feat(psychometric): restore Driver Table 3 T0TDPREDEFFECTstd on main

CHANGELOG.md

@@ -13,6 +13,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 - **TDT/CHRONOS durable result contract**: canonical typed JSON and deterministic GraphML now export the actual bounded Allen reasoner result, observed/derived status, and conservative accepted-assertion support; canonical payload digest and `tdt_chronos_interval_consistency_v1` type bind the immutable bytes into ADR 0013's append-only `model_artifact` chain.
 - **Analysis engine**: deterministic end-to-end analysis-run execution with cutoff-safe eligibility, immutable evidence binding, and reproducibility manifests (`analysis_engine` crate).
 - **Restore Driver p.16 `MANIFESTVARstd`**: `recover_standardised_manifest_variance` maps `θ / θ = 1` with strictly positive `MANIFESTVAR`, refusing unstandardised manifest-variance, `MANIFESTTRAITVARstd`, and Equation 5 `Var(y)` substitutions (`psychometric_core`).
+- **Restore Driver Table 3 / p.16 `T0TDPREDEFFECTstd`**: `recover_standardised_initial_time_dependent_predictor_effect` maps `t0_m · √v / √p_0` after strictly positive free `T0VAR` and `TDPREDVAR`, refusing unstandardised `t0_m`, `TDPREDEFFECTstd`, `T0TIPREDEFFECTstd`, and trait-contaminated total-variance substitutions (`psychometric_core`).
 - **Posterior network estimator**: cross-draw Pearson correlations in ILR space, jackknife SE and CI, Benjamini–Hochberg FDR edge admission, nonparametric bootstrap stability, greedy modularity consensus clustering (`network_analysis` crate).
 - **Topic measurement reference estimator**: bounded deterministic CPU `f64` TRSL-TM fitting with ALR/ILR coordinates, Aitchison distance, and lexical-inferential-weight refusal gates (`topic_measurement` crate).
 - **Psychometric core**: Driver et al. (2017) SDE discrete-time recovery suite including drift, diffusion, T0VAR, TIPRED/TDPRED effects, standardised parameters, trait/state variance decomposition, and observed-indicator mapping — 18 K lines of production Rust with true-parameter RMSE tests.
@@ -40,6 +41,8 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 - `event_core` adds bounded Allen interval-consistency classification, atomic path-consistency closure, contradiction/resource refusals, and an explicit dependency-error fallback without claiming unrestricted global satisfiability.
 
