feat(membership): recover nested ICC and refuse cross-classified collapse

ARCHITECTURE.md

@@ -55,7 +55,7 @@ boundaries above remain the target modular MSA architecture.
 | `temporal_core` | typed clocks, intervals, and temporal reasoning |
 | `event_core` | event instances, mentions, roles, and provenance |
 | `relation_graph` | typed relations and forward-transition validation |
-| `membership_core` | time-varying cross-classified multiple membership |
+| `membership_core` | time-varying cross-classified multiple membership, Kish ESS, nested ICC with non-nested refusal |
 | `persistence_postgres` | PostgreSQL repositories and migrations |
 | `corpus_split` | cutoff-safe, relation-aware partitioning |
 | `tepp_simulation` | known-truth temporal/event data generation |

CHANGELOG.md

@@ -6,6 +6,7 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ### Added
 
+- `membership_core` nested ICC: CPU `f64` unbalanced ANOVA recovers a known cluster ICC and refuses to treat cross-classified or multiple-membership designs as a single hierarchy (ADR 0003).
 - `persistence_postgres` typed `text_segment` SQL: insert/lookup of exact UTF-8 half-open byte spans on the existing `0006` table, cutoff-eligible document reads (`available_time <= knowledge_cutoff`), and live recovery of a known `hello` span. No new migration number (`#45` still owns `0007`).
 - Hourly contextual-orchestrator discovery records all provider models but routes OpenCode only through general-chat candidates, excluding embedding, image, reranker, transcription, moderation, safety, and other endpoint-only identifiers before price selection.
 - Live `docs/product-technical-gap-baseline.md` mapping operator-visible gaps to

crates/membership_core/src/error.rs

@@ -19,6 +19,16 @@ pub enum MembershipError {
     UnknownMembershipRole,
     /// A duplicate assignment key was rejected by the membership network.
     DuplicateMembershipAssignment,
+    /// Nested ICC is undefined for cross-classified or multiple-membership designs.
+    NestedIccInapplicable,
+    /// Clusters or within-group residual degrees of freedom are insufficient.
+    InsufficientClusterStructure,
+    /// An outcome value was non-finite.
+    InvalidOutcome,
+    /// The same member contributed more than one nested ICC outcome.
+    DuplicateOutcomeMember,
+    /// An outcome member has no active nested membership at the requested time.
+    UnknownOutcomeMember,
 }
 
 impl fmt::Display for MembershipError {
@@ -30,6 +40,11 @@ impl fmt::Display for MembershipError {
             Self::UnsupportedWireVersion => "unsupported membership wire version",
             Self::UnknownMembershipRole => "unknown membership role",
             Self::DuplicateMembershipAssignment => "duplicate membership assignment",
+            Self::NestedIccInapplicable => "nested ICC is inapplicable to this membership design",
+            Self::InsufficientClusterStructure => "insufficient cluster structure for nested ICC",
+            Self::InvalidOutcome => "invalid nested ICC outcome",
+            Self::DuplicateOutcomeMember => "duplicate nested ICC outcome member",
+            Self::UnknownOutcomeMember => "unknown nested ICC outcome member",
         };
         formatter.write_str(message)
     }
@@ -68,6 +83,26 @@ mod tests {
                 MembershipError::DuplicateMembershipAssignment,
                 "duplicate membership assignment",
             ),
+            (
+                MembershipError::NestedIccInapplicable,
+                "nested ICC is inapplicable to this membership design",
+            ),
+            (
+                MembershipError::InsufficientClusterStructure,
+                "insufficient cluster structure for nested ICC",
+            ),
+            (
+                MembershipError::InvalidOutcome,
+                "invalid nested ICC outcome",
+            ),
+            (
+                MembershipError::DuplicateOutcomeMember,
+                "duplicate nested ICC outcome member",
+            ),
+            (
+                MembershipError::UnknownOutcomeMember,
+                "unknown nested ICC outcome member",
+            ),
         ] {
             assert_eq!(error.to_string(), message);
         }

