diff --git a/crates/devtools/src/bin/stage_pipeline.rs b/crates/devtools/src/bin/stage_pipeline.rs
index 78649233e..c294ab555 100644
--- a/crates/devtools/src/bin/stage_pipeline.rs
+++ b/crates/devtools/src/bin/stage_pipeline.rs
@@ -107,6 +107,35 @@
 //     `timing` and predicted CPU (`cpu_core_seconds_per_second`), and each
 //     shown candidate's `cpu_core_seconds_per_second` is their sum: report
 //     only, as `plan_installable`'s predicted usage names them.
+// `memo` (unless `--no-memo`) is the memo the search built, from the
+// planning round whose plan was selected (`MemoSteps`): `steps`, one per
+// memo step in pipeline order (`stage0`: the frontends' DAG hash-consed,
+// groups without candidates; `pass1`: Pass 1's candidates, with the
+// accuracy-scoped sizes; `pass2`: local window composition's pane
+// candidates; `concrete_states`: the Pass 2 memo rules (scan labels,
+// summary inputs, top-k reuse, finer aggregates, rollups, summary results,
+// state configurations) and the concrete summary-state groups, the memo the
+// search selects from). Each step lists its groups (`id`, `label`,
+// `children`, `parents`, `queries`, `roots_of`, the group's `dag`) and their
+// candidates (`candidate_count`, `candidate_count_by_origin`, and the first
+// `--max-memo-candidates` (default 64) under `candidates`, with
+// `candidates_capped`): each with its `index` in the group, `implements`,
+// `children`, `origin` (`CandidateOrigin` in snake case), `budget_share`,
+// `added` (not in the group at the step before), a one-line `label`, its
+// `dag` (its node and everything below) and `group_of_node` (the `dag`
+// nodes that are a child group's node, to that group's id).
+// `selected_choice` maps each group of the last step the selected plan uses
+// (by id, as a string) to its candidate's index; it is null, with
+// `selected_choice_unavailable` saying why, when the plan cannot be read as
+// one candidate per group. `enumeration` counts each step's candidate DAGs
+// (`memo::enumeration::enumerate`) up to `--memo-enumeration-limit`
+// (default 1000) under `per_step` (`count`, `complete`; Stage 0 counts its
+// one DAG), and lists the first `--max-enumerated` (default 200) `choices`
+// of `step`: the last step enumerated completely within that many, else
+// the last step. Each choice has its `id` (`E1`, ...), `choice`, `dag`
+// (`memo::enumeration::compose`; null with `error` when it does not
+// compose), `budget_share_1` (every chosen candidate sized for the whole
+// budget) and `selected` (it is `selected_choice`). `priced` is null.
 // `workload.data_workload` is the `DataWorkload` the run planned with, as
 // declared (`--workload`, `--example`) or built from `--sample-interval-ms`
 // (`--promql`); each query also carries its `recurrence` and
@@ -213,17 +242,21 @@
 
 use std::collections::btree_map::Entry;
 use std::collections::{BTreeSet, HashSet};
+use std::rc::Rc;
 
 use asap_devtools::candidate_labels::{candidate_labels, computation_label, query_of_each_target};
 use asap_devtools::planner_layering_examples::{
     example1, example2, pattern_a, pattern_b, PatternARecurrence, SHARED_ROWS_PER_SECOND,
 };
 use asap_devtools::planning_stages::{
-    lower_promql_roots, lower_sql_roots, run_search_over, sql_catalog, PlanningStagesError,
-    PlanningStagesRun,
+    lower_promql_roots, lower_sql_roots, run_search_over, sql_catalog, MemoSteps,
+    PlanningStagesError, PlanningStagesRun,
 };
 use asap_devtools::SqlCatalog;
 use asap_frontend_promql::{counter_function_over_gauge_warnings, promql_metric_names};
+use asap_logical_asap_optimization::memo::candidates::{CandidateMemo, CandidateOrigin};
+use asap_logical_asap_optimization::memo::enumeration::{compose, enumerate, MemoChoice};
+use asap_logical_asap_optimization::memo::MemoGroupId;
 use asap_logical_asap_optimization::per_computation_candidates::{
     ComputationCandidate, PerComputationCandidates, PruneReason,
 };
@@ -249,7 +282,8 @@ const USAGE: &str =
 [--name <name>]... [--table <json>...] [--max-error <f64> --failure-probability <f64> --accuracy-metric <metric>] [--sample-interval-ms <u64>] [--series-count <u64>] [--rows-per-second <f64>] [--rows-held <u64>])) \
 [--cost-model usage-over-time|aws-fargate-us-east-1|provisioned-capacity|cluster-capacity [--cluster-memory-bytes <n> \
 --cluster-disk-bytes <n> [--cluster-cpu-cores <n>] --cluster-objective lowest-latency|least-memory|pareto-front]] \
-[--plan-selection-settings <file>] [--enforce-accuracy-guarantees] [--deployment-capabilities <json>] [--exhaustive [--max-combinations <n>] | --search candidate-connections] [--milp-time-limit-s <f64>] [--max-displayed <n>] --out <file>\n\
+[--plan-selection-settings <file>] [--enforce-accuracy-guarantees] [--deployment-capabilities <json>] [--exhaustive [--max-combinations <n>] | --search candidate-connections] [--milp-time-limit-s <f64>] [--max-displayed <n>] \
+[--no-memo] [--max-memo-candidates <n>] [--memo-enumeration-limit <n>] [--max-enumerated <n>] --out <file>\n\
 --search candidate-connections is the default search.";
 
 /// Default evaluator-assignment budget for an exhaustive archive run.