+- `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 3, p. 13 `T0TDPREDEFFECT`; Table 2, p. 12 `TDPREDVAR`; p. 16 `T0TDPREDEFFECTstd`; footnote 4; Eq. 3, p. 5; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-30T00:17Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised first-occasion time-dependent predictor effect rebased onto protected `main` `6444a81` after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 77–78). Page 16 prints continuous-time parameters and, when appropriate, standardised matrices with the suffix `std`. The printed example on p. 16 is `discreteDRIFTstd`, not `T0TDPREDEFFECTstd`. Footnote 4 standardises using only the relevant variance, not the total. Table 3 names `T0TDPREDEFFECT` the effect of time-dependent predictors on latents at `T0`. Table 2 names `TDPREDEFFECT` `M` for the process dynamics and names `TDPREDVAR` the time-dependent predictor variance. The affecting variance is `TDPREDVAR` `v`. The affected variance is free first-occasion `T0VAR` `p_0`, not within-subject `asymDIFFUSION` `p = −q / (2 a)`, because Table 3 is the first occasion, not the process dynamics. The 2017-era `summary.ctsemFit.R` forms `T0TIPREDEFFECTstd` when `verbose = TRUE` as `T0TIPREDEFFECT * (sqrt(TIPREDVAR) / sqrt(T0VAR))`. That file does not form `T0TDPREDEFFECT` or `T0TDPREDEFFECTstd`. The `n.TDpred` section forms unstandardised `TDPREDEFFECT` only and comments out `TDPREDVAR` and `TDPREDVARstd`. The scalar analog of that `T0TIPREDEFFECTstd` formation using Table 3 `T0TDPREDEFFECT` and Table 2 `TDPREDVAR` is `t0_m · √v / √p_0`. Form strictly positive `p_0` first, then strictly positive `v`, then the first-occasion coefficient, then the SD ratio. Form the SD ratio before multiplying by the coefficient. A zero coefficient with positive `v` and `p_0` is exactly zero even when `√v / √p_0` overflows (`0 · Inf` is NaN). When that ratio overflows, form `(t0_m / √p_0) √v`. Unstandardised `t0_m` is defined for a zero coefficient and for zero predictor variance; standardised `T0TDPREDEFFECT` is not. Zero `v` has no positive predictor SD and fails closed. Zero `p_0` has no positive first-occasion SD and fails closed. `T0` is an event-time occasion, so a non-event clock fails closed. Free `T0VAR` does not require stable `a < 0`; this map has no log-rate argument. A larger positive `p_0` yields a smaller `|std|`. The continuous standardisation `m · √v / √p` uses `asymDIFFUSION` and is not this first-occasion map. Table 3 `T0TIPREDEFFECTstd` `t0_b · √v / √p_0` is a different named matrix even when `t0_m = t0_b`. `t0_m · √v / √(trait + p_0 + added)` uses the total, not free `T0VAR`, and is not `T0TDPREDEFFECTstd` when `TRAITVAR` is nonzero. `TRAITVAR` is not the standardisation variance. Independent of open `#302` `T0TIPREDEFFECTstd`, `#300` `TIPREDEFFECTstd`, `#299` `asymTIPREDEFFECTstd`, `#298` `DRIFTstd`, `#280` `discreteDRIFTstd`, `#296` `discreteDIFFUSIONstd`, `#297` `DIFFUSIONstd`, and `#272` `TIPREDVARstd`. Meredith (1993) remains unread (Unpaywall 2026-08-30T00:17Z: `is_oa: false`; Springer `content/pdf` is a 3038-byte HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; Unpaywall this cycle `is_oa: false`; Springer `content/pdf` is a 3038-byte HTML stub). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
+
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `MANIFESTTRAITVAR`; §7.1, p. 19; p. 16 `MANIFESTTRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-27T14:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest-trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 83–84). Table 2 names `MANIFESTTRAITVAR` `Ψ_τ` the additional time-invariant variance-covariance on the measurement level and sets it `NULL` when there is no manifest trait. Equation 5 writes `Γ ~ N(τ, Ψ)` and names that covariance the manifest traits. Section 7.1 names manifest traits stable individual differences in indicator levels, distinct from process-level `TRAITVAR` `φ_ξ`. Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `MANIFESTTRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named indicator-level correlation is `MANIFESTTRAITVAR`, not process-level `TRAITVAR` and not residual `MANIFESTVAR` `θ`. The 2017-era source forms `MANIFESTTRAITVARstd` only when `MANIFESTTRAITVAR != 0`, as `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(c(ridging), n.manifest)`. The default `ridging = FALSE` adds 0, not `0.0001`; that ridge is a numerical hack and is not this exact map. The scalar correlation is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR`. Form strictly positive `ψ` first, then `1 / √ψ`, then `(1 / √ψ) ψ (1 / √ψ)`. Unstandardised `MANIFESTTRAITVAR` is defined for a zero trait; standardised `MANIFESTTRAITVAR` is not. Zero `MANIFESTTRAITVAR` skips forming `MANIFESTTRAITVARstd` in the 2017-era source and fails closed here. Indicator-level trait variance is an event-time structural quantity, so a non-event clock fails closed. `MANIFESTTRAITVAR` does not require stable `a < 0`. Distinct positive `ψ` recover the same 1. `trait / trait = 1` is `TRAITVARstd` and recovers the same number and remains a distinct named quantity. `θ` is `MANIFESTVAR` and is measurement error, not this correlation. Meredith (1993) remains unread (web search 2026-08-27T14:20Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `TRAITVAR`; §7.1, pp. 18–19; p. 16 `TRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-26T17:45Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 81–82). Table 2 names `TRAITVAR` `φ_ξ` the latent trait variance/covariance and sets it `NULL` when there is no trait. Section 7.1 names traits the stable between-subject differences (unit-level unobserved heterogeneity). Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `TRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named between-subject correlation is `TRAITVAR`, not free first-occasion `T0VAR` and not process-dynamics `asymDIFFUSION`. The 2017-era source forms `TRAITVARstd` only when `TRAITVAR != 0`, as `solve(sqrt(diag(TRAITVAR))) %&% TRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `T0VARstd`, that formation uses `diag(diag(TRAITVAR))` and does not add `diag(c(ridging))`. The ridge is a `T0VAR` numerical hack and is not this exact map. The scalar correlation is `trait / trait = 1` after strictly positive `TRAITVAR`. Form strictly positive `trait` first, then `1 / √trait`, then `(1 / √trait) trait (1 / √trait)`. Unstandardised `TRAITVAR` is defined for a zero trait; standardised `TRAITVAR` is not. Zero `TRAITVAR` skips forming `TRAITVARstd` in the 2017-era source and fails closed here. Between-subject variance is an event-time structural quantity, so a non-event clock fails closed. `TRAITVAR` does not require stable `a < 0`. Distinct positive `trait` recover the same 1. `p_0 / p_0 = 1` is `T0VARstd` and recovers the same number and remains a distinct named quantity. `t0_b² v` is `addedT0TIPREDVAR` and is extra first-occasion TI variance, not this correlation. Meredith (1993) remains unread (Unpaywall 2026-08-26T17:20Z: `is_oa: false`; OpenAlex closed; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`; Unpaywall `is_oa: false`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/psychometric_core/src/error.rs

