diff --git a/CHANGELOG.md b/CHANGELOG.md
index 062a69412..ad42b796b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -38,6 +38,8 @@ All notable changes to TEPP are documented here. The format follows Keep a Chang
 
 ## [Unreleased]
 
+- **Pareto candidate-`K` analysis-run profile**: cutoff-safe `pareto_candidate_k_v1` binds `select_candidate_k` and selected-`K` RMSE and refuses LLM-vote authority (`analysis_engine`). Not Schwarz fitted selection, not a Bayesian sampler, 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.
diff --git a/Cargo.lock b/Cargo.lock
index 454a7d612..0949729f1 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -74,6 +74,7 @@ dependencies = [
  "corpus_split",
  "event_core",
  "membership_core",
+ "model_selection",
  "relation_graph",
  "serde",
  "serde_json",
diff --git a/crates/analysis_engine/Cargo.toml b/crates/analysis_engine/Cargo.toml
index 7322212b2..c45e2eed7 100644
--- a/crates/analysis_engine/Cargo.toml
+++ b/crates/analysis_engine/Cargo.toml
@@ -15,6 +15,7 @@ publish = false
 
 [dependencies]
 event_core = { path = "../event_core", version = "0.2.0" }
+model_selection = { path = "../model_selection", version = "0.2.0" }
 serde = { workspace = true }
 serde_json = { workspace = true }
 sha2 = { workspace = true }
diff --git a/crates/analysis_engine/src/lib.rs b/crates/analysis_engine/src/lib.rs
index 72bd5854c..1629fff02 100644
--- a/crates/analysis_engine/src/lib.rs
+++ b/crates/analysis_engine/src/lib.rs
@@ -8,13 +8,17 @@
 //! 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. Pareto candidate-`K`
+//! selection is invoked through [`model_selection`] and is not a Bayesian
+//! sampler.
 
 mod case_deletion_refit;
 mod lineage_criterion;
+mod pareto_candidate_k_artifact;
 mod topic_context_posterior;
 mod topic_lineage_artifact;
 
+use model_selection::ModelSelectionError;
 use serde::Serialize;
 use sha2::{Digest, Sha256};
 use std::collections::BTreeSet;
@@ -46,6 +50,13 @@ pub use lineage_criterion::{
     LineageCriterionFit, LineageCriterionFitError, LineageCriterionObservation,
     fit_lineage_criterion_posteriors,
 };
+/// Pareto candidate-`K` artifact and execution contracts from this engine.
+pub use pareto_candidate_k_artifact::{
+    PARETO_CANDIDATE_K_ARTIFACT_BYTE_LIMIT, PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION,
+    PARETO_CANDIDATE_K_MODEL_CONTRACT_VERSION, PARETO_CANDIDATE_K_OUTPUT_PROFILE,
+    ParetoCandidateKArtifact, ParetoCandidateKExecution, ParetoCandidateKInput,
+    execute_pareto_candidate_k_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 +259,10 @@ pub enum AnalysisEngineError {
     TopicMeasurement(TopicMeasurementError),
     /// A topic-lineage artifact violated its bounded schema or count invariants.
     InvalidTopicLineageArtifact,
+    /// A model-selection gate rejected the offered candidates or method.
+    ModelSelection(ModelSelectionError),
+    /// A Pareto candidate-`K` artifact violated its bounded schema or counts.
+    InvalidParetoCandidateKArtifact,
 }
 
 impl fmt::Display for AnalysisEngineError {
@@ -262,6 +277,8 @@ 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::ModelSelection(error) => return error.fmt(formatter),
+            Self::InvalidParetoCandidateKArtifact => "invalid pareto candidate-k artifact",
         };
         formatter.write_str(message)
     }
@@ -281,6 +298,12 @@ impl From<TopicMeasurementError> for AnalysisEngineError {
     }
 }
 
+impl From<ModelSelectionError> for AnalysisEngineError {
+    fn from(error: ModelSelectionError) -> Self {
+        Self::ModelSelection(error)
+    }
+}
+
 /// Execute the cutoff-safe temporal evidence readiness analysis.
 ///
 /// Evidence whose `available_time` is later than the request cutoff is excluded
@@ -413,7 +436,8 @@ mod tests {
     use super::{
         ANALYSIS_ARTIFACT_SCHEMA_VERSION, ANALYSIS_STATISTIC_COUNT, AnalysisCorpus,
         AnalysisEngineError, AnalysisEvidenceUnit, MAX_ANALYSIS_IDENTIFIER_BYTES,
-        MAX_EVIDENCE_UNITS, TopicMeasurementError, add_membership_count, execute_analysis_run,
+        MAX_EVIDENCE_UNITS, ModelSelectionError, TopicMeasurementError, add_membership_count,
+        execute_analysis_run,
     };
     use temporal_core::{AvailableTime, EventTime};
     use tepp_api::{AnalysisRunAccepted, AnalysisRunRequest, AnalysisRunTerminalState, ApiError};
@@ -681,6 +705,14 @@ mod tests {
                 AnalysisEngineError::InvalidTopicLineageArtifact,
                 "invalid topic lineage artifact",
             ),
+            (
+                AnalysisEngineError::InvalidParetoCandidateKArtifact,
+                "invalid pareto candidate-k artifact",
+            ),
+            (
+                AnalysisEngineError::ModelSelection(ModelSelectionError::EmptyCandidateSet),
+                "empty model-selection candidate set",
+            ),
         ];
         for (error, message) in messages {
             assert_eq!(error.to_string(), message);
@@ -689,6 +721,12 @@ mod tests {
         assert_eq!(converted.to_string(), "invalid API wire payload");
         let from_topic: AnalysisEngineError = TopicMeasurementError::DidNotConverge.into();
         assert_eq!(from_topic.to_string(), "topic estimator did not converge");
+        let from_selection: AnalysisEngineError =
+            ModelSelectionError::LlmVoteIsNotStatisticalAuthority.into();
+        assert_eq!(
+            from_selection.to_string(),
+            "llm vote is not statistical authority"
+        );
         assert_eq!(
             add_membership_count(u64::MAX, 1),
             Err(AnalysisEngineError::ArithmeticOverflow)
diff --git a/crates/analysis_engine/src/pareto_candidate_k_artifact.rs b/crates/analysis_engine/src/pareto_candidate_k_artifact.rs
new file mode 100644
index 000000000..ddd038370
--- /dev/null
+++ b/crates/analysis_engine/src/pareto_candidate_k_artifact.rs
@@ -0,0 +1,372 @@
+//! Digest-bound Pareto candidate-`K` selection as an analysis-run profile.