@@ -343,6 +377,12 @@ fn run(args: Vec<String>) -> Result<(), Failure> {
     let mut search_algorithm: Option<SearchAlgorithm> = None;
     let mut milp_time_limit_ms: Option<u64> = None;
     let mut max_combinations_given = false;
+    let mut write_memo = true;
+    let mut memo_caps = MemoCaps {
+        candidates_per_group: 64,
+        enumeration_limit: 1000,
+        enumerated: 200,
+    };
     let mut args = args.into_iter();
     while let Some(flag) = args.next() {
         let mut value = || args.next().ok_or(format!("{flag} needs a value"));
@@ -404,6 +444,16 @@ fn run(args: Vec<String>) -> Result<(), Failure> {
             "--plan-selection-settings" => plan_selection_settings_path = Some(value()?),
             "--enforce-accuracy-guarantees" => enforce_accuracy_guarantees = true,
             "--exhaustive" => exhaustive = true,
+            "--no-memo" => write_memo = false,
+            "--max-memo-candidates" => {
+                memo_caps.candidates_per_group = value()?.parse().map_err(|e| format!("{e}"))?
+            }
+            "--memo-enumeration-limit" => {
+                memo_caps.enumeration_limit = value()?.parse().map_err(|e| format!("{e}"))?
+            }
+            "--max-enumerated" => {
+                memo_caps.enumerated = value()?.parse().map_err(|e| format!("{e}"))?
+            }
             "--search" => {
                 search_algorithm = Some(match value()?.as_str() {
                     "candidate-connections" => SearchAlgorithm::CandidateConnections,
@@ -688,7 +738,16 @@ fn run(args: Vec<String>) -> Result<(), Failure> {
                 )
             }),
     );
+    let memo = result
+        .as_ref()
+        .ok()
+        .and_then(|run| run.memo_steps.as_ref())
+        .filter(|_| write_memo)
+        .map(|steps| memo_json(steps, &memo_caps));
     let mut document = document_of(described, &roots, &entries, result, max_displayed)?;
+    if let Some(memo) = memo {
+        document["memo"] = memo;
+    }
     if !warnings.is_empty() {
         document["stage3_plan_selection"]["warnings"] = json!(warnings);
     }
@@ -1387,6 +1446,337 @@ fn query_batch(
     }
 }
 
+/// How much of the memo the document writes (`--max-memo-candidates`,
+/// `--memo-enumeration-limit`, `--max-enumerated`).
+struct MemoCaps {
+    candidates_per_group: usize,
+    enumeration_limit: usize,
+    enumerated: usize,
+}
+
+/// The document's `memo` section: the memo after each step, the selected
+/// plan's choice over the last step's memo, and the candidate DAGs each
+/// step's memo stands for (`memo::enumeration::enumerate`; each listed
+/// choice composed by `memo::enumeration::compose`).
+fn memo_json(steps: &MemoSteps, caps: &MemoCaps) -> Value {
+    let named = [
+        (
+            "stage0",
+            "Stage 0, the frontends' DAG hash-consed",
+            &steps.stage0,
+        ),
+        ("pass1", "Stage 1, Pass 1", &steps.pass1),
+        (
+            "pass2",
+            "Stage 1, Pass 2: local window composition",
+            &steps.pass2,
+        ),
+        (
+            "concrete_states",
+            "Stage 1, Pass 2 rules and concrete state groups",
+            &steps.concrete_states,
+        ),
+    ];
+    let mut previous: Option<&CandidateMemo> = None;
+    let mut json_steps = Vec::new();
+    let mut per_step = serde_json::Map::new();
+    // The last step (with candidates) enumerated completely within `enumerated`.