@@ -710,6 +710,36 @@ pub enum PsychometricError {
     /// `MANIFESTVARstd`. `λ² Var(η) + θ` is `Var(y)`, not the
     /// correlation form of `Θ`.
     ObservedVarianceIsNotStandardisedManifestVariance,
+    /// Driver Table 3 / p. 16 `T0TDPREDEFFECTstd` was requested with
+    /// a non-positive free first-occasion variance. Footnote 4
+    /// standardises the affected first-occasion latent using only
+    /// strictly positive free `T0VAR`.
+    StandardisedInitialTimeDependentEffectRequiresPositiveInitialLatentVariance,
+    /// Driver Table 3 / p. 16 `T0TDPREDEFFECTstd` was requested with
+    /// a non-positive time-dependent predictor variance. Footnote 4
+    /// standardises the affecting predictor using only strictly
+    /// positive `TDPREDVAR`.
+    StandardisedInitialTimeDependentEffectRequiresPositivePredictorVariance,
+    /// Driver Table 3 unstandardised `T0TDPREDEFFECT` `t0_m` was
+    /// treated as p. 16 `T0TDPREDEFFECTstd`. Unstandardised `t0_m`
+    /// is defined for a zero coefficient or zero predictor variance;
+    /// standardised `T0TDPREDEFFECT` is not.
+    UnstandardisedInitialTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect,
+    /// Driver p. 16 `TDPREDEFFECTstd`
+    /// `m · √v / √(-q / (2 a))` was treated as Table 3 / p. 16
+    /// `T0TDPREDEFFECTstd`. The continuous map uses `asymDIFFUSION`;
+    /// the first-occasion map uses free `T0VAR`.
+    StandardisedContinuousTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect,
+    /// Driver Table 3 / p. 16 `T0TIPREDEFFECTstd`
+    /// `t0_b · √v / √p_0` was treated as Table 3 / p. 16
+    /// `T0TDPREDEFFECTstd`. Equal numbers when `t0_m = t0_b` remain
+    /// distinct named quantities.
+    StandardisedInitialTimeIndependentEffectIsNotStandardisedInitialTimeDependentEffect,
+    /// Driver §7.1 trait-contaminated first-occasion TD effect
+    /// `t0_m · √v / √(trait + p_0 + added)` was treated as Table 3 /
+    /// p. 16 `T0TDPREDEFFECTstd`. Footnote 4 uses only free `T0VAR`,
+    /// not `TRAITVAR`.
+    TraitContaminatedInitialTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect,
 }
 
 impl fmt::Display for PsychometricError {
@@ -1235,6 +1265,24 @@ impl fmt::Display for PsychometricError {
             Self::ObservedVarianceIsNotStandardisedManifestVariance => {
                 "observed-indicator variance is not standardised measurement-error variance"
             }
+            Self::StandardisedInitialTimeDependentEffectRequiresPositiveInitialLatentVariance => {
+                "standardised initial time-dependent predictor effect requires strictly positive initial latent variance"
+            }
+            Self::StandardisedInitialTimeDependentEffectRequiresPositivePredictorVariance => {
+                "standardised initial time-dependent predictor effect requires strictly positive predictor variance"
+            }
+            Self::UnstandardisedInitialTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect => {
+                "unstandardised initial time-dependent predictor effect is not standardised initial time-dependent predictor effect"
+            }
+            Self::StandardisedContinuousTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect => {
+                "standardised continuous time-dependent predictor effect is not standardised initial time-dependent predictor effect"
+            }
+            Self::StandardisedInitialTimeIndependentEffectIsNotStandardisedInitialTimeDependentEffect => {
+                "standardised initial time-independent predictor effect is not standardised initial time-dependent predictor effect"
+            }
+            Self::TraitContaminatedInitialTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect => {
+                "trait-contaminated initial time-dependent predictor effect is not standardised initial time-dependent predictor effect"
+            }
         };
         formatter.write_str(message)
     }
@@ -2073,4 +2121,38 @@ mod tests {
             "measurement error is not standardised manifest-trait variance"
         );
     }
+
+    #[test]
+    fn standardised_initial_time_dependent_effect_boundary_messages_are_stable() {
+        assert_eq!(
+            PsychometricError::StandardisedInitialTimeDependentEffectRequiresPositiveInitialLatentVariance
+                .to_string(),
+            "standardised initial time-dependent predictor effect requires strictly positive initial latent variance"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedInitialTimeDependentEffectRequiresPositivePredictorVariance
+                .to_string(),
+            "standardised initial time-dependent predictor effect requires strictly positive predictor variance"
+        );
+        assert_eq!(
+            PsychometricError::UnstandardisedInitialTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect
+                .to_string(),
+            "unstandardised initial time-dependent predictor effect is not standardised initial time-dependent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedContinuousTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect
+                .to_string(),
+            "standardised continuous time-dependent predictor effect is not standardised initial time-dependent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::StandardisedInitialTimeIndependentEffectIsNotStandardisedInitialTimeDependentEffect
+                .to_string(),
+            "standardised initial time-independent predictor effect is not standardised initial time-dependent predictor effect"
+        );
+        assert_eq!(
+            PsychometricError::TraitContaminatedInitialTimeDependentEffectIsNotStandardisedInitialTimeDependentEffect
+                .to_string(),
+            "trait-contaminated initial time-dependent predictor effect is not standardised initial time-dependent predictor effect"
+        );
+    }
 }