+
+use model_selection::{ModelCandidate, select_candidate_k, selected_k_root_mean_square_error};
+use serde::{Deserialize, Serialize};
+use sha2::{Digest, Sha256};
+use temporal_core::KnowledgeCutoff;
+use tepp_api::{
+    AnalysisResultSummary, AnalysisRunAccepted, AnalysisRunRequest, AnalysisRunTerminalResult,
+};
+
+use crate::{AnalysisEngineError, format_digest, require_receipt_identity, valid_identifier};
+
+/// Versioned schema for a completed Pareto candidate-`K` artifact.
+pub const PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION: &str = "tepp.pareto_candidate_k.v1";
+/// Model contract required by the Pareto candidate-`K` execution path.
+pub const PARETO_CANDIDATE_K_MODEL_CONTRACT_VERSION: &str = "pareto_candidate_k_v1";
+/// Analysis-run output profile required for a Pareto candidate-`K` artifact.
+pub const PARETO_CANDIDATE_K_OUTPUT_PROFILE: &str = "pareto_candidate_k_v1";
+/// Maximum canonical artifact JSON size.
+pub const PARETO_CANDIDATE_K_ARTIFACT_BYTE_LIMIT: usize = 256 * 1024;
+const PARETO_CANDIDATE_K_INFERENCE_STATUS: &str =
+    "pareto_statistical_front_not_fitted_schwarz_sampler";
+
+/// Cutoff-safe Pareto-front input bound to offered candidates and known truth.
+#[derive(Clone, Debug, PartialEq)]
+pub struct ParetoCandidateKInput {
+    candidates: Vec<ModelCandidate>,
+    selected_replications: Vec<u32>,
+    truth_k: u32,
+}
+
+impl ParetoCandidateKInput {
+    /// Construct a Pareto-front selection payload.
+    #[must_use]
+    pub fn new(
+        candidates: Vec<ModelCandidate>,
+        selected_replications: Vec<u32>,
+        truth_k: u32,
+    ) -> Self {
+        Self {
+            candidates,
+            selected_replications,
+            truth_k,
+        }
+    }
+
+    /// Borrow the offered candidates.
+    #[must_use]
+    pub fn candidates(&self) -> &[ModelCandidate] {
+        &self.candidates
+    }
+
+    /// Borrow selected-`K` replications used for RMSE.
+    #[must_use]
+    pub fn selected_replications(&self) -> &[u32] {
+        &self.selected_replications
+    }
+
+    /// Return the known-truth topic count.
+    #[must_use]
+    pub const fn truth_k(&self) -> u32 {
+        self.truth_k
+    }
+}
+
+/// Completed, bounded Pareto candidate-`K` selection for analysis-run clients.
+#[derive(Clone, Debug, Deserialize, PartialEq, Serialize)]
+#[serde(deny_unknown_fields)]
+pub struct ParetoCandidateKArtifact {
+    /// Exact versioned schema identity.
+    pub schema_version: String,
+    /// Opaque accepted-run identity.
+    pub run_id: String,
+    /// Immutable source snapshot identity.
+    pub snapshot_id: String,
+    /// Historical evidence cutoff used by the selection.
+    pub knowledge_cutoff: String,
+    /// Statistically selected topic count `K`.
+    pub selected_k: u64,
+    /// Number of candidates offered to the Pareto gate.
+    pub candidate_count: u64,
+    /// Number of statistically supported candidates.
+    pub statistical_count: u64,
+    /// Known-truth topic count used for RMSE.
+    pub truth_k: u64,
+    /// RMSE of selected-`K` replications against known truth.
+    pub selected_k_rmse: f64,
+    /// Fixed claim boundary for consumer copy.
+    pub inference_status: String,
+}
+
+impl ParetoCandidateKArtifact {
+    /// Parse and fully validate a bounded artifact JSON payload.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`AnalysisEngineError::InvalidParetoCandidateKArtifact`] when the
+    /// schema, identifiers, counts, RMSE, or claim boundary fail.
+    pub fn from_json(payload: &str) -> Result<Self, AnalysisEngineError> {
+        if payload.len() > PARETO_CANDIDATE_K_ARTIFACT_BYTE_LIMIT {
+            return Err(AnalysisEngineError::LimitExceeded);
+        }
+        let artifact: Self = serde_json::from_str(payload)
+            .map_err(|_| AnalysisEngineError::InvalidParetoCandidateKArtifact)?;
+        artifact.validate()?;
+        Ok(artifact)
+    }
+
+    /// Serialize canonical validated artifact JSON.