+    let mut listed = None;
+    for &(step, title, memo) in &named {
+        json_steps.push(json!({
+            "step": step,
+            "title": title,
+            "groups": memo_groups_json(memo, previous, caps.candidates_per_group),
+        }));
+        previous = Some(memo);
+        if step == "stage0" {
+            // One DAG: the frontends' own.
+            per_step.insert(step.into(), json!({ "count": 1, "complete": true }));
+            continue;
+        }
+        let enumeration = enumerate(memo, caps.enumeration_limit);
+        if enumeration.complete && enumeration.choices.len() <= caps.enumerated {
+            listed = Some((step, memo));
+        }
+        per_step.insert(
+            step.into(),
+            json!({ "count": enumeration.choices.len(), "complete": enumeration.complete }),
+        );
+    }
+    let last = &steps.concrete_states;
+    let (step, memo) = listed.unwrap_or(("concrete_states", last));
+    let selected = steps.selected_choice.as_ref().ok();
+    let choices: Vec<_> = enumerate(memo, caps.enumerated)
+        .choices
+        .iter()
+        .enumerate()
+        .map(|(index, choice)| {
+            let mut entry = json!({
+                "id": format!("E{}", index + 1),
+                "choice": choice_json(choice),
+                "budget_share_1": choice.iter().all(|(group, &candidate)| {
+                    memo.candidates[group.0 as usize][candidate].budget_share == 1
+                }),
+                "selected": step == "concrete_states" && selected == Some(choice),
+            });
+            match compose(memo, choice) {
+                Ok(roots) => {
+                    let roots: Vec<_> = roots
+                        .into_iter()
+                        .map(|(_, node)| QueryRoot::Operator(node))
+                        .collect();
+                    entry["dag"] = json!(export(&roots));
+                }
+                Err(error) => {
+                    entry["dag"] = Value::Null;
+                    entry["error"] = json!(error.to_string());
+                }
+            }
+            entry
+        })
+        .collect();
+    let mut memo = json!({
+        "steps": json_steps,
+        "selected_choice": selected.map_or(Value::Null, choice_json),
+        "enumeration": {
+            "step": step,
+            "per_step": per_step,
+            "limit": caps.enumeration_limit,
+            "choices": choices,
+            "priced": null,
+        },
+    });
+    if let Err(reason) = &steps.selected_choice {
+        memo["selected_choice_unavailable"] = json!(reason);
+    }
+    memo
+}
+
+/// Group id (as a string) to candidate index.
+fn choice_json(choice: &MemoChoice) -> Value {
+    Value::Object(
+        choice
+            .iter()
+            .map(|(group, &candidate)| (group.0.to_string(), json!(candidate)))
+            .collect(),
+    )
+}
+
+/// `memo`'s groups, each with its first `max_candidates` candidates; a
+/// candidate is `added` when `previous` (the memo at the step before) has no
+/// candidate of that group with the same node and children.
+fn memo_groups_json(
+    memo: &CandidateMemo,
+    previous: Option<&CandidateMemo>,
+    max_candidates: usize,
+) -> Vec<Value> {
+    let ids = |groups: &[MemoGroupId]| groups.iter().map(|g| g.0).collect::<Vec<_>>();
+    memo.groups
+        .iter()
+        .zip(&memo.candidates)
+        .enumerate()
+        .map(|(id, (group, candidates))| {
+            let (dag, _) = flatten(&[QueryRoot::Operator(group.node.clone())]);
+            let mut by_origin = serde_json::Map::new();
+            for candidate in candidates {
+                let count = by_origin
+                    .entry(origin_name(&candidate.origin))
+                    .or_insert(json!(0));
+                *count = json!(count.as_u64().unwrap_or(0) + 1);
+            }
+            let earlier = previous
+                .and_then(|memo| memo.candidates.get(id))
+                .map_or(&[][..], Vec::as_slice);
+            let listed: Vec<_> = candidates
+                .iter()
+                .take(max_candidates)
+                .enumerate()
+                .map(|(index, candidate)| {
+                    let (dag, originals) = flatten(&[QueryRoot::Operator(candidate.node.clone())]);
+                    let group_of_node: serde_json::Map<_, _> = originals
+                        .iter()
+                        .enumerate()
+                        .filter_map(|(node, original)| {
+                            candidate
+                                .children
+                                .iter()
+                                .find(|child| {
+                                    Rc::ptr_eq(&memo.groups[child.0 as usize].node, original)
+                                })
+                                .map(|child| (node.to_string(), json!(child.0)))
+                        })
+                        .collect();
+                    json!({
+                        "index": index,
+                        "implements": ids(&candidate.implements),
+                        "children": ids(&candidate.children),
+                        "origin": origin_name(&candidate.origin),
+                        "budget_share": candidate.budget_share,
+                        "added": !earlier.iter().any(|before| {
+                            Rc::ptr_eq(&before.node, &candidate.node)
+                                && before.children == candidate.children
+                        }),
+                        "label": candidate_node_label(&dag, &group_of_node),
+                        "dag": dag,
+                        "group_of_node": group_of_node,
+                    })
+                })
+                .collect();
+            json!({
+                "id": id,
+                "label": node_label(&dag.nodes[dag.nodes.len() - 1]),
+                "children": ids(&group.children),
+                "parents": ids(&group.parents),
+                "queries": group.queries,
+                "roots_of": group.roots_of,
+                "dag": dag,
+                "candidate_count": candidates.len(),
+                "candidate_count_by_origin": by_origin,
+                "candidates_capped": listed.len() < candidates.len(),
+                "candidates": listed,
+            })
+        })
+        .collect()
+}
+
+/// `CandidateOrigin` in snake case.
