feat(analysis): bind nested ICC of posterior coordinates to an analysis-run profile

CHANGELOG.md

@@ -38,6 +38,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- **Membership-posterior ICC analysis-run profile**: cutoff-safe `membership_posterior_icc_v1` binds `posterior_draw_point_estimate_mean`, nested ANOVA ICC, and Kish ESS, and refuses nested ICC for multiple-membership and cross-classified designs (`analysis_engine`). Not MMMC and not implemented-main.
 - `event_core` adds bounded Allen interval-consistency classification, atomic path-consistency closure, contradiction/resource refusals, and an explicit dependency-error fallback without claiming unrestricted global satisfiability.
 
 - `psychometric_core` recovers the Driver, Oud, and Voelkle (2017, Table 2, p. 12 `MANIFESTTRAITVAR`; §7.1, p. 19; p. 16 `MANIFESTTRAITVARstd`; footnote 4; 2017-era ctsem `summary.ctsemFit.R`; JSS PDF re-opened 2026-08-27T14:20Z from https://www.jstatsoft.org/index.php/jss/article/download/v077i05/1104) scalar standardised manifest-trait variance on current main after `0ce16e8` dropped the pre-consolidation code while research notes already named the map (register items 83–84). Table 2 names `MANIFESTTRAITVAR` `Ψ_τ` the additional time-invariant variance-covariance on the measurement level and sets it `NULL` when there is no manifest trait. Equation 5 writes `Γ ~ N(τ, Ψ)` and names that covariance the manifest traits. Section 7.1 names manifest traits stable individual differences in indicator levels, distinct from process-level `TRAITVAR` `φ_ξ`. Page 16 prints standardised matrices with the suffix `std` when appropriate. The printed example on p. 16 is `discreteDRIFTstd`, not `MANIFESTTRAITVARstd`. Footnote 4 standardises using only the relevant variance, not the total. The relevant variance for that named indicator-level correlation is `MANIFESTTRAITVAR`, not process-level `TRAITVAR` and not residual `MANIFESTVAR` `θ`. The 2017-era source forms `MANIFESTTRAITVARstd` only when `MANIFESTTRAITVAR != 0`, as `solve(sqrt(diag(MANIFESTTRAITVAR) + ridging)) %&% MANIFESTTRAITVAR` when `verbose = TRUE`. OpenMx `%&%` is `t(A) %*% B %*% A`. Unlike `TRAITVARstd`, that formation adds `diag(c(ridging), n.manifest)`. The default `ridging = FALSE` adds 0, not `0.0001`; that ridge is a numerical hack and is not this exact map. The scalar correlation is `ψ / ψ = 1` after strictly positive `MANIFESTTRAITVAR`. Form strictly positive `ψ` first, then `1 / √ψ`, then `(1 / √ψ) ψ (1 / √ψ)`. Unstandardised `MANIFESTTRAITVAR` is defined for a zero trait; standardised `MANIFESTTRAITVAR` is not. Zero `MANIFESTTRAITVAR` skips forming `MANIFESTTRAITVARstd` in the 2017-era source and fails closed here. Indicator-level trait variance is an event-time structural quantity, so a non-event clock fails closed. `MANIFESTTRAITVAR` does not require stable `a < 0`. Distinct positive `ψ` recover the same 1. `trait / trait = 1` is `TRAITVARstd` and recovers the same number and remains a distinct named quantity. `θ` is `MANIFESTVAR` and is measurement error, not this correlation. Meredith (1993) remains unread (web search 2026-08-27T14:20Z: Springer/Cambridge Core paywalled; Unpaywall historically `is_oa: false`; Springer `content/pdf` is an HTML stub). Mislevy (1991, *Psychometrika, 56*, 177–196) remains unread on the same terms (DOI `10.1007/bf02294457`). Still not a Kalman filter, not a matrix `expm`, not ESEM estimation, not DSEM, and not ctsem estimation.

crates/analysis_engine/Cargo.toml

@@ -15,6 +15,8 @@ publish = false
 
 [dependencies]
 event_core = { path = "../event_core", version = "0.2.0" }
+membership_core = { path = "../membership_core", version = "0.2.0" }
+psychometric_core = { path = "../psychometric_core", version = "0.2.0" }
 serde = { workspace = true }
 serde_json = { workspace = true }
 sha2 = { workspace = true }
@@ -25,7 +27,6 @@ uuid.workspace = true
 
