 13; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T19:10Z; form `t0_b² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; `t0_b² v` is the latent extra, not the observed extra; `λ² p_0 + θ` is first-occasion observed variance, not this extra; `λ² (B / a)² v` is Eq. 5 of `addedTIPREDVAR`, not this first-occasion observed extra; `MANIFESTVAR` `θ` is not this extra; Equation 5 of §7.2 `addedTIPREDVAR` is `λ² (B / a)² v`; form `(B / a)² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; lasting asymptotic extra requires `a < 0`; `(B / a)² v` is the latent extra, not the observed extra; `λ² t0_b² v` is first-occasion extra observed TI variance, not this extra; `λ² p + θ` is stationary observed variance, not this extra; `MANIFESTVAR` `θ` is not this extra; p. 16 `TDPREDEFFECTstd` is `m · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` and strictly positive time-dependent predictor variance; unstandardised `M` is not `TDPREDEFFECTstd`; `TIPREDEFFECTstd` is not `TDPREDEFFECTstd` even when `M = B`; intercept-style `A^{-1}[e^{A Δt} − I] M · √v / √p` is not `TDPREDEFFECTstd`; `m · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TDPREDEFFECTstd`; Table 3 / p. 16 `T0TDPREDEFFECTstd` is `t0_m · √v / √p_0` after strictly positive free `T0VAR` and strictly positive TD predictor variance; unstandardised `t0_m` is not `T0TDPREDEFFECTstd`; `TDPREDEFFECTstd` uses `asymDIFFUSION` and is not `T0TDPREDEFFECTstd`; `T0TIPREDEFFECTstd` is not `T0TDPREDEFFECTstd` even when `t0_m = t0_b`; `t0_m · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TDPREDEFFECTstd`; free `T0VAR` does not require `a < 0`; p. 16 `T0VARstd` is `p_0 / p_0 = 1` after strictly positive free `T0VAR` (`solve(sqrt(diag(T0VAR))) %&% T0VAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; default ridge is 0); unstandardised `T0VAR` is not `T0VARstd`; `T0TDPREDEFFECTstd` is not `T0VARstd`; `addedT0TIPREDVAR` is not `T0VARstd`; p. 16 `TRAITVARstd` is `trait / trait = 1` after strictly positive `TRAITVAR` (`solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; no ridge addend); unstandardised `TRAITVAR` is not `TRAITVARstd`; `T0VARstd` is not `TRAITVARstd` even when both equal 1; `addedT0TIPREDVAR` is not `TRAITVARstd`; p. 16 `MANIFESTTRAITVARstd` is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR` (`solve(sqrt(diag(MANIFESTTRAITVAR))) %&% MANIFESTTRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0); unstandardised `MANIFESTTRAITVAR` is not `MANIFESTTRAITVARstd`; `TRAITVARstd` is not `MANIFESTTRAITVARstd` even when both equal 1; `MANIFESTVAR` is not `MANIFESTTRAITVARstd`; p. 16 `MANIFESTVARstd` is `θ / θ = 1` after strictly positive `MANIFESTVAR` (`solve(sqrt(diag(MANIFESTVAR))) %&% MANIFESTVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; 2017-era `dimnames` assignment to `latentNames` is a source bug); unstandardised `MANIFESTVAR` is not `MANIFESTVARstd`; `MANIFESTTRAITVARstd` is not `MANIFESTVARstd` even when both equal 1; Equation 5 `Var(y)` is not `MANIFESTVARstd`; p. 16 `TIPREDVARstd` is `v / v = 1` after strictly positive `TIPREDVAR` (`solve(sqrt(diag(TIPREDVAR))) %&% TIPREDVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `TIpredNames`); unstandardised `TIPREDVAR` is not `TIPREDVARstd`; `MANIFESTVARstd` is not `TIPREDVARstd` even when both equal 1; §7.2 `addedTIPREDVAR` is not `TIPREDVARstd`; p. 16 `asymDIFFUSIONstd` is `p / p = 1` after strictly positive `asymDIFFUSION` (`solve(sqrt(diag(asymDIFFUSION))) %&% asymDIFFUSION`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `latentNames`); unstandardised `asymDIFFUSION` is not `asymDIFFUSIONstd`; `TIPREDVARstd` is not `asymDIFFUSIONstd` even when both equal 1; `DIFFUSIONstd` `−2 a` is not `asymDIFFUSIONstd`; p. 16 `discreteCINTstd` is `A^{-1}[e^{A Δt} − I] κ / √p` after strictly positive `asymDIFFUSION`; unstandardised `discreteCINT` is not `discreteCINTstd`; `κ / √p` is not `discreteCINTstd`; `(-κ / a) / √p` is not `discreteCINTstd`; `asymCINTstd` is `(-κ / a) / √p` after strictly positive `asymDIFFUSION`; unstandardised `asymCINT` is not `asymCINTstd`; `κ / √p` is not `asymCINTstd`; `discreteCINTstd` is not `asymCINTstd`; `T0MEANSstd` is `μ_0 / √p_0` after strictly positive free `T0VAR`; unstandardised `T0MEANS` is not `T0MEANSstd`; `T0VARstd` is not `T0MEANSstd`; `μ_0 / √asymDIFFUSION` is not `T0MEANSstd`;))))), CWC-then-event-time residual lag, irregular already-centered residual log-rate, and strong/strict-gated two-group OLS latent-mean difference are implemented on the consolidation vehicle PR `integration/psychometric-standardisation` (folding draft stack #181–#218) and are not implemented-main until exact-head checks, review, and protected-main integration complete; full ESEM/set-ESEM, formative composites, DSEM, and matrix continuous-time dynamics remain accepted-target
+**Implementation maturity:** partial — construct classification, valid log-ratio/logistic-normal indicator gates, CPU `f64` OLS and posterior-draw loading point-estimate averaging, Rubin `T_m = Ū_m + (1+1/m) B_m` on draw-level OLS loadings, cluster-mean within/between OLS with the CWC contextual effect and Kish ESS WLS, event-time discrete lag-1 and exact scalar local log-rate, exact scalar forward map and unequal-interval remapping, exact scalar discrete effect of a constant predictor, first-order discrete effect of a time-varying predictor with matched sampling and constancy intervals (Voelkle et al., 2012, Eq. 14), exact scalar discrete process noise (Driver, Oud, & Voelkle, 2017, Eq. 3), exact scalar lagged latent covariance and unconditional latent variance (Driver et al., 2017, Eq. 3–4), exact scalar stationary within-subject variance (Driver et al., 2017, Eq. 4 as `Δt → ∞`; §4.3; p. 16 `asymDIFFUSION`), exact scalar trait-plus-state variance and lagged covariance (Driver et al., 2017, §4.3 `TRAITVAR`; not process noise and not `asymDIFFUSION`), exact scalar observed-indicator variance and lagged observed covariance (Driver et al., 2017, Eq. 5, p. 5; Table 2, p. 12; `λ² Var(η) + θ` when `MANIFESTTRAITVAR` is zero, else `λ² Var(η) + θ + ψ`; lagged `λ² cov(η_t, η_{t-1}) + ψ`; `MANIFESTVAR` is `Θ`, not `Var(y)`; `Θ` does not enter lagged observed covariance; `MANIFESTTRAITVAR` is not `MANIFESTVAR`; observed-indicator mean is `τ + λ μ` (`MANIFESTMEANS` is `τ`, not `E(y)`; `CINT` is not `MANIFESTMEANS`; `T0MEANS` is not `E(y)`; Equation 1 is the SDE; not a Kalman filter), exact scalar discrete latent mean `exp(a Δt) μ_0 + (exp(a Δt) − 1)/a κ` (Driver et al., 2017, Eq. 3; `T0MEANS` is not `μ_t`; `CINT` is not the discrete increment), exact scalar evolved observed-indicator mean `τ + λ μ_t` (Driver et al., 2017, Eq. 5 of that Eq. 3 map; the first-occasion map `τ + λ μ_0` is not `E(y_t)`), exact scalar contemporaneous `TDPREDEFFECT` impulse `m x` (Driver et al., 2017, Eq. 3 fourth summand; Table 2 `TDPREDEFFECT` is `M`, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14; the §7.2 level-change form is not that impulse), exact scalar observed mean of that contemporaneous impulse `τ + λ(μ_t + m x)` (Driver et al., 2017, Eq. 5 of that Eq. 3 composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar time-independent `TIPREDEFFECT` increment `A^{-1}[e^{A Δt} − I] B z` (Driver et al., 2017, Eq. 