+    ///
+    /// # Errors
+    ///
+    /// Returns a typed validation, serialization, or size failure.
+    pub fn to_json(&self) -> Result<String, AnalysisEngineError> {
+        self.validate()?;
+        let payload =
+            serde_json::to_string(self).map_err(|_| AnalysisEngineError::SerializationFailure)?;
+        if payload.len() > PARETO_CANDIDATE_K_ARTIFACT_BYTE_LIMIT {
+            return Err(AnalysisEngineError::LimitExceeded);
+        }
+        Ok(payload)
+    }
+
+    /// Return the lowercase SHA-256 digest of canonical artifact JSON.
+    ///
+    /// # Errors
+    ///
+    /// Returns a typed validation or serialization failure.
+    pub fn sha256(&self) -> Result<String, AnalysisEngineError> {
+        self.to_json()
+            .map(|json| format_digest(Sha256::digest(json.into_bytes())))
+    }
+
+    fn validate(&self) -> Result<(), AnalysisEngineError> {
+        if self.schema_version != PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION
+            || !valid_identifier(&self.run_id)
+            || !valid_identifier(&self.snapshot_id)
+            || KnowledgeCutoff::parse_rfc3339(&self.knowledge_cutoff).is_err()
+            || self.selected_k < 2
+            || self.candidate_count == 0
+            || self.statistical_count == 0
+            || self.statistical_count > self.candidate_count
+            || self.truth_k < 2
+            || !self.selected_k_rmse.is_finite()
+            || self.selected_k_rmse < 0.0
+            || self.inference_status != PARETO_CANDIDATE_K_INFERENCE_STATUS
+        {
+            return Err(AnalysisEngineError::InvalidParetoCandidateKArtifact);
+        }
+        Ok(())
+    }
+}
+
+/// One completed Pareto candidate-`K` artifact and its terminal result.
+#[derive(Clone, Debug, PartialEq)]
+pub struct ParetoCandidateKExecution {
+    /// Digest-bound completed selection artifact.
+    pub artifact: ParetoCandidateKArtifact,
+    /// Terminal result carrying the artifact identity, digest, and schema.
+    pub terminal_result: AnalysisRunTerminalResult,
+}
+
+/// Execute cutoff-safe Pareto candidate-`K` selection as one analysis-run profile.
+///
+/// The executor invokes [`select_candidate_k`] and
+/// [`selected_k_root_mean_square_error`] and does not reimplement Pareto
+/// dominance or RMSE. LLM votes cannot define the numerical optimum. This is
+/// not Schwarz fitted selection, not a Bayesian sampler, and not GPU execution.
+///
+/// # Errors
+///
+/// Returns a request/receipt/snapshot/cutoff/profile error, model-selection
+/// failure, or invalid artifact error.
+pub fn execute_pareto_candidate_k_run(
+    request: &AnalysisRunRequest,
+    accepted: &AnalysisRunAccepted,
+    snapshot_id: &str,
+    knowledge_cutoff: KnowledgeCutoff,
+    input: &ParetoCandidateKInput,
+    completed_at: impl Into<String>,
+) -> Result<ParetoCandidateKExecution, AnalysisEngineError> {
+    request.to_json()?;
+    accepted.to_json()?;
+    require_receipt_identity(request, accepted)?;
+    if request.snapshot_id != snapshot_id {
+        return Err(AnalysisEngineError::SnapshotMismatch);
+    }
+    if request.knowledge_cutoff != knowledge_cutoff.to_rfc3339()
+        || request.model_contract_version != PARETO_CANDIDATE_K_MODEL_CONTRACT_VERSION
+        || request.output_profile != PARETO_CANDIDATE_K_OUTPUT_PROFILE
+    {
+        return Err(AnalysisEngineError::InvalidEvidence);
+    }
+
+    let selected_k = u64::from(select_candidate_k(input.candidates())?);
+    let selected_k_rmse =
+        selected_k_root_mean_square_error(input.selected_replications(), input.truth_k())?;
+    let candidate_count = u64::try_from(input.candidates().len())
+        .map_err(|_| AnalysisEngineError::ArithmeticOverflow)?;
+    let statistical_count = u64::try_from(
+        input
+            .candidates()
+            .iter()
+            .filter(|candidate| candidate.is_statistically_supported())
+            .count(),
+    )
+    .map_err(|_| AnalysisEngineError::ArithmeticOverflow)?;
+    let artifact = ParetoCandidateKArtifact {
+        schema_version: PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION.into(),
+        run_id: accepted.run_id.clone(),
+        snapshot_id: snapshot_id.to_owned(),
+        knowledge_cutoff: knowledge_cutoff.to_rfc3339(),
+        selected_k,
+        candidate_count,
+        statistical_count,
+        truth_k: u64::from(input.truth_k()),
+        selected_k_rmse,
+        inference_status: PARETO_CANDIDATE_K_INFERENCE_STATUS.into(),
+    };