 [dev-dependencies]
 corpus_split = { path = "../corpus_split", version = "0.2.0" }
-membership_core = { path = "../membership_core", version = "0.2.0" }
 relation_graph = { path = "../relation_graph", version = "0.2.0" }
 
 [lints]

crates/analysis_engine/src/lib.rs

@@ -8,13 +8,18 @@
 //! through [`tepp_api`]. It deliberately does not claim latent-variable or topic
 //! estimation authority; those estimators remain separate scientific crates.
 //! estimation authority; it invokes estimators through their scientific crate
-//! contracts and preserves their artifact meaning.
+//! contracts and preserves their artifact meaning. Membership-posterior ICC
+//! composition is invoked through [`membership_core`] and [`psychometric_core`]
+//! and is not an MMMC sampler.
 
 mod case_deletion_refit;
 mod lineage_criterion;
+mod membership_posterior_icc_artifact;
 mod topic_context_posterior;
 mod topic_lineage_artifact;
 
+use membership_core::MembershipError;
+use psychometric_core::PsychometricError;
 use serde::Serialize;
 use sha2::{Digest, Sha256};
 use std::collections::BTreeSet;
@@ -46,6 +51,13 @@ pub use lineage_criterion::{
     LineageCriterionFit, LineageCriterionFitError, LineageCriterionObservation,
     fit_lineage_criterion_posteriors,
 };
+/// Membership-posterior ICC artifact and execution contracts.
+pub use membership_posterior_icc_artifact::{
+    MEMBERSHIP_POSTERIOR_ICC_ARTIFACT_BYTE_LIMIT, MEMBERSHIP_POSTERIOR_ICC_ARTIFACT_SCHEMA_VERSION,
+    MEMBERSHIP_POSTERIOR_ICC_MODEL_CONTRACT_VERSION, MEMBERSHIP_POSTERIOR_ICC_OUTPUT_PROFILE,
+    MembershipPosteriorIccArtifact, MembershipPosteriorIccExecution,
+    MembershipPosteriorObservation, execute_membership_posterior_icc_run,
+};
 /// Bounded posterior topic-context producer contract and record types.
 pub use topic_context_posterior::{
     TOPIC_CONTEXT_POSTERIOR_BYTE_LIMIT, TOPIC_CONTEXT_POSTERIOR_SCHEMA_VERSION,
@@ -248,6 +260,12 @@ pub enum AnalysisEngineError {
     TopicMeasurement(TopicMeasurementError),
     /// A topic-lineage artifact violated its bounded schema or count invariants.
     InvalidTopicLineageArtifact,
+    /// A psychometric recovery rejected the offered coordinates.
+    Psychometric(PsychometricError),
+    /// A membership-network estimator rejected the offered design or weights.
+    Membership(MembershipError),
+    /// A membership-posterior ICC artifact violated its bounded schema or counts.
+    InvalidMembershipPosteriorIccArtifact,
 }
 
 impl fmt::Display for AnalysisEngineError {
@@ -262,6 +280,11 @@ impl fmt::Display for AnalysisEngineError {
             Self::LimitExceeded => "analysis corpus exceeded its execution bound",
             Self::TopicMeasurement(error) => return error.fmt(formatter),
             Self::InvalidTopicLineageArtifact => "invalid topic lineage artifact",
+            Self::Psychometric(error) => return error.fmt(formatter),
+            Self::Membership(error) => return error.fmt(formatter),
+            Self::InvalidMembershipPosteriorIccArtifact => {
+                "invalid membership-posterior ICC artifact"
+            }
         };
         formatter.write_str(message)
     }
@@ -281,6 +304,18 @@ impl From<TopicMeasurementError> for AnalysisEngineError {
     }
 }
 
+impl From<PsychometricError> for AnalysisEngineError {
+    fn from(error: PsychometricError) -> Self {
+        Self::Psychometric(error)
+    }
+}
+
+impl From<MembershipError> for AnalysisEngineError {
+    fn from(error: MembershipError) -> Self {
+        Self::Membership(error)
+    }
+}
+
 /// Execute the cutoff-safe temporal evidence readiness analysis.
 ///
 /// Evidence whose `available_time` is later than the request cutoff is excluded
@@ -681,6 +716,10 @@ mod tests {
                 AnalysisEngineError::InvalidTopicLineageArtifact,
                 "invalid topic lineage artifact",
             ),
+            (
+                AnalysisEngineError::InvalidMembershipPosteriorIccArtifact,
+                "invalid membership-posterior ICC artifact",
+            ),
         ];
         for (error, message) in messages {
             assert_eq!(error.to_string(), message);