3 second summand; Table 2 `TIPREDEFFECT` is `B`, not `κ`, not `M`, and not Voelkle Eq. 14; `B` is not that discrete increment), exact scalar observed mean of that increment `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` (Driver et al., 2017, Eq. 5 of that Eq. 3 printed addend after the `T0MEANS` carry and the `CINT` increment; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar within-interval `TDPREDEFFECT` carry `e^{A(t−u)} M x` for `t0 < u < t` (Driver et al., 2017, Eq. 1–2 Green-function integral of Eq. 2; §7.2 dissipation; not the contemporaneous Dirac, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14), exact scalar observed mean of that carry `τ + λ(μ_t + e^{a(t−u)} m x)` (Driver et al., 2017, Eq. 5 of that carried latent mean; `τ + λ μ_t` is not that observed mean), exact scalar first-occasion `T0TIPREDEFFECT` shift `t0_b z` and Eq. 3 first-summand carry `e^{A Δt} t0_b z` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; `T0TIPREDEFFECT` is not `TIPREDEFFECT` `B`; `t0_b z` is not `A^{-1}[e^{A Δt} − I] B z`; `e^{A Δt} t0_b z` is not `t0_b z`), exact scalar observed mean of that first-occasion carry `τ + λ(μ_t + e^{a Δt} t0_b z)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean), exact scalar first-occasion `T0TDPREDEFFECT` shift `t0_m x0` and Eq. 3 first-summand carry `e^{A Δt} t0_m x0` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; JSS PDF re-opened 2026-08-20T19:10Z; `T0TDPREDEFFECT` is not `TDPREDEFFECT` `M`; `t0_m x0` is not `M x`; `e^{A Δt} t0_m x0` is not `t0_m x0`; `e^{A Δt} t0_m x0` is not `e^{A(t−u)} M x` for `t0 < u < t`; `t0_m x0` is not `t0_b z`; an impulse at `u ≤ t0` that used `M` is already in `η(t0)` as `TDPREDEFFECT`, not as `T0TDPREDEFFECT`), exact scalar observed mean of that first-occasion TD carry `τ + λ(μ_t + e^{a Δt} t0_m x0)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand TD composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean; `τ + λ(μ_t + e^{a Δt} t0_b z)` is not that observed mean), exact scalar §7.2 level-change `CINT` `κ = −a m x` (Driver et al., 2017, §7.2, pp. 20–21; `a < 0` so `−κ / a = m x`; not the dissipating Dirac, not a free `CINT`, not `TIPREDEFFECT`, and not the extra near-zero-drift latent process also named in §7.2), exact scalar Eq. 3 increment of that setting `(1 − e^{a Δt}) m x` (not `m x`, not `κ`, and not `TIPREDEFFECT`), exact scalar §7.2 extra near-zero-drift latent process contribution `a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a)` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-20T23:10Z; identification `TDPREDEFFECT` on the extra process is 1; extra `DRIFT` printed as `−0.000001`; precisely 0 causes computational problems; `ε = a` is `a_{ηξ} x Δt e^{a Δt}`; not `κ = −a m x`, not `(1 − e^{a Δt}) m x`, and not the dissipating Dirac `m x`; `ε ≥ 0` fails closed), exact scalar observed mean of that extra-process contribution `τ + λ(μ_t + a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a))` (Driver et al., 2017, Eq. 5, p. 5; §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:12Z; the extra process has `LAMBDA` 0 and is not an observed indicator; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; the contribution is not `E(y_t)`; the evolved-plus-contribution latent mean is not `E(y_t)`), exact scalar after-t0 extra-process contribution `a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a)` for `t0 < u < t` and Eq. 5 observed mean `τ + λ(μ_t + a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a))` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:32Z; `T0TDPREDEFFECT` uses `Δt` for both the evolution and the extra drive; `TDPREDEFFECT` after `t0` uses `t − u`; `e^{a(t−u)} m x` is a Dirac on the original process, not this `DRIFT` drive), exact scalar §7.2 `asymTIPREDEFFECT` `-B z / a` (Driver et al., 2017, §7.2, pp. 20–21; JSS PDF opened 2026-08-21T13:08Z; expected total change in process means given a time-independent predictor; `a < 0`; not the coefficient `B`, not `A^{-1}[e^{A Δt} − I] B z`, not `CINT`, and not `M x`; `a ≥ 0` fails closed), exact scalar §7.2 `addedTIPREDVAR` `(B / a)² v` (Driver et al., 2017, §7.2, pp. 20–21; stable between-subject variance accounted for by a time-independent predictor; not `TRAITVAR`, not `asymDIFFUSION`, and not `-B z / a`), exact scalar Table 2 `asymCINT` `-κ / a` (Driver et al., 2017, Table 2, p. 12; Eq. 3 as `Δt → ∞`; `a < 0`; not `κ`, not `A^{-1}[e^{A Δt} − I] κ`, not `T0MEANS`, and not `-B z / a`; `a ≥ 0` fails closed), exact scalar p. 16 stationary `T0MEANS` `-κ / a + −B z / a` (Driver et al., 2017, p. 16; constrained first-occasion mean using `T0MEANSbase` / `T0MEANSfree`; not free `T0MEANS`, not `asymCINT` alone, not `asymTIPREDEFFECT` alone, and not the finite-interval discrete latent mean), exact scalar Eq. 5 of that constrained mean `τ + λ(−κ / a + −B z / a)` (Driver et al., 2017, §4.3, pp. 9–10; Eq. 5, p. 5; JSS PDF re-opened 2026-08-21T20:07Z; form the stationary latent mean first, then `τ + λ` of that mean; `τ + λ μ_0` is not that observed mean; `τ + λ(−κ / a)` is not that observed mean when `B z ≠ 0`; `τ + λ μ_t` is not that observed mean; `MANIFESTMEANS` is not `E(y_0)`; the constrained latent mean is not `E(y_0)`), exact scalar §4.3 / p. 16 stationary `T0VAR` `trait + −q / (2 a) + (B / a)² v` (Driver et al., 2017, §4.3, pp. 9–10; p. 16; JSS PDF re-opened 2026-08-22T03:07Z; not free `T0VAR`, not `asymDIFFUSION` alone, not `TRAITVAR` alone, not `addedTIPREDVAR` alone, and not the finite-interval discrete latent variance. Eq. 5 of that constrained variance is `λ²(trait + −q / (2 a) + (B / a)² v) + θ + ψ` (JSS PDF re-opened 2026-08-22T03:20Z; form the stationary latent variance first, then `λ² p + θ + ψ`; `λ² p_0` is not that observed variance; `λ²(−q / (2 a)) + θ` is not that observed variance when `TRAITVAR` or `addedTIPREDVAR` is nonzero; `MANIFESTVAR` is not `Var(y_0)`; the constrained latent variance is not `Var(y_0)`), exact scalar lagged covariance of that constrained process `trait + e^{a Δt}(−q / (2 a)) + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T19:13Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; contemporaneous `T0VAR` is not that lagged map; decaying the constrained total as if it were all state is not that lagged map), exact scalar Eq. 5 of that lagged covariance `λ²(trait + e^{a Δt}(−q / (2 a)) + (B / a)² v) + ψ` (`Θ` does not enter; contemporaneous `Var(y_0)` is not that lagged observed covariance; the lagged latent covariance is not that observed covariance), exact scalar later-occasion variance of that constrained process `trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T23:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; under stationarity that composition equals contemporaneous `T0VAR`; evolving the constrained total as if it were all state is not that later map; the lagged covariance omits `Q_Δt` and is not that later map; `Q_Δt` is not that later map), exact scalar Eq. 5 of that later-occasion variance `λ²(trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v) + θ + ψ` (the lagged observed covariance omits `Q_Δt` and `θ`; `MANIFESTVAR` is not that later observed variance; the later-occasion latent variance is not that observed variance)), exact scalar later-occasion variance