+    let digest = artifact.sha256()?;
+    let summary = AnalysisResultSummary::new(
+        "pareto_candidate_k",
+        candidate_count,
+        2,
+        PARETO_CANDIDATE_K_INFERENCE_STATUS,
+    )?;
+    let terminal_result = AnalysisRunTerminalResult::succeeded(
+        request,
+        accepted,
+        format!("pareto_candidate_k_artifact_{}", &digest[..16]),
+        digest,
+        PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION,
+        completed_at,
+        summary,
+    )?;
+    Ok(ParetoCandidateKExecution {
+        artifact,
+        terminal_result,
+    })
+}
+
+#[cfg(test)]
+mod tests {
+    use super::{
+        PARETO_CANDIDATE_K_ARTIFACT_BYTE_LIMIT, PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION,
+        PARETO_CANDIDATE_K_INFERENCE_STATUS, ParetoCandidateKArtifact, ParetoCandidateKInput,
+    };
+    use crate::AnalysisEngineError;
+    use model_selection::ModelCandidate;
+
+    fn artifact() -> ParetoCandidateKArtifact {
+        ParetoCandidateKArtifact {
+            schema_version: PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION.into(),
+            run_id: "run-1".into(),
+            snapshot_id: "snapshot-1".into(),
+            knowledge_cutoff: "2026-08-01T00:00:00Z".into(),
+            selected_k: 2,
+            candidate_count: 2,
+            statistical_count: 2,
+            truth_k: 2,
+            selected_k_rmse: 0.0,
+            inference_status: PARETO_CANDIDATE_K_INFERENCE_STATUS.into(),
+        }
+    }
+
+    fn assert_invalid(artifact: &ParetoCandidateKArtifact) {
+        assert_eq!(
+            artifact.to_json(),
+            Err(AnalysisEngineError::InvalidParetoCandidateKArtifact)
+        );
+    }
+
+    #[test]
+    fn artifact_round_trip_and_size_bounds_fail_closed() {
+        let artifact = artifact();
+        let payload = artifact.to_json().expect("json");
+        assert_eq!(
+            ParetoCandidateKArtifact::from_json(&payload),
+            Ok(artifact.clone())
+        );
+        assert_eq!(artifact.sha256().expect("digest").len(), 64);
+        assert_eq!(
+            ParetoCandidateKArtifact::from_json("{}"),
+            Err(AnalysisEngineError::InvalidParetoCandidateKArtifact)
+        );
+        assert_eq!(
+            ParetoCandidateKArtifact::from_json(
+                &"x".repeat(PARETO_CANDIDATE_K_ARTIFACT_BYTE_LIMIT + 1)
+            ),
+            Err(AnalysisEngineError::LimitExceeded)
+        );
+    }
+
+    #[test]
+    fn artifact_metadata_tampering_fails_closed() {
+        let artifact = artifact();
+        let invalid_artifacts = [
+            {
+                let mut value = artifact.clone();
+                value.schema_version.clear();
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.run_id.clear();
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.snapshot_id.clear();
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.knowledge_cutoff = "invalid".into();
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.selected_k = 1;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.candidate_count = 0;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.statistical_count = 0;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.statistical_count = 3;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.truth_k = 1;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.selected_k_rmse = f64::NAN;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.selected_k_rmse = -0.1;
+                value
+            },
+            {
+                let mut value = artifact.clone();
+                value.inference_status.clear();
+                value
+            },
+        ];
+        for invalid in invalid_artifacts {
+            assert_invalid(&invalid);
+        }
+    }
+
+    #[test]
+    fn input_accessors_expose_candidates_and_truth() {
+        let a = ModelCandidate::statistical(2, -30.0, 8.0).expect("a");
+        let input = ParetoCandidateKInput::new(vec![a], vec![2], 2);
+        assert_eq!(input.candidates(), &[a]);
+        assert_eq!(input.selected_replications(), &[2]);
+        assert_eq!(input.truth_k(), 2);
+    }
+}
diff --git a/crates/analysis_engine/tests/pareto_candidate_k_execution_contract.rs b/crates/analysis_engine/tests/pareto_candidate_k_execution_contract.rs
new file mode 100644
index 000000000..1ce883c05
--- /dev/null
+++ b/crates/analysis_engine/tests/pareto_candidate_k_execution_contract.rs
@@ -0,0 +1,188 @@
+//! End-to-end contract for cutoff-safe Pareto candidate-`K` selection.