crates/membership_core/src/icc.rs

@@ -0,0 +1,246 @@
+//! Nested ICC with fail-closed cross-classified and multiple-membership gates.
+
+use crate::{MemberId, MembershipError, MembershipNetwork, MembershipRole};
+use std::collections::{BTreeMap, BTreeSet};
+use temporal_core::EventTime;
+
+/// Membership design implied by active assignments at one event time.
+#[derive(Clone, Copy, Debug, Eq, PartialEq)]
+#[non_exhaustive]
+pub enum MembershipDesign {
+    /// Each active member belongs to exactly one group in one role.
+    Nested,
+    /// At least one member is active in two or more roles.
+    CrossClassified,
+    /// At least one member is active in two or more groups of the same role.
+    MultipleMembership,
+}
+
+impl MembershipDesign {
+    /// Return whether a one-way nested ICC is identified for this design.
+    #[must_use]
+    pub const fn allows_nested_icc(self) -> bool {
+        match self {
+            Self::Nested => true,
+            Self::CrossClassified | Self::MultipleMembership => false,
+        }
+    }
+}
+
+/// One finite outcome attached to an opaque member for nested ICC recovery.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct NestedOutcome {
+    member_id: MemberId,
+    value: f64,
+}
+
+impl NestedOutcome {
+    /// Construct a finite nested ICC outcome.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`MembershipError::InvalidOutcome`] when `value` is not finite.
+    pub fn new(member_id: MemberId, value: f64) -> Result<Self, MembershipError> {
+        if value.is_finite() {
+            Ok(Self { member_id, value })
+        } else {
+            Err(MembershipError::InvalidOutcome)
+        }
+    }
+
+    /// Return the outcome member.
+    #[must_use]
+    pub const fn member_id(self) -> MemberId {
+        self.member_id
+    }
+
+    /// Return the finite outcome value.
+    #[must_use]
+    pub const fn value(self) -> f64 {
+        self.value
+    }
+}
+
+/// Classify active memberships at `instant` without collapsing structure.
+///
+/// Multiple membership is reported before cross-classification so a member
+/// who occupies two groups in one role is not misread as a nested hierarchy.
+///
+/// # Errors
+///
+/// Returns [`MembershipError::InsufficientClusterStructure`] when no assignment
+/// is active at `instant`.
+pub fn classify_membership_design(
+    network: &MembershipNetwork,
+    instant: EventTime,
+) -> Result<MembershipDesign, MembershipError> {
+    let mut members = BTreeSet::new();
+    for assignment in network.assignments() {
+        members.insert(assignment.member_id());
+    }
+    classify_members(network, instant, members.iter().copied())
+}
+
+/// Recover the one-way random-intercept ICC for a nested membership design.
+///
+/// The CPU `f64` estimator is the unbalanced ANOVA (Snijders & Bosker)
+/// estimator
+/// `σ²_u / (σ²_u + σ²_e)` with
+/// `σ²_e = MSW` and `σ²_u = max(0, (MSB − MSW) / n₀)`.
+/// Cross-classified and multiple-membership designs fail closed: a nested
+/// ICC is not a substitute for an MMMC model.
+///
+/// # Errors
+///
+/// Returns a membership error when outcomes are empty, duplicated, unknown,
+/// inactive, non-nested, or when cluster residual structure is insufficient.
+pub fn nested_intraclass_correlation(
+    network: &MembershipNetwork,
+    instant: EventTime,
+    outcomes: &[NestedOutcome],
+) -> Result<f64, MembershipError> {
+    if outcomes.is_empty() {
+        return Err(MembershipError::InsufficientClusterStructure);
+    }
+    let mut seen = BTreeSet::new();
+    let mut groups: BTreeMap<crate::GroupId, Vec<f64>> = BTreeMap::new();
+    let mut outcome_members = BTreeSet::new();
+    for outcome in outcomes {
+        if !seen.insert(outcome.member_id()) {
+            return Err(MembershipError::DuplicateOutcomeMember);
+        }
+        let active = network.active_memberships_for(outcome.member_id(), instant);
+        if active.is_empty() {
+            return Err(MembershipError::UnknownOutcomeMember);
+        }
+        outcome_members.insert(outcome.member_id());
+        let group = active[0].group_id();
+        groups.entry(group).or_default().push(outcome.value());
+    }
+    match classify_members(network, instant, outcome_members.iter().copied())? {
+        MembershipDesign::Nested => {}
+        MembershipDesign::CrossClassified | MembershipDesign::MultipleMembership => {
+            return Err(MembershipError::NestedIccInapplicable);
+        }
+    }
+    anova_nested_icc(&groups)
+}
+
+fn classify_members<I>(
+    network: &MembershipNetwork,
+    instant: EventTime,
+    members: I,
+) -> Result<MembershipDesign, MembershipError>
+where
+    I: IntoIterator<Item = MemberId>,
+{
+    let mut saw_active = false;
+    let mut saw_cross = false;