of §4.3 predetermined `T0VAR` `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T05:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; free `T0VAR` `p_0` is not that later map; setting `p_0 = −q / (2 a)` recovers the stationary later-occasion map; stationary later variance uses `−q / (2 a)` in place of `p_0` and is not that later map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that later 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. Eq. 5 of that predetermined later-occasion variance is `λ²(trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that later observed variance; the predetermined later-occasion latent variance is not that observed variance; stationary later observed variance is not that observed variance when `p_0` is free)), exact scalar lagged covariance of §4.3 predetermined `T0VAR` `trait + e^{a Δt} p_0 + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T09:04Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; free `T0VAR` `p_0` is not that lagged map; setting `p_0 = −q / (2 a)` recovers the stationary lagged map; stationary lagged covariance uses `−q / (2 a)` in place of `p_0` and is not that lagged map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that lagged map; later-occasion variance includes `Q_Δt` and is not that lagged map. Eq. 5 of that predetermined lagged covariance is `λ²(trait + e^{a Δt} p_0 + (B / a)² v) + ψ` (`MANIFESTVAR` does not enter; the predetermined lagged latent covariance is not that observed covariance; predetermined later observed variance includes `Q_Δt` and `θ` and is not that lagged observed covariance; stationary lagged observed covariance is not that observed covariance when `p_0` is free)), exact scalar first-occasion variance of §4.3 predetermined `T0VAR` `trait + p_0 + (B / a)² v` (free `p_0` is not that map; stationary first-occasion variance uses `−q / (2 a)` in place of `p_0` and is not that map when `p_0` is free; lagged covariance decays the state and is not that map; later-occasion variance includes `Q_Δt` and is not that map), exact scalar Eq. 5 of that predetermined first-occasion variance `λ²(trait + p_0 + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that first-occasion observed variance; the predetermined first-occasion latent variance is not that observed variance; stationary first-occasion observed variance is not that observed variance when `p_0` is free; predetermined later observed variance includes `Q_Δt` and is not that first-occasion observed variance; later-start lagged covariance of predetermined `T0VAR` is `trait + e^{a s}(e^{2 a u} p_0 + Q_u) + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 4; JSS PDF re-opened 2026-08-23T10:27Z; first-occasion lagged omits `e^{a s} Q_u`; later-occasion variance does not lag; stationary lagged uses `−q / (2 a)`; decaying the later total is not that map; Eq. 5 of that later-start lagged covariance is `λ²` of it plus `ψ`; `Θ` does not enter; first-occasion lagged observed omits `e^{a s} Q_u`; later observed variance includes `Q_u` and `θ`; later-start later-occasion variance of predetermined `T0VAR` is `trait + e^{2 a s}(e^{2 a u} p_0 + Q_u) + Q_s + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 3–4 Chapman–Kolmogorov `Q_{u+s} = e^{2 a s} Q_u + Q_s`; JSS PDF re-opened 2026-08-23T11:05Z; later-occasion variance at `u` omits `Q_s`; later-start lagged covariance omits `Q_s`; stationary later uses `−q / (2 a)`; evolving the later total as if it were all state is not that map; ignoring `startoffset` omits `e^{2 a s} Q_u`; Eq. 5 of that later-start later-occasion variance is `λ²` of it plus `θ + ψ`; `MANIFESTVAR` is not that observed variance; p. 16 `discreteDRIFTstd` is `e^{a Δt}` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; footnote 4; §7.1; JSS PDF re-opened 2026-08-23T11:40Z; unstandardised `e^{a Δt}` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDRIFTstd`; the trait-plus-state autocorrelation uses `TRAITVAR` and is not `discreteDRIFTstd`; p. 16 `discreteDIFFUSIONstd` is `Q_Δt / (−q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-28T13:24Z; unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDIFFUSIONstd`; the continuous standardisation `−2 a` is not `discreteDIFFUSIONstd`; `Q_Δt / (trait + p + added)` uses `TRAITVAR` and is not `discreteDIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DIFFUSIONstd` is `q / (−q / (2 a)) = −2 a` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-23T13:20Z; unstandardised `q` is defined for growing `a ≥ 0` and for zero diffusion and is not `DIFFUSIONstd`; the discrete standardisation `Q_Δt / (−q / (2 a))` depends on `Δt` and is not `DIFFUSIONstd`; `q / (trait + p + added)` uses `TRAITVAR` and is not `DIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DRIFTstd` is the continuous auto-effect after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 1; footnote 4; JSS PDF re-opened 2026-08-23T13:28Z); unstandardised `a` is defined for growing `a ≥ 0` and for zero diffusion and is not `DRIFTstd`; the discrete standardisation `e^{a Δt}` depends on the event interval and is not `DRIFTstd`; `a p / (trait + p + added)` uses `TRAITVAR` and is not `DRIFTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `asymTIPREDEFFECTstd` is `(-B / a) · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T14:25Z; unstandardised `-B / a` is defined for a zero coefficient and for zero predictor variance and is not `asymTIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `asymTIPREDEFFECTstd`; `(-B / a) · √v / √(trait + p + added)` uses `TRAITVAR` and is not `asymTIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `TIPREDEFFECTstd` is `B · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T16:21Z; unstandardised `B` is defined for a zero coefficient and for zero predictor variance and is not `TIPREDEFFECTstd`; the asymptotic standardisation `(-B / a) · √v / √p` is the total change and is not `TIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `TIPREDEFFECTstd`; `B · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); Table 3 `T0TIPREDEFFECTstd` is `t0_b · √v / √p_0` after strictly positive free `T0VAR` `p_0` and strictly positive predictor variance `v` (Driver et al., 2017, Table 3, p. 13; p. 16; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T17:20Z; the affected variance is free `T0VAR`, not `asymDIFFUSION`; unstandardised `t0_b` is defined for a zero coefficient and for zero predictor variance and is not `T0TIPREDEFFECTstd`; `TIPREDEFFECTstd` `B · √v / √(-q / (2 a))` is the continuous coefficient and is not `T0TIPREDEFFECTstd`; `asymTIPREDEFFECTstd` `(-B / a) · √v / √p` is the total change and is not `T0TIPREDEFFECTstd`; `t0_b · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); 2017-era `addedT0TIPREDVAR` is `t0_b² v` (Driver et al., 2017, Table 3, p. 13; p. 16; §7.2; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T18:20Z; `T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` immediately after `T0TIPREDEFFECTstd`; form `t0_b` first, then square, then multiply by `v`; a zero coefficient or zero predictor variance is exactly zero; free `T0TIPREDEFFECT` does not require `a < 0`; `(B / a)² v` is `addedTIPREDVAR` and is not this first-occasion map; `t0_b · √v / √p_0` is `T0TIPREDEFFECTstd` and