+
+use analysis_engine::{
+    AnalysisEngineError, PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION,
+    PARETO_CANDIDATE_K_MODEL_CONTRACT_VERSION, PARETO_CANDIDATE_K_OUTPUT_PROFILE,
+    ParetoCandidateKInput, execute_pareto_candidate_k_run,
+};
+use model_selection::{ModelCandidate, ModelSelectionError};
+use temporal_core::KnowledgeCutoff;
+use tepp_api::{AnalysisRunAccepted, AnalysisRunRequest, AnalysisRunTerminalState};
+
+fn cutoff() -> KnowledgeCutoff {
+    KnowledgeCutoff::parse_rfc3339("2026-02-01T00:00:00Z").expect("cutoff")
+}
+
+fn request() -> AnalysisRunRequest {
+    AnalysisRunRequest {
+        contract_version: 1,
+        idempotency_key: "pareto-candidate-k-idem".into(),
+        tenant_workspace_id: "tenant-workspace".into(),
+        snapshot_id: "snapshot-pareto-candidate-k".into(),
+        knowledge_cutoff: "2026-02-01T00:00:00Z".into(),
+        model_contract_version: PARETO_CANDIDATE_K_MODEL_CONTRACT_VERSION.into(),
+        output_profile: PARETO_CANDIDATE_K_OUTPUT_PROFILE.into(),
+    }
+}
+
+fn accepted(request: &AnalysisRunRequest) -> AnalysisRunAccepted {
+    AnalysisRunAccepted::new(
+        "run-pareto-candidate-k",
+        "accepted",
+        &request.idempotency_key,
+    )
+    .expect("accepted")
+}
+
+fn statistical_front() -> ParetoCandidateKInput {
+    ParetoCandidateKInput::new(
+        vec![
+            ModelCandidate::statistical(2, -30.0, 8.0).expect("k2"),
+            ModelCandidate::statistical(4, -30.0, 8.0).expect("k4"),
+            ModelCandidate::llm_vote_only(8).expect("llm"),
+        ],
+        vec![2, 2, 2],
+        2,
+    )
+}
+
+fn execute(
+    request: &AnalysisRunRequest,
+    input: &ParetoCandidateKInput,
+) -> Result<analysis_engine::ParetoCandidateKExecution, AnalysisEngineError> {
+    execute_pareto_candidate_k_run(
+        request,
+        &accepted(request),
+        "snapshot-pareto-candidate-k",
+        cutoff(),
+        input,
+        "2026-02-02T00:00:00Z",
+    )
+}
+
+#[test]
+fn pareto_front_selects_smaller_k_and_refuses_llm_vote_as_authority() {
+    let request = request();
+    let execution = execute(&request, &statistical_front()).expect("execution");
+    assert_eq!(
+        execution.artifact.schema_version,
+        PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION
+    );
+    assert_eq!(execution.artifact.selected_k, 2);
+    assert_eq!(execution.artifact.candidate_count, 3);
+    assert_eq!(execution.artifact.statistical_count, 2);
+    assert_eq!(execution.artifact.truth_k, 2);
+    assert!((execution.artifact.selected_k_rmse - 0.0).abs() < f64::EPSILON);
+    assert_eq!(
+        execution.artifact.inference_status,
+        "pareto_statistical_front_not_fitted_schwarz_sampler"
+    );
+    assert_eq!(
+        execution.terminal_result.run_state,
+        AnalysisRunTerminalState::Succeeded
+    );
+    assert_eq!(
+        execution.terminal_result.result_sha256.as_deref(),
+        Some(execution.artifact.sha256().expect("digest").as_str())
+    );
+    assert_eq!(
+        execution.terminal_result.result_schema_version.as_deref(),
+        Some(PARETO_CANDIDATE_K_ARTIFACT_SCHEMA_VERSION)
+    );
+}
+
+#[test]
+fn higher_likelihood_wins_and_llm_only_sets_fail_closed() {
+    let request = request();
+    let higher = ParetoCandidateKInput::new(
+        vec![
+            ModelCandidate::statistical(2, -30.0, 8.0).expect("k2"),
+            ModelCandidate::statistical(8, -20.0, 9.0).expect("k8"),
+        ],
+        vec![8],
+        8,
+    );
+    let execution = execute(&request, &higher).expect("likelihood");
+    assert_eq!(execution.artifact.selected_k, 8);
+    assert!((execution.artifact.selected_k_rmse - 0.0).abs() < f64::EPSILON);
+
+    let llm_only = ParetoCandidateKInput::new(
+        vec![ModelCandidate::llm_vote_only(3).expect("llm")],
+        vec![3],
+        3,
+    );
+    assert_eq!(
+        execute(&request, &llm_only),
+        Err(AnalysisEngineError::ModelSelection(
+            ModelSelectionError::LlmVoteIsNotStatisticalAuthority
+        ))
+    );
+    let empty = ParetoCandidateKInput::new(Vec::new(), vec![2], 2);
+    assert_eq!(
+        execute(&request, &empty),
+        Err(AnalysisEngineError::ModelSelection(
+            ModelSelectionError::EmptyCandidateSet
+        ))
+    );
+}
+
+#[test]
+fn mismatched_replications_record_positive_rmse() {
+    let request = request();
+    let mismatched = ParetoCandidateKInput::new(
+        vec![ModelCandidate::statistical(2, -30.0, 8.0).expect("k2")],
+        vec![4, 4, 4],
+        2,
+    );
+    let execution = execute(&request, &mismatched).expect("rmse");
+    assert_eq!(execution.artifact.selected_k, 2);
+    assert!((execution.artifact.selected_k_rmse - 2.0).abs() < f64::EPSILON);
+}
+
+#[test]
+fn execution_refuses_snapshot_profile_and_cutoff_mismatch() {
+    let request = request();
+    assert_eq!(
+        execute_pareto_candidate_k_run(
+            &request,
+            &accepted(&request),
+            "other-snapshot",
+            cutoff(),
+            &statistical_front(),
+            "2026-02-02T00:00:00Z",
+        ),
+        Err(AnalysisEngineError::SnapshotMismatch)
+    );
+    for invalid_request in [
+        {
+            let mut value = request.clone();