+    for member_id in members {
+        let active = network.active_memberships_for(member_id, instant);
+        if active.is_empty() {
+            continue;
+        }
+        saw_active = true;
+        let mut groups_by_role: BTreeMap<MembershipRole, BTreeSet<crate::GroupId>> =
+            BTreeMap::new();
+        for assignment in active {
+            groups_by_role
+                .entry(assignment.role())
+                .or_default()
+                .insert(assignment.group_id());
+        }
+        for groups in groups_by_role.values() {
+            if groups.len() >= 2 {
+                return Ok(MembershipDesign::MultipleMembership);
+            }
+        }
+        if groups_by_role.len() >= 2 {
+            saw_cross = true;
+        }
+    }
+    if !saw_active {
+        return Err(MembershipError::InsufficientClusterStructure);
+    }
+    if saw_cross {
+        Ok(MembershipDesign::CrossClassified)
+    } else {
+        Ok(MembershipDesign::Nested)
+    }
+}
+
+fn anova_nested_icc(groups: &BTreeMap<crate::GroupId, Vec<f64>>) -> Result<f64, MembershipError> {
+    let cluster_count = groups.len();
+    if cluster_count < 2 {
+        return Err(MembershipError::InsufficientClusterStructure);
+    }
+    let mut sample_size = 0_usize;
+    let mut total = 0.0;
+    for values in groups.values() {
+        sample_size += values.len();
+        for &value in values {
+            total += value;
+        }
+    }
+    if sample_size <= cluster_count {
+        return Err(MembershipError::InsufficientClusterStructure);
+    }
+    let n = sample_size as f64;
+    let j = cluster_count as f64;
+    let grand_mean = total / n;
+    let mut sum_of_squares_between = 0.0;
+    let mut sum_of_squares_within = 0.0;
+    let mut sum_cluster_size_squared = 0.0;
+    for values in groups.values() {
+        let cluster_size = values.len() as f64;
+        sum_cluster_size_squared += cluster_size * cluster_size;
+        let mut cluster_total = 0.0;
+        for &value in values {
+            cluster_total += value;
+        }
+        let cluster_mean = cluster_total / cluster_size;
+        let between = cluster_mean - grand_mean;
+        sum_of_squares_between += cluster_size * between * between;
+        for &value in values {
+            let within = value - cluster_mean;
+            sum_of_squares_within += within * within;
+        }
+    }
+    if sum_of_squares_between + sum_of_squares_within == 0.0 {
+        return Err(MembershipError::InsufficientClusterStructure);
+    }
+    let mean_square_between = sum_of_squares_between / (j - 1.0);
+    let mean_square_within = sum_of_squares_within / (n - j);
+    let harmonic_cluster_size = (n - sum_cluster_size_squared / n) / (j - 1.0);
+    let cluster_variance =
+        ((mean_square_between - mean_square_within) / harmonic_cluster_size).max(0.0);
+    Ok(cluster_variance / (cluster_variance + mean_square_within))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::{MembershipDesign, NestedOutcome, anova_nested_icc};
+    use crate::{GroupId, MemberId, MembershipError};
+    use std::collections::BTreeMap;
+
+    #[test]
+    fn design_gate_and_outcome_accessors_cover_local_branches() {
+        assert!(MembershipDesign::Nested.allows_nested_icc());
+        assert!(!MembershipDesign::CrossClassified.allows_nested_icc());
+        assert!(!MembershipDesign::MultipleMembership.allows_nested_icc());
+        let member = MemberId::new();
+        let outcome = NestedOutcome::new(member, 1.5).expect("finite");
+        assert_eq!(outcome.member_id(), member);
+        assert!((outcome.value() - 1.5).abs() < 1e-12);
+        assert_eq!(
+            NestedOutcome::new(member, f64::NEG_INFINITY),
+            Err(MembershipError::InvalidOutcome)
+        );
+        let mut one = BTreeMap::new();
+        one.insert(GroupId::new(), vec![1.0, 2.0]);
+        assert_eq!(
+            anova_nested_icc(&one),
+            Err(MembershipError::InsufficientClusterStructure)
+        );
+    }
+}

crates/membership_core/src/lib.rs

@@ -13,6 +13,7 @@
 mod assignment;
 mod error;
 mod ess;
+mod icc;
 mod identifier;
 mod network;
 mod role;
@@ -39,3 +40,11 @@ pub use ess::design_effect;
 pub use ess::group_normalized_kish_ess;
 /// Kish effective sample size for membership weights.
 pub use ess::kish_effective_sample_size;
+/// Membership design implied by active assignments.
+pub use icc::MembershipDesign;
+/// Finite outcome used by the nested ICC estimator.
+pub use icc::NestedOutcome;
+/// Classify nested versus cross-classified versus multiple-membership designs.
+pub use icc::classify_membership_design;
+/// CPU `f64` nested ICC that refuses non-nested membership designs.
+pub use icc::nested_intraclass_correlation;