is not this variance; free `T0VAR` is not this extra TI variance; `TRAITVAR` is not this extra TI variance; Equation 5 of 2017-era `addedT0TIPREDVAR` is `λ² t0_b² v` (Driver et al., 2017, Eq. 5, p. 5; Table 3, p. 13; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T19:10Z; form `t0_b² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; `t0_b² v` is the latent extra, not the observed extra; `λ² p_0 + θ` is first-occasion observed variance, not this extra; `λ² (B / a)² v` is Eq. 5 of `addedTIPREDVAR`, not this first-occasion observed extra; `MANIFESTVAR` `θ` is not this extra; Equation 5 of §7.2 `addedTIPREDVAR` is `λ² (B / a)² v`; form `(B / a)² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; lasting asymptotic extra requires `a < 0`; `(B / a)² v` is the latent extra, not the observed extra; `λ² t0_b² v` is first-occasion extra observed TI variance, not this extra; `λ² p + θ` is stationary observed variance, not this extra; `MANIFESTVAR` `θ` is not this extra; p. 16 `TDPREDEFFECTstd` is `m · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` and strictly positive time-dependent predictor variance; unstandardised `M` is not `TDPREDEFFECTstd`; `TIPREDEFFECTstd` is not `TDPREDEFFECTstd` even when `M = B`; intercept-style `A^{-1}[e^{A Δt} − I] M · √v / √p` is not `TDPREDEFFECTstd`; `m · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TDPREDEFFECTstd`; Table 3 / p. 16 `T0TDPREDEFFECTstd` is `t0_m · √v / √p_0` after strictly positive free `T0VAR` and strictly positive TD predictor variance; unstandardised `t0_m` is not `T0TDPREDEFFECTstd`; `TDPREDEFFECTstd` uses `asymDIFFUSION` and is not `T0TDPREDEFFECTstd`; `T0TIPREDEFFECTstd` is not `T0TDPREDEFFECTstd` even when `t0_m = t0_b`; `t0_m · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TDPREDEFFECTstd`; free `T0VAR` does not require `a < 0`; p. 16 `T0VARstd` is `p_0 / p_0 = 1` after strictly positive free `T0VAR` (`solve(sqrt(diag(T0VAR))) %&% T0VAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; default ridge is 0); unstandardised `T0VAR` is not `T0VARstd`; `T0TDPREDEFFECTstd` is not `T0VARstd`; `addedT0TIPREDVAR` is not `T0VARstd`; p. 16 `TRAITVARstd` is `trait / trait = 1` after strictly positive `TRAITVAR` (`solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; no ridge addend); unstandardised `TRAITVAR` is not `TRAITVARstd`; `T0VARstd` is not `TRAITVARstd` even when both equal 1; `addedT0TIPREDVAR` is not `TRAITVARstd`; p. 16 `MANIFESTTRAITVARstd` is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR` (`solve(sqrt(diag(MANIFESTTRAITVAR))) %&% MANIFESTTRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0); unstandardised `MANIFESTTRAITVAR` is not `MANIFESTTRAITVARstd`; `TRAITVARstd` is not `MANIFESTTRAITVARstd` even when both equal 1; `MANIFESTVAR` is not `MANIFESTTRAITVARstd`; p. 16 `MANIFESTVARstd` is `θ / θ = 1` after strictly positive `MANIFESTVAR` (`solve(sqrt(diag(MANIFESTVAR))) %&% MANIFESTVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; 2017-era `dimnames` assignment to `latentNames` is a source bug); unstandardised `MANIFESTVAR` is not `MANIFESTVARstd`; `MANIFESTTRAITVARstd` is not `MANIFESTVARstd` even when both equal 1; Equation 5 `Var(y)` is not `MANIFESTVARstd`; p. 16 `TIPREDVARstd` is `v / v = 1` after strictly positive `TIPREDVAR` (`solve(sqrt(diag(TIPREDVAR))) %&% TIPREDVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `TIpredNames`); unstandardised `TIPREDVAR` is not `TIPREDVARstd`; `MANIFESTVARstd` is not `TIPREDVARstd` even when both equal 1; §7.2 `addedTIPREDVAR` is not `TIPREDVARstd`; p. 16 `asymDIFFUSIONstd` is `p / p = 1` after strictly positive `asymDIFFUSION` (`solve(sqrt(diag(asymDIFFUSION))) %&% asymDIFFUSION`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `latentNames`); unstandardised `asymDIFFUSION` is not `asymDIFFUSIONstd`; `TIPREDVARstd` is not `asymDIFFUSIONstd` even when both equal 1; `DIFFUSIONstd` `−2 a` is not `asymDIFFUSIONstd`; p. 16 `discreteCINTstd` is `A^{-1}[e^{A Δt} − I] κ / √p` after strictly positive `asymDIFFUSION`; unstandardised `discreteCINT` is not `discreteCINTstd`; `κ / √p` is not `discreteCINTstd`; `(-κ / a) / √p` is not `discreteCINTstd`; `asymCINTstd` is `(-κ / a) / √p` after strictly positive `asymDIFFUSION`; unstandardised `asymCINT` is not `asymCINTstd`; `κ / √p` is not `asymCINTstd`; `discreteCINTstd` is not `asymCINTstd`; `T0MEANSstd` is `μ_0 / √p_0` after strictly positive free `T0VAR`; unstandardised `T0MEANS` is not `T0MEANSstd`; `T0VARstd` is not `T0MEANSstd`; `μ_0 / √asymDIFFUSION` is not `T0MEANSstd`; `MANIFESTMEANSstd` is `τ / √θ` after strictly positive `MANIFESTVAR`; unstandardised `MANIFESTMEANS` is not `MANIFESTMEANSstd`; `MANIFESTVARstd` is not `MANIFESTMEANSstd`; `τ / √(λ² Var(η) + θ)` is not `MANIFESTMEANSstd`;))))), CWC-then-event-time residual lag, irregular already-centered residual log-rate, and strong/strict-gated two-group OLS latent-mean difference are implemented on the stacked psychometric PR and are not implemented-main until exact-head checks, review, and protected-main integration complete; full ESEM/set-ESEM, formative composites, DSEM, and matrix continuous-time dynamics remain accepted-target
+**Implementation maturity:** partial — construct classification, valid log-ratio/logistic-normal indicator gates, CPU `f64` OLS and posterior-draw loading point-estimate averaging, Rubin `T_m = Ū_m + (1+1/m) B_m` on draw-level OLS loadings, cluster-mean within/between OLS with the CWC contextual effect and Kish ESS WLS, event-time discrete lag-1 and exact scalar local log-rate, exact scalar forward map and unequal-interval remapping, exact scalar discrete effect of a constant predictor, first-order discrete effect of a time-varying predictor with matched sampling and constancy intervals (Voelkle et al., 2012, Eq. 14), exact scalar discrete process noise (Driver, Oud, & Voelkle, 2017, Eq. 3), exact scalar lagged latent covariance and unconditional latent variance (Driver et al., 2017, Eq. 3–4), exact scalar stationary within-subject variance (Driver et al., 2017, Eq. 4 as `Δt → ∞`; §4.3; p. 16 `asymDIFFUSION`), exact scalar trait-plus-state variance and lagged covariance (Driver et al., 2017, §4.3 `TRAITVAR`; not process noise and not `asymDIFFUSION`), exact scalar observed-indicator variance and lagged observed covariance (Driver et al., 2017, Eq. 5, p. 5; Table 2, p. 12; `λ² Var(η) + θ` when `MANIFESTTRAITVAR` is zero, else `λ² Var(η) + θ + ψ`; lagged `λ² cov(η_t, η_{t-1}) + ψ`; `MANIFESTVAR` is `Θ`, not `Var(y)`; `Θ` does not enter lagged observed covariance; `MANIFESTTRAITVAR` is not `MANIFESTVAR`; observed-indicator mean is `τ + λ μ` (`MANIFESTMEANS` is `τ`, not `E(y)`; `CINT` is not `MANIFESTMEANS`; `T0MEANS` is not `E(y)`; Equation 1 is the SDE; not a Kalman filter), exact scalar discrete latent mean `exp(a Δt) μ_0 + (exp(a Δt) − 1)/a κ` (Driver et al., 2017, Eq. 3; `T0MEANS` is not `μ_t`; `CINT` is not the discrete increment), exact scalar evolved observed-indicator mean `τ + λ μ_t` (Driver et al., 2017, Eq. 5 of that Eq. 3 map; the first-occasion map `τ + λ μ_0` is not `E(y_t)`), exact scalar contemporaneous `TDPREDEFFECT` impulse `m x` (Driver et al., 2017, Eq. 3 fourth summand; Table 2 `TDPREDEFFECT` is `M`, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14; the §7.2 level-change form is not that impulse), exact scalar observed mean of that contemporaneous impulse `τ + λ(μ_t + m x)` (Driver et al., 2017, Eq. 5 of that Eq. 3 composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar time-independent `TIPREDEFFECT` increment `A^{-1}[e^{A Δt} − I] B z` (Driver et al., 2017, Eq. 3 second summand; Table 2 `TIPREDEFFECT` is `B`, not `κ`, not `M`, and not Voelkle Eq. 14; `B` is not that discrete increment), exact scalar observed mean of that increment `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` (Driver et al., 2017, Eq. 5 of that Eq. 3 printed addend after the `T0MEANS` carry and the `CINT` increment; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; `τ + λ(μ_t + e^{a(t−u)} m x)` is not that observed mean when `u ≠ t`), exact scalar within-interval `TDPREDEFFECT` carry `e^{A(t−u)} M x` for `t0 < u < t` (Driver et al., 2017, Eq. 1–2 Green-function integral of Eq. 2; §7.2 dissipation; not the contemporaneous Dirac, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14), exact scalar observed mean of that carry `τ + λ(μ_t + e^{a(t−u)} m x)` (Driver et al., 2017, Eq. 5 of that carried latent mean; `τ + λ μ_t` is not that observed mean), exact scalar first-occasion `T0TIPREDEFFECT` shift `t0_b z` and Eq. 3 first-summand carry `e^{A Δt} t0_b z` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; `T0TIPREDEFFECT` is not `TIPREDEFFECT` `B`; `t0_b z` is not `A^{-1}[e^{A Δt} − I] B z`; `e^{A Δt} t0_b z` is not `t0_b z`), exact scalar observed mean of that first-occasion carry `τ + λ(μ_t + e^{a Δt} t0_b z)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean), exact scalar first-occasion `T0TDPREDEFFECT` shift `t0_m x0` and Eq. 3 first-summand carry `e^{A Δt} t0_m x0` (Driver et al., 2017, Table 3, p. 13; Eq. 3, p. 5; JSS PDF re-opened 2026-08-20T19:10Z; `T0TDPREDEFFECT` is not `TDPREDEFFECT` `M`; `t0_m x0` is not `M x`; `e^{A Δt} t0_m x0` is not `t0_m x0`; `e^{A Δt} t0_m x0` is not `e^{A(t−u)} M x` for `t0 < u < t`; `t0_m x0` is not `t0_b z`; an impulse at `u ≤ t0` that used `M` is already in `η(t0)` as `TDPREDEFFECT`, not as `T0TDPREDEFFECT`), exact scalar observed mean of that first-occasion TD carry `τ + λ(μ_t + e^{a Δt} t0_m x0)` (Driver et al., 2017, Eq. 5 of that Table 3 / Eq. 3 first-summand TD composition; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)` is not that observed mean; `τ + λ(μ_t + e^{a Δt} t0_b z)` is not that observed mean), exact scalar §7.2 level-change `CINT` `κ = −a m x` (Driver et al., 2017, §7.2, pp. 20–21; `a < 0` so `−κ / a = m x`; not the dissipating Dirac, not a free `CINT`, not `TIPREDEFFECT`, and not the extra near-zero-drift latent process also named in §7.2), exact scalar Eq. 3 increment of that setting `(1 − e^{a Δt}) m x` (not `m x`, not `κ`, and not `TIPREDEFFECT`), exact scalar §7.2 extra near-zero-drift latent process contribution `a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a)` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-20T23:10Z; identification `TDPREDEFFECT` on the extra process is 1; extra `DRIFT` printed as `−0.000001`; precisely 0 causes computational problems; `ε = a` is `a_{ηξ} x Δt e^{a Δt}`; not `κ = −a m x`, not `(1 − e^{a Δt}) m x`, and not the dissipating Dirac `m x`; `ε ≥ 0` fails closed), exact scalar observed mean of that extra-process contribution `τ + λ(μ_t + a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a))` (Driver et al., 2017, Eq. 5, p. 5; §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:12Z; the extra process has `LAMBDA` 0 and is not an observed indicator; `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that observed mean; the contribution is not `E(y_t)`; the evolved-plus-contribution latent mean is not `E(y_t)`), exact scalar after-t0 extra-process contribution `a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a)` for `t0 < u < t` and Eq. 5 observed mean `τ + λ(μ_t + a_{ηξ} x (e^{ε(t−u)} − e^{a(t−u)}) / (ε − a))` (Driver et al., 2017, §7.2, pp. 22–23; JSS PDF re-opened 2026-08-21T06:32Z; `T0TDPREDEFFECT` uses `Δt` for both the evolution and the extra drive; `TDPREDEFFECT` after `t0` uses `t − u`; `e^{a(t−u)} m x` is a Dirac on the original process, not this `DRIFT` drive), exact scalar §7.2 `asymTIPREDEFFECT` `-B z / a` (Driver et al., 2017, §7.2, pp. 20–21; JSS PDF opened 2026-08-21T13:08Z; expected total change in process means given a time-independent predictor; `a < 0`; not the coefficient `B`, not `A^{-1}[e^{A Δt} − I] B z`, not `CINT`, and not `M x`; `a ≥ 0` fails closed), exact scalar §7.2 `addedTIPREDVAR` `(B / a)² v` (Driver et al., 2017, §7.2, pp. 20–21; stable between-subject variance accounted for by a time-independent predictor; not `TRAITVAR`, not `asymDIFFUSION`, and not `-B z / a`), exact scalar Table 2 `asymCINT` `-κ / a` (Driver et al., 2017, Table 2, p. 12; Eq. 3 as `Δt → ∞`; `a < 0`; not `κ`, not `A^{-1}[e^{A Δt} − I] κ`, not `T0MEANS`, and not `-B z / a`; `a ≥ 0` fails closed), exact scalar p. 16 stationary `T0MEANS` `-κ / a + −B z / a` (Driver et al., 2017, p. 16; constrained first-occasion mean using `T0MEANSbase` / `T0MEANSfree`; not free `T0MEANS`, not `asymCINT` alone, not `asymTIPREDEFFECT` alone, and not the finite-interval discrete latent mean), exact scalar Eq. 5 of that constrained mean `τ + λ(−κ / a + −B z / a)` (Driver et al., 2017, §4.3, pp. 9–10; Eq. 5, p. 5; JSS PDF re-opened 2026-08-21T20:07Z; form the stationary latent mean first, then `τ + λ` of that mean; `τ + λ μ_0` is not that observed mean; `τ + λ(−κ / a)` is not that observed mean when `B z ≠ 0`; `τ + λ μ_t` is not that observed mean; `MANIFESTMEANS` is not `E(y_0)`; the constrained latent mean is not `E(y_0)`), exact scalar §4.3 / p. 16 stationary `T0VAR` `trait + −q / (2 a) + (B / a)² v` (Driver et al., 2017, §4.3, pp. 9–10; p. 16; JSS PDF re-opened 2026-08-22T03:07Z; not free `T0VAR`, not `asymDIFFUSION` alone, not `TRAITVAR` alone, not `addedTIPREDVAR` alone, and not the finite-interval discrete latent variance. Eq. 5 of that constrained variance is `λ²(trait + −q / (2 a) + (B / a)² v) + θ + ψ` (JSS PDF re-opened 2026-08-22T03:20Z; form the stationary latent variance first, then `λ² p + θ + ψ`; `λ² p_0` is not that observed variance; `λ²(−q / (2 a)) + θ` is not that observed variance when `TRAITVAR` or `addedTIPREDVAR` is nonzero; `MANIFESTVAR` is not `Var(y_0)`; the constrained latent variance is not `Var(y_0)`), exact scalar lagged covariance of that constrained process `trait + e^{a Δt}(−q / (2 a)) + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T19:13Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; contemporaneous `T0VAR` is not that lagged map; decaying the constrained total as if it were all state is not that lagged map), exact scalar Eq. 5 of that lagged covariance `λ²(trait + e^{a Δt}(−q / (2 a)) + (B / a)² v) + ψ` (`Θ` does not enter; contemporaneous `Var(y_0)` is not that lagged observed covariance; the lagged latent covariance is not that observed covariance), exact scalar later-occasion variance of that constrained process `trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 / p. 16 `T0VAR`; JSS PDF re-opened 2026-08-22T23:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; under