+            value.knowledge_cutoff = "2026-08-02T00:00:00Z".into();
+            value
+        },
+        {
+            let mut value = request.clone();
+            value.model_contract_version = "other-model".into();
+            value
+        },
+        {
+            let mut value = request.clone();
+            value.output_profile = "fitted_candidate_k_v1".into();
+            value
+        },
+        {
+            let mut value = request.clone();
+            value.output_profile = "joint_posterior_draws_v1".into();
+            value
+        },
+        {
+            let mut value = request.clone();
+            value.output_profile = "trsl_topic_lineage_v1".into();
+            value
+        },
+    ] {
+        assert_eq!(
+            execute(&invalid_request, &statistical_front()),
+            Err(AnalysisEngineError::InvalidEvidence)
+        );
+    }
+}
diff --git a/docs/TRACEABILITY.md b/docs/TRACEABILITY.md
index 2b783c2ab..192119080 100644
--- a/docs/TRACEABILITY.md
+++ b/docs/TRACEABILITY.md
@@ -75,6 +75,7 @@ The full APA 7th standards/literature register remains `docs/research/standards-
 | report template/section/copied/style/modality method effects | ADR 0004/0012; PRD/TRD | simulation truth factors implemented; `corpus_background` background-versus-unique-content identity on the active PR; estimator-side method model remains future | partial |
 | report template/section/copied/style/modality method effects | ADR 0004/0012; PRD/TRD | simulation truth factors implemented; `prompt_source` prompt-versus-unique-content identity on the active PR; estimator-side method model remains future | partial |
 | candidate K statistical/Pareto gates | ADR 0012; research | `model_selection` fits each candidate `K` with the CPU `f64` reference and scores the actual mixture likelihood plus Schwarz's (1978) `ℓ − (p ln N)/2` penalty before the Pareto gate; candidate blinding, blinded LLM review, GPU, and backend comparison remain accepted-target | active-PR |
+| Pareto candidate-K analysis-run selection | ADR 0012/0022/0053 | `analysis_engine` `pareto_candidate_k_v1` binds `select_candidate_k` and selected-`K` RMSE; refuses LLM-vote authority; not Schwarz fitted selection, not joint Laplace draws, not a Bayesian sampler, and not implemented-main | active-PR |
 | compositional topic correlation / stable clustering | ADR 0005/0012; research | future `network_analysis` | accepted-target |
 | posterior ESEM / longitudinal invariance / DSEM | ADR 0005 | `psychometric_core` construct/input gates, true-loading OLS recovery, posterior-draw point-estimate averaging, Rubin `T` on draw-level OLS loadings, CWC within/between OLS plus the contextual effect, event-time log-rate, constant- and time-varying-predictor discrete effects (Voelkle Eqs. 12 and 14), exact scalar discrete process noise (Driver et al., 2017, Eq. 3), lagged latent covariance and unconditional latent variance (Driver et al., 2017, Eq. 3–4), stationary within-subject variance (Driver et al., 2017, Eq. 4 as `Δt → ∞`; `asymDIFFUSION`), trait-plus-state variance (Driver et al., 2017, §4.3 `TRAITVAR`; not process noise), observed-indicator variance and lagged observed covariance (Driver et al., 2017, Eq. 5; Table 2 `MANIFESTVAR` is `Θ`, not `Var(y)`; `MANIFESTTRAITVAR` is not `MANIFESTVAR`; `Θ` does not enter lagged observed covariance; observed-indicator mean is `τ + λ μ`; `MANIFESTMEANS` is not `E(y)`; `CINT` is not `MANIFESTMEANS`; discrete latent mean is `exp(a Δt) μ_0 + (exp(a Δt) − 1)/a κ`; `T0MEANS` is not `μ_t`; evolved observed mean is `τ + λ μ_t`; `τ + λ μ_0` is not `E(y_t)`; contemporaneous `TDPREDEFFECT` impulse is `m x`, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14; Eq. 5 of that contemporaneous impulse is `τ + λ(μ_t + m x)`, and `τ + λ μ_t` is not that observed mean; time-independent `TIPREDEFFECT` increment is `A^{-1}[e^{A Δt} − I] B z`, not `CINT`, not `M x`, not Voelkle Eq. 14, and not the coefficient `B`; Eq. 5 of that increment is `τ + λ(μ_t + A^{-1}[e^{A Δt} − I] B z)`, and `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`; within-interval `TDPREDEFFECT` carry is `e^{A(t−u)} M x` for `t0 < u < t`, not the contemporaneous Dirac, not `CINT`, not `TIPREDEFFECT`, and not Voelkle Eq. 14; Eq. 5 of that carry is `τ + λ(μ_t + e^{a(t−u)} m x)`, and `τ + λ μ_t` is not that observed mean; `τ + λ(μ_t + m x)` is not that carried observed mean when `u ≠ t`; §7.2 level-change `CINT` is `κ = −a m x` (`a < 0`; not the dissipating Dirac, not a free `CINT`, not `TIPREDEFFECT`; Eq. 3 of that setting is `(1 − e^{a Δt}) m x`); §7.2 extra-process contribution is `a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a)` (not `κ = −a m x`, not `(1 − e^{a Δt}) m x`, not the dissipating Dirac; `ε ≥ 0` fails closed; Eq. 5 of that contribution is `τ + λ(μ_t + a_{ηξ} x (e^{ε Δt} − e^{a Δt}) / (ε − a)`; extra `LAMBDA` is 0; `τ + λ μ_t` is not that observed mean; after-t0 extra-process `TDPREDEFFECT` uses `t − u` with `t0 < u < t` while `μ_t` uses `Δt`; that after-t0 observed mean is not the first-occasion extra-process observed mean; §7.2 `asymTIPREDEFFECT` is `-B z / a` for `a < 0` and is not `B`, not `A^{-1}[e^{A Δt} − I] B z`, not `CINT`, and not `M x`; §7.2 `addedTIPREDVAR` is `(B / a)² v` and is not `TRAITVAR`, not `asymDIFFUSION`, and not `-B z / a`; Table 2 `asymCINT` is `-κ / a` for `a < 0` and is not `κ`, not `A^{-1}[e^{A Δt} − I] κ`, not `T0MEANS`, and not `-B z / a`; p. 16 stationary `T0MEANS` is `-κ / a + −B z / a` and is not free `T0MEANS`, not `asymCINT` alone, not `asymTIPREDEFFECT` alone, and not the finite-interval discrete latent mean; Eq. 5 of that constrained mean is `τ + λ(−κ / a + −B z / a)`; `τ + λ μ_0` is not that observed mean; `MANIFESTMEANS` is not `E(y_0)`; the constrained latent mean is not `E(y_0)`; stationary `T0VAR` is `trait + −q / (2 a) + (B / a)² v` (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)`)); lagged stationary `T0VAR` is `trait + e^{a Δt}(−q / (2 a)) + (B / a)² v` (trait and `addedTIPREDVAR` do not decay; contemporaneous `T0VAR` is not that lagged map; decaying the constrained total as if it were all state is not that lagged map; Eq. 5 of that lagged covariance is `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); later-occasion stationary `T0VAR` is `trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v` (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`; `Q_Δt` is not that later map; Eq. 5 of that later-occasion variance is `λ²(trait + e^{2 a Δt}(−q / (2 a)) + Q_Δt + (B / a)² v) + θ + ψ`; lagged observed covariance omits `Q_Δt` and `θ`; `MANIFESTVAR` is not `Var(y_t)`; the later-occasion latent variance is not `Var(y_t)`); predetermined later-occasion `T0VAR` is `trait + e^{2 a Δt} p_0 + Q_Δt + (B / a)² v` (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; 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 `Var(y_t)`; the predetermined later-occasion latent variance is not `Var(y_t)`; stationary later observed variance is not that observed variance when `p_0` is free); predetermined lagged `T0VAR` is `trait + e^{a Δt} p_0 + (B / a)² v` (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; the predetermined first-occasion variance of §4.3 predetermined `T0VAR` is `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; Eq. 5 of that predetermined first-occasion variance is `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)` (footnote 4; unstandardised `e^{a Δt}` is defined for growing `a ≥ 0` and for zero diffusion and is not `discreteDRIFTstd`; the §7.1 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)` (footnote 4; 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`; p. 16 `CINTstd` is `κ / √p` after strictly positive `asymDIFFUSION`; unstandardised `CINT` is not `CINTstd`; `asymCINTstd` is not `CINTstd`; `discreteCINTstd` is not `CINTstd`; `κ / √(trait + p + added)` is not `CINTstd`;))))), irregular already-centered residual lag, and strong/strict-gated latent means on the stacked psychometric PR (two-observation residual variance is identically `0` and caps at strong/scalar; Putnick & Bornstein, 2016, PMC5145197 opened 2026-08-19T22:15Z); full ESEM/DSEM remaining | partial |
 | CPU bounded multithreading + GPU/VRAM streaming/parity | ADR 0001/0006 | future `compute_backend` | accepted-target |
diff --git a/docs/adr/0053-pareto-candidate-k-analysis-run.md b/docs/adr/0053-pareto-candidate-k-analysis-run.md
new file mode 100644
index 000000000..1250e2da8
--- /dev/null
+++ b/docs/adr/0053-pareto-candidate-k-analysis-run.md
@@ -0,0 +1,82 @@
+# ADR 0053 — Pareto candidate-`K` selection as an analysis-run output profile
+
+**Decision status:** Accepted
+**Implementation maturity:** active-PR — composed on this branch; not implemented-main
+**Date:** 2026-08-31
+**Supersedes:** None; complements ADR 0012 (candidate-`K` / Pareto gates) and ADR 0022 (cutoff-safe analysis-run execution).
+**Figma File ID:** N/A — this increment changes a Rust service crate and has no user-interface surface.
+**Storybook inventory:** N/A — no reusable web object or interaction changed.
+
+## Context
+
+Protected main already admits a unique `K` from a Pareto-filtered statistical
+front inside `model_selection::select_candidate_k` and scores selected-`K`
+RMSE against known truth. Operators still cannot request that gate as a
+digest-bound analysis-run output. Schwarz fitted candidate-`K` selection is a
+different profile. Joint Gauss-Newton Laplace draws are a different profile.
+Topic activity/dormancy is a different profile. Full Bayesian sampling, GPU,
+and topic birth/split/merge remain later GAP-004 work and are not this slice.
+
+An LLM vote must not define the numerical optimum.
+
+## Decision
+
+Add the `pareto_candidate_k_v1` analysis-run output profile to
+`analysis_engine`. The executor:
+
+- consumes already-constructed `ModelCandidate` values plus selected-`K`
+  replications and known-truth `K`;
+- requires the request snapshot and knowledge cutoff to match the offered
+  construction;
+- invokes `select_candidate_k` and `selected_k_root_mean_square_error`
+  without reimplementing Pareto dominance or RMSE;
+- refuses LLM-vote-only authority and empty candidate sets;
+- emits a canonical SHA-256-digested `tepp.pareto_candidate_k.v1` artifact
+  with selected `K`, candidate/statistical counts, truth `K`, RMSE, and
+  inference status `pareto_statistical_front_not_fitted_schwarz_sampler`;
+- does not invent a Bayesian sampler, persist rows, select GPU backends, or
+  emit topic-lineage edges.
+
+This is Pareto-front statistical selection, not Schwarz fitted selection, not
+joint Laplace plausible-value draws, and not a posterior sampler.
+
+## Alternatives considered
+
+1. Bind another Schwarz `select_fitted_candidate_k` profile — rejected
+   because that bind is already live as a separate analysis-run profile.
+2. Bind joint Gauss-Newton Laplace draws — rejected because that bind is
+   already live as a separate analysis-run profile.
+3. Invent a Bayesian sampler or topic birth/split/merge engine — rejected
+   because those functions do not exist on protected main.
+4. Bind topic activity/dormancy — already live as a separate analysis-run
+   profile.
+5. Bind the existing Pareto `select_candidate_k` gate to ADR 0022's
+   analysis-run profile — accepted.
+
+## Consequences
+
+Operators can request cutoff-safe Pareto candidate-`K` as a digest-bound
+terminal result. The artifact does not claim Schwarz fitted selection,
+joint Laplace draws, Bayesian sampling, GPU parity, or topic
+birth/split/merge. Snapshot/profile/cutoff mismatch, empty sets, and
+LLM-only authority fail closed.
+
+## Verification
+
+The PR includes Rust unit and integration tests for smaller-`K` ties, higher
+held-out likelihood, LLM-vote non-authority, empty sets, positive RMSE,
+snapshot/profile/cutoff mismatch, and artifact tampering. Run:
+
+```text
+cargo fmt --all -- --check
+cargo test -p analysis_engine
+cargo clippy -p analysis_engine --all-targets -- -D warnings
+python3 scripts/validate_documentation.py
+```
+
+## Rollback and supersession
+
+Rollback removes the `pareto_candidate_k_v1` profile. No persisted schema
+migration is introduced. Supersede only with an ADR that keeps Pareto
+statistical selection distinct from LLM votes, Schwarz fitted selection,
+joint Laplace draws, and Bayesian sampling.
diff --git a/docs/adr/README.md b/docs/adr/README.md
index 1254c8079..294c25aae 100644
--- a/docs/adr/README.md
+++ b/docs/adr/README.md
@@ -28,6 +28,7 @@ Read [`ADR_POLICY.md`](ADR_POLICY.md) first. **Decision status and implementatio
 | [0020](0020-span-grounded-semantic-units.md) | Span-grounded semantic units; language tags are not identity | Accepted | active-PR | First ADR 0004 production slice; concept alignment, invariance, and topic estimation are not claimed. |
 | [0021](0021-lineageweave-project-history-boundary.md) | LineageWeave project-history service boundary | Accepted | active-PR | Credential-free bounded project-history API preserves LineageWeave authorization ownership. |
 | [0022](0022-deterministic-analysis-run-execution.md) | Deterministic cutoff-safe analysis-run execution | Accepted | active-PR | Closes the first executable product path from accepted run to digest-bound terminal result without claiming estimator authority. |
+| [0053](0053-pareto-candidate-k-analysis-run.md) | Pareto candidate-`K` as an analysis-run profile | Accepted | active-PR | Complements ADR 0012/0022; Pareto statistical front, not Schwarz fitted selection, not joint Laplace draws, and not a Bayesian sampler. |
 | [0024](0024-lineage-pair-criterion-and-project-journey-posterior.md) | Independent Event Lineage pair criterion and posterior Project Journey | Proposed | active-PR | Strict artifacts preserve criterion/event-time draws, branches, ties, and CPU/GPU receipts without claiming the scientific estimator is complete. |
 | [0025](0025-macos-native-rust-mlx-metal-boundary.md) | macOS-native Rust-owned MLX Metal execution | Accepted | accepted-target | Compose authenticates to a native host service; Linux never claims Metal, and actual backend/parity receipts fail closed. |
 | [0023](0023-lineage-criterion-anchor-contract.md) | TEPP-owned Event Lineage criterion anchor | Accepted | active-PR | PR #237 publishes the strict accepted/rejected artifact and identities; estimator execution remains fail-closed future work. |
@@ -138,6 +139,7 @@ Use the narrowest owning ADR when decisions overlap:
 - **project-history wire-size symmetry:** ADR 0019.
 - **LineageWeave project-history service boundary:** ADR 0021.
 - **accepted-run execution and terminal artifact production:** ADR 0022.
+- **Pareto candidate-K analysis-run claim boundary:** ADR 0053.
 - **independent lineage criterion and posterior Project Journey:** ADR 0023.
 - **macOS-native Rust-owned MLX Metal execution:** ADR 0024.
 
diff --git a/docs/doctoring/pareto-candidate-k-analysis-run.md b/docs/doctoring/pareto-candidate-k-analysis-run.md
new file mode 100644
index 000000000..6d5335391
--- /dev/null
+++ b/docs/doctoring/pareto-candidate-k-analysis-run.md
@@ -0,0 +1,16 @@
+# Pareto candidate-`K` analysis-run composition
+
+**Active slice:** ADR 0053 / `pareto_candidate_k_v1`
+**Protected-main status:** not implemented-main
+
+`model_selection` already admits a unique `K` from a Pareto-filtered
+statistical front and scores selected-`K` RMSE against known truth. This
+slice binds that gate to a cutoff-safe analysis-run profile so an operator
+can request a digest-bound terminal result.
+
+The executor refuses LLM-vote-only authority. It is not Schwarz fitted
+selection, not joint Gauss-Newton Laplace draws, not a Bayesian sampler, not
+GPU execution, and not topic birth/split/merge.
+
+Exact-head Checks and two independent approvals are required before any
+implemented-main claim.