stationarity that composition equals contemporaneous `T0VAR`; evolving the constrained total as if it were all state is not that later map; the lagged covariance omits `Q_Δt` and is not that later map; `Q_Δt` is not that later map), exact scalar Eq. 5 of that later-occasion variance `λ²(trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v) + θ + ψ` (the lagged observed covariance omits `Q_Δt` and `θ`; `MANIFESTVAR` is not that later observed variance; the later-occasion latent variance is not that observed variance)), exact scalar later-occasion variance of §4.3 predetermined `T0VAR` `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T05:12Z; trait and `addedTIPREDVAR` do not enter `Q_Δt`; free `T0VAR` `p_0` is not that later map; setting `p_0 = −q / (2 a)` recovers the stationary later-occasion map; stationary later variance uses `−q / (2 a)` in place of `p_0` and is not that later map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that later 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. Eq. 5 of that predetermined later-occasion variance is `λ²(trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that later observed variance; the predetermined later-occasion latent variance is not that observed variance; stationary later observed variance is not that observed variance when `p_0` is free)), exact scalar lagged covariance of §4.3 predetermined `T0VAR` `trait + e^{a Δt} p_0 + (B / a)² v` (Driver et al., 2017, Eq. 3–4 of §4.3 predetermined first occasion; JSS PDF re-opened 2026-08-23T09:04Z; trait and `addedTIPREDVAR` do not decay with `e^{a Δt}`; free `T0VAR` `p_0` is not that lagged map; setting `p_0 = −q / (2 a)` recovers the stationary lagged map; stationary lagged covariance uses `−q / (2 a)` in place of `p_0` and is not that lagged map when `p_0` is free; evolving `trait + p_0 + (B / a)² v` as if it were all state is not that lagged map; later-occasion variance includes `Q_Δt` and is not that lagged map. Eq. 5 of that predetermined lagged covariance is `λ²(trait + e^{a Δt} p_0 + (B / a)² v) + ψ` (`MANIFESTVAR` does not enter; the predetermined lagged latent covariance is not that observed covariance; predetermined later observed variance includes `Q_Δt` and `θ` and is not that lagged observed covariance; stationary lagged observed covariance is not that observed covariance when `p_0` is free)), exact scalar first-occasion variance of §4.3 predetermined `T0VAR` `trait + p_0 + (B / a)² v` (free `p_0` is not that map; stationary first-occasion variance uses `−q / (2 a)` in place of `p_0` and is not that map when `p_0` is free; lagged covariance decays the state and is not that map; later-occasion variance includes `Q_Δt` and is not that map), exact scalar Eq. 5 of that predetermined first-occasion variance `λ²(trait + p_0 + (B / a)² v) + θ + ψ` (`MANIFESTVAR` is not that first-occasion observed variance; the predetermined first-occasion latent variance is not that observed variance; stationary first-occasion observed variance is not that observed variance when `p_0` is free; predetermined later observed variance includes `Q_Δt` and is not that first-occasion observed variance; later-start lagged covariance of predetermined `T0VAR` is `trait + e^{a s}(e^{2 a u} p_0 + Q_u) + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 4; JSS PDF re-opened 2026-08-23T10:27Z; first-occasion lagged omits `e^{a s} Q_u`; later-occasion variance does not lag; stationary lagged uses `−q / (2 a)`; decaying the later total is not that map; Eq. 5 of that later-start lagged covariance is `λ²` of it plus `ψ`; `Θ` does not enter; first-occasion lagged observed omits `e^{a s} Q_u`; later observed variance includes `Q_u` and `θ`; later-start later-occasion variance of predetermined `T0VAR` is `trait + e^{2 a s}(e^{2 a u} p_0 + Q_u) + Q_s + (B / a)² v` (Driver et al., 2017, §4.3 `startoffset`; Eq. 3–4 Chapman–Kolmogorov `Q_{u+s} = e^{2 a s} Q_u + Q_s`; JSS PDF re-opened 2026-08-23T11:05Z; later-occasion variance at `u` omits `Q_s`; later-start lagged covariance omits `Q_s`; stationary later uses `−q / (2 a)`; evolving the later total as if it were all state is not that map; ignoring `startoffset` omits `e^{2 a s} Q_u`; Eq. 5 of that later-start later-occasion variance is `λ²` of it plus `θ + ψ`; `MANIFESTVAR` is not that observed variance; p. 16 `discreteDRIFTstd` is `e^{a Δt}` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; footnote 4; §7.1; JSS PDF re-opened 2026-08-23T11:40Z; unstandardised `e^{a Δt}` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDRIFTstd`; the trait-plus-state autocorrelation uses `TRAITVAR` and is not `discreteDRIFTstd`; p. 16 `discreteDIFFUSIONstd` is `Q_Δt / (−q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-28T13:24Z; unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDIFFUSIONstd`; the continuous standardisation `−2 a` is not `discreteDIFFUSIONstd`; `Q_Δt / (trait + p + added)` uses `TRAITVAR` and is not `discreteDIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DIFFUSIONstd` is `q / (−q / (2 a)) = −2 a` after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4; footnote 4; JSS PDF re-opened 2026-08-23T13:20Z; unstandardised `q` is defined for growing `a ≥ 0` and for zero diffusion and is not `DIFFUSIONstd`; the discrete standardisation `Q_Δt / (−q / (2 a))` depends on `Δt` and is not `DIFFUSIONstd`; `q / (trait + p + added)` uses `TRAITVAR` and is not `DIFFUSIONstd`; `TRAITVAR` is not the standardisation variance; p. 16 `DRIFTstd` is the continuous auto-effect after strictly positive `asymDIFFUSION` `-q / (2 a)` (Driver et al., 2017, p. 16; Eq. 1; footnote 4; JSS PDF re-opened 2026-08-23T13:28Z); unstandardised `a` is defined for growing `a ≥ 0` and for zero diffusion and is not `DRIFTstd`; the discrete standardisation `e^{a Δt}` depends on the event interval and is not `DRIFTstd`; `a p / (trait + p + added)` uses `TRAITVAR` and is not `DRIFTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `asymTIPREDEFFECTstd` is `(-B / a) · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T14:25Z; unstandardised `-B / a` is defined for a zero coefficient and for zero predictor variance and is not `asymTIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `asymTIPREDEFFECTstd`; `(-B / a) · √v / √(trait + p + added)` uses `TRAITVAR` and is not `asymTIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); p. 16 `TIPREDEFFECTstd` is `B · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` `-q / (2 a)` and strictly positive predictor variance `v` (Driver et al., 2017, p. 16; §7.2; footnote 4; JSS PDF re-opened 2026-08-23T16:21Z; unstandardised `B` is defined for a zero coefficient and for zero predictor variance and is not `TIPREDEFFECTstd`; the asymptotic standardisation `(-B / a) · √v / √p` is the total change and is not `TIPREDEFFECTstd`; the finite-interval standardisation `A^{-1}[e^{A Δt} − I] B · √v / √p` depends on the event interval and is not `TIPREDEFFECTstd`; `B · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); Table 3 `T0TIPREDEFFECTstd` is `t0_b · √v / √p_0` after strictly positive free `T0VAR` `p_0` and strictly positive predictor variance `v` (Driver et al., 2017, Table 3, p. 13; p. 16; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T17:20Z; the affected variance is free `T0VAR`, not `asymDIFFUSION`; unstandardised `t0_b` is defined for a zero coefficient and for zero predictor variance and is not `T0TIPREDEFFECTstd`; `TIPREDEFFECTstd` `B · √v / √(-q / (2 a))` is the continuous coefficient and is not `T0TIPREDEFFECTstd`; `asymTIPREDEFFECTstd` `(-B / a) · √v / √p` is the total change and is not `T0TIPREDEFFECTstd`; `t0_b · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TIPREDEFFECTstd`; `TRAITVAR` is not the standardisation variance); 2017-era `addedT0TIPREDVAR` is `t0_b² v` (Driver et al., 2017, Table 3, p. 13; p. 16; §7.2; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T18:20Z; `T0TIPREDEFFECT %*% TIPREDVAR %*% t(T0TIPREDEFFECT)` immediately after `T0TIPREDEFFECTstd`; form `t0_b` first, then square, then multiply by `v`; a zero coefficient or zero predictor variance is exactly zero; free `T0TIPREDEFFECT` does not require `a < 0`; `(B / a)² v` is `addedTIPREDVAR` and is not this first-occasion map; `t0_b · √v / √p_0` is `T0TIPREDEFFECTstd` and is not this variance; free `T0VAR` is not this extra TI variance; `TRAITVAR` is not this extra TI variance; Equation 5 of 2017-era `addedT0TIPREDVAR` is `λ² t0_b² v` (Driver et al., 2017, Eq. 5, p. 5; Table 3, p. 13; Table 2, p. 12; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-23T19:10Z; form `t0_b² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; `t0_b² v` is the latent extra, not the observed extra; `λ² p_0 + θ` is first-occasion observed variance, not this extra; `λ² (B / a)² v` is Eq. 5 of `addedTIPREDVAR`, not this first-occasion observed extra; `MANIFESTVAR` `θ` is not this extra; Equation 5 of §7.2 `addedTIPREDVAR` is `λ² (B / a)² v`; form `(B / a)² v` first, then `(λ extra) λ` with `θ = 0`; a zero loading or zero extra is exactly zero; lasting asymptotic extra requires `a < 0`; `(B / a)² v` is the latent extra, not the observed extra; `λ² t0_b² v` is first-occasion extra observed TI variance, not this extra; `λ² p + θ` is stationary observed variance, not this extra; `MANIFESTVAR` `θ` is not this extra; p. 16 `TDPREDEFFECTstd` is `m · √v / √(-q / (2 a))` after strictly positive `asymDIFFUSION` and strictly positive time-dependent predictor variance; unstandardised `M` is not `TDPREDEFFECTstd`; `TIPREDEFFECTstd` is not `TDPREDEFFECTstd` even when `M = B`; intercept-style `A^{-1}[e^{A Δt} − I] M · √v / √p` is not `TDPREDEFFECTstd`; `m · √v / √(trait + p + added)` uses `TRAITVAR` and is not `TDPREDEFFECTstd`; Table 3 / p. 16 `T0TDPREDEFFECTstd` is `t0_m · √v / √p_0` after strictly positive free `T0VAR` and strictly positive TD predictor variance; unstandardised `t0_m` is not `T0TDPREDEFFECTstd`; `TDPREDEFFECTstd` uses `asymDIFFUSION` and is not `T0TDPREDEFFECTstd`; `T0TIPREDEFFECTstd` is not `T0TDPREDEFFECTstd` even when `t0_m = t0_b`; `t0_m · √v / √(trait + p_0 + added)` uses `TRAITVAR` and is not `T0TDPREDEFFECTstd`; free `T0VAR` does not require `a < 0`; p. 16 `T0VARstd` is `p_0 / p_0 = 1` after strictly positive free `T0VAR` (`solve(sqrt(diag(T0VAR))) %&% T0VAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; default ridge is 0); unstandardised `T0VAR` is not `T0VARstd`; `T0TDPREDEFFECTstd` is not `T0VARstd`; `addedT0TIPREDVAR` is not `T0VARstd`; p. 16 `TRAITVARstd` is `trait / trait = 1` after strictly positive `TRAITVAR` (`solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; no ridge addend); unstandardised `TRAITVAR` is not `TRAITVARstd`; `T0VARstd` is not `TRAITVARstd` even when both equal 1; `addedT0TIPREDVAR` is not `TRAITVARstd`; p. 16 `MANIFESTTRAITVARstd` is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR` (`solve(sqrt(diag(MANIFESTTRAITVAR))) %&% MANIFESTTRAITVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0); unstandardised `MANIFESTTRAITVAR` is not `MANIFESTTRAITVARstd`; `TRAITVARstd` is not `MANIFESTTRAITVARstd` even when both equal 1; `MANIFESTVAR` is not `MANIFESTTRAITVARstd`; p. 16 `MANIFESTVARstd` is `θ / θ = 1` after strictly positive `MANIFESTVAR` (`solve(sqrt(diag(MANIFESTVAR))) %&% MANIFESTVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; 2017-era `dimnames` assignment to `latentNames` is a source bug); unstandardised `MANIFESTVAR` is not `MANIFESTVARstd`; `MANIFESTTRAITVARstd` is not `MANIFESTVARstd` even when both equal 1; Equation 5 `Var(y)` is not `MANIFESTVARstd`; p. 16 `TIPREDVARstd` is `v / v = 1` after strictly positive `TIPREDVAR` (`solve(sqrt(diag(TIPREDVAR))) %&% TIPREDVAR`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `TIpredNames`); unstandardised `TIPREDVAR` is not `TIPREDVARstd`; `MANIFESTVARstd` is not `TIPREDVARstd` even when both equal 1; §7.2 `addedTIPREDVAR` is not `TIPREDVARstd`; p. 16 `asymDIFFUSIONstd` is `p / p = 1` after strictly positive `asymDIFFUSION` (`solve(sqrt(diag(asymDIFFUSION))) %&% asymDIFFUSION`; OpenMx `%&%` is `t(A) %*% B %*% A`; 2017-era source adds ridging; default ridge is 0; `dimnames` are `latentNames`); unstandardised `asymDIFFUSION` is not `asymDIFFUSIONstd`; `TIPREDVARstd` is not `asymDIFFUSIONstd` even when both equal 1; `DIFFUSIONstd` `−2 a` is not `asymDIFFUSIONstd`; p. 16 `discreteCINTstd` is `A^{-1}[e^{A Δt} − I] κ / √p` after strictly positive `asymDIFFUSION`; unstandardised `discreteCINT` is not `discreteCINTstd`; `κ / √p` is not `discreteCINTstd`; `(-κ / a) / √p` is not `discreteCINTstd`; `asymCINTstd` is `(-κ / a) / √p` after strictly positive `asymDIFFUSION`; unstandardised `asymCINT` is not `asymCINTstd`; `κ / √p` is not `asymCINTstd`; `discreteCINTstd` is not `asymCINTstd`; `T0MEANSstd` is `μ_0 / √p_0` after strictly positive free `T0VAR`; unstandardised `T0MEANS` is not `T0MEANSstd`; `T0VARstd` is not `T0MEANSstd`; `μ_0 / √asymDIFFUSION` is not `T0MEANSstd`;))))), CWC-then-event-time residual lag, irregular already-centered residual log-rate, and strong/strict-gated two-group OLS latent-mean difference are implemented on the consolidation vehicle PR `integration/psychometric-standardisation` (folding draft stack #181–#218) and are not implemented-main until exact-head checks, review, and protected-main integration complete; full ESEM/set-ESEM, formative composites, DSEM, and matrix continuous-time dynamics remain accepted-target
 **Date:** 2026-08-05
 **Supersedes:** None. ADR 0012 governs upstream topic measurement/network coordinates; this ADR governs higher-order psychometric structure and longitudinal interpretation.
 
@@ -37,6 +37,7 @@ The executable standardised-initial-variance slice recovers Driver et al. (2017,
 The executable standardised-asymptotic-diffusion slice recovers Driver et al. (2017, p. 16 `asymDIFFUSIONstd`) as `p / p = 1` after strictly positive `asymDIFFUSION` `p = −q / (2 a)` (footnote 4; 2017-era `summary.ctsemFit.R` `solve(sqrt(diag(asymDIFFUSION))) %&% asymDIFFUSION`; JSS PDF re-opened 2026-08-26T17:20Z). Unstandardised `p` is defined for a zero process and is not that map. `p_0 / p_0 = 1` is the named `T0VARstd` first-occasion correlation and is not `asymDIFFUSIONstd` even when both equal 1. `q / p = −2 a` is the named `DIFFUSIONstd` continuous-diffusion ratio and is not this correlation. `v / v = 1` is the named `TIPREDVARstd` predictor correlation and is not this map even when both equal 1. Zero `q` and `a ≥ 0` fail closed. This is not ctsem estimation.
 The executable standardised-manifest-trait-variance slice recovers Driver et al. (2017, p. 16 `MANIFESTTRAITVARstd`) as `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR` (Table 2 `Ψ_τ`; §7.1, p. 19; footnote 4; 2017-era `summary.ctsemFit.R` `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR`; JSS PDF re-opened 2026-08-27T14:20Z). Unstandardised `ψ` is defined for a zero manifest trait and is not that map. `trait / trait = 1` is the named `TRAITVARstd` process-level correlation and is not `MANIFESTTRAITVARstd` even when both equal 1. `θ` is `MANIFESTVAR` and is not that correlation. `MANIFESTTRAITVAR` does not require `a < 0`. This is not ctsem estimation.
 The executable standardised-manifest-variance slice recovers Driver et al. (2017, p. 16 `MANIFESTVARstd`) as `θ / θ = 1` after strictly positive `MANIFESTVAR` (Table 2 measurement-error Cholesky; Eq. 5 `ε ~ N(0, Θ)`; footnote 4; 2017-era `summary.ctsemFit.R` `solve(sqrt(diag(MANIFESTVAR) + ridging)) %&% MANIFESTVAR`; default ridge 0; JSS PDF re-opened 2026-08-27T14:25Z). Unstandardised `θ` is defined for a zero residual and is not that map. `ψ / ψ = 1` is `MANIFESTTRAITVARstd` and is not `MANIFESTVARstd` even when both equal 1. `MANIFESTVAR` does not require `a < 0`.
+The executable standardised-discrete-diffusion slice recovers Driver et al. (2017, p. 16 `discreteDIFFUSIONstd`) as `Q_Δt / p` after strictly positive `asymDIFFUSION` `p = −q / (2 a)` (Eq. 3–4; footnote 4; 2017-era `summary.ctsemFit.R` forms unstandardised `discreteDIFFUSION` and does not form a `discreteDIFFUSIONstd` matrix; JSS PDF re-opened 2026-08-28T13:24Z). Unstandardised `Q_Δt` is defined for growing `a ≥ 0` and for zero diffusion and is not that map. `q / p = −2 a` is the named `DIFFUSIONstd` continuous-diffusion ratio and does not depend on `Δt`. `Q_Δt / (trait + p + added)` uses `TRAITVAR` and is not `discreteDIFFUSIONstd`. Zero `q` and `a ≥ 0` fail closed. This is not ctsem estimation.
 
 The executable standardised-trait-variance slice recovers Driver et al. (2017, p. 16 `TRAITVARstd`) as `trait / trait = 1` after strictly positive `TRAITVAR` (Table 2 `φ_ξ`; §7.1; footnote 4; 2017-era `summary.ctsemFit.R` `solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR`; JSS PDF re-opened 2026-08-26T17:45Z). Unlike `T0VARstd` there is no ridge addend. Unstandardised `TRAITVAR` is defined for a zero trait and is not that map. `p_0 / p_0 = 1` is the named `T0VARstd` first-occasion correlation and is not `TRAITVARstd` even when both equal 1. `t0_b² v` is `addedT0TIPREDVAR` and is not this correlation. Zero `TRAITVAR` and a non-event clock fail closed. `TRAITVAR` does not require `a < 0`. This is not ctsem estimation.
 
diff --git a/docs/research/multilevel-event-time-recovery.md b/docs/research/multilevel-event-time-recovery.md
index 3701dcb4b..761555c80 100644
--- a/docs/research/multilevel-event-time-recovery.md
+++ b/docs/research/multilevel-event-time-recovery.md
@@ -60,7 +60,7 @@ This slice stays inside `psychometric_core`. It does not add a second invariance
 54. recover the exact scalar Eq. 5 of later-start later-occasion §4.3 predetermined `T0VAR` `λ²(trait + e^{2 a s}(e^{2 a u} p_0 + Q_u) + Q_s + (B / a)² v) + θ + ψ` (Driver et al., 2017, Eq. 5, p. 5; Eq. 3–4, pp. 4–5; Table 2, p. 12; JSS PDF re-opened 2026-08-23T11:05Z; form the later-start later-occasion latent variance first, then `λ² p + θ + ψ`; a zero loading is exactly `θ + ψ`) and refuse treating `θ`, the later-start later-occasion latent variance, predetermined later observed variance, later-start lagged observed covariance, or stationary later-occasion observed variance as `Var(y_{t0+u+s})` when `p_0` is free;
 55. recover the exact scalar p. 16 `discreteDRIFTstd` `e^{a Δt}` after forming strictly positive `asymDIFFUSION` `−q / (2 a)` (Driver et al., 2017, p. 16; Eq. 3, p. 5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T11:40Z; form the within-subject variance first, then `φ = exp(a Δt)`; scalar stationary SD ratio is 1; `a ≥ 0` and `q = 0` fail closed);
 56. refuse treating unstandardised `discreteDRIFT` `e^{a Δt}` as `discreteDRIFTstd`, refuse treating the §7.1 trait-plus-state autocorrelation `(trait + e^{a Δt} p + added) / (trait + p + added)` as `discreteDRIFTstd`, and refuse treating `TRAITVAR` as the footnote 4 standardisation variance;
-57. recover the exact scalar p. 16 `discreteDIFFUSIONstd` `Q_Δt / (−q / (2 a))` after forming strictly positive `asymDIFFUSION` `−q / (2 a)` (Driver et al., 2017, p. 16; Eq. 3–4, pp. 4–5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T13:06Z; form the within-subject variance first, then `Q_Δt`, then the ratio; scalar stationary map is `1 − exp(2 a Δt)`; `a ≥ 0` and `q = 0` fail closed);
+57. recover the exact scalar p. 16 `discreteDIFFUSIONstd` `Q_Δt / (−q / (2 a))` after forming strictly positive `asymDIFFUSION` `−q / (2 a)` (Driver et al., 2017, p. 16; Eq. 3–4, pp. 4–5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-28T13:24Z; form the within-subject variance first, then `Q_Δt`, then the ratio; scalar stationary map is `1 − exp(2 a Δt)`; `a ≥ 0` and `q = 0` fail closed);
 58. refuse treating unstandardised `discreteDIFFUSION` `Q_Δt` as `discreteDIFFUSIONstd`, refuse treating the continuous standardisation `q / (−q / (2 a)) = −2 a` as `discreteDIFFUSIONstd`, refuse treating `Q_Δt / (trait + p + added)` as `discreteDIFFUSIONstd`, and refuse treating `TRAITVAR` as the footnote 4 standardisation variance;
 59. recover the exact scalar p. 16 `DIFFUSIONstd` `q / (−q / (2 a)) = −2 a` after forming strictly positive `asymDIFFUSION` `−q / (2 a)` (Driver et al., 2017, p. 16; Eq. 4, p. 5; footnote 4; §7.1, pp. 18–19; JSS PDF re-opened 2026-08-23T13:20Z; form the within-subject variance first, then `q / p`; scalar stationary map is `−2 a` and does not depend on `q` once `q > 0`; `a ≥ 0` and `q = 0` fail closed);
 60. refuse treating unstandardised `DIFFUSION` `q` as `DIFFUSIONstd`, refuse treating the discrete standardisation `Q_Δt / (−q / (2 a)) = 1 − exp(2 a Δt)` as `DIFFUSIONstd`, refuse treating `q / (trait + p + added)` as `DIFFUSIONstd`, and refuse treating `TRAITVAR` as the footnote 4 standardisation variance;