+fn origin_name(origin: &CandidateOrigin) -> String {
+    match origin {
+        CandidateOrigin::Pass1 => "pass1",
+        CandidateOrigin::SharedBuild => "shared_build",
+        CandidateOrigin::SummaryResult => "summary_result",
+        CandidateOrigin::SummaryInput => "summary_input",
+        CandidateOrigin::Panes => "panes",
+        CandidateOrigin::Rollup => "rollup",
+        CandidateOrigin::TopKReuse => "top_k_reuse",
+        CandidateOrigin::WidenedScans => "widened_scans",
+    }
+    .into()
+}
+
+/// A candidate's own nodes (those above its child groups' nodes), root
+/// first, as `node_label`s joined by " ← ".
+fn candidate_node_label(dag: &FlatDag, group_of_node: &serde_json::Map<String, Value>) -> String {
+    let Some(QueryRoot::Operator(root)) = dag.roots.first() else {
+        return String::new();
+    };
+    let mut labels = Vec::new();
+    let mut pending = vec![*root];
+    let mut seen = HashSet::new();
+    while let Some(id) = pending.pop() {
+        if group_of_node.contains_key(&id.to_string()) || !seen.insert(id) {
+            continue;
+        }
+        labels.push(node_label(&dag.nodes[id]));
+        pending.extend(dag.nodes[id].operator.children().into_iter().rev().copied());
+    }
+    labels.join(" ← ")
+}
+
+/// One node's operator kind with its sketch family and parameters, its
+/// summary query and its time range, when it has them: e.g.
+/// `SummaryAgg Kll(k=200)`, `SummaryEstimate Quantile(q=0.5)`.
+fn node_label(node: &asap_types::ir::flat::FlatNode) -> String {
+    let operator = serde_json::to_value(&node.operator).unwrap_or_default();
+    // `{"ASAP": {"SummaryAgg": {...}}}` (or a unit variant's string).
+    let (kind, fields) = match operator.as_object().and_then(|o| o.values().next()) {
+        Some(Value::Object(inner)) => match inner.iter().next() {
+            Some((kind, fields)) => (kind.clone(), fields.clone()),
+            None => (String::new(), Value::Null),
+        },
+        Some(Value::String(kind)) => (kind.clone(), Value::Null),
+        _ => (operator.to_string(), Value::Null),
+    };
+    let mut details = Vec::new();
+    find_details(&fields, &mut details, 0);
+    let mut label = kind;
+    for detail in details {
+        label.push(' ');
+        label.push_str(&detail);
+    }
+    label
+}
+
+/// Sketch algorithms with parameters, summary queries and time ranges found
+/// in an operator's fields (not inside its schemas).
+fn find_details(value: &Value, details: &mut Vec<String>, depth: usize) {
+    if depth > 6 || details.len() >= 3 {
+        return;
+    }
+    let compact = |value: &Value| -> String {
+        match value {
+            Value::Object(fields) => fields
+                .iter()
+                .map(|(key, value)| match value {
+                    Value::Object(inner) if inner.len() == 1 => {
+                        let (k, v) = inner.iter().next().unwrap();
+                        format!("{key}({k}={v})")
+                    }
+                    Value::Object(inner) => format!(
+                        "{key}({})",
+                        inner
+                            .iter()
+                            .filter(|(_, v)| !v.is_object() && !v.is_array())
+                            .map(|(k, v)| format!("{k}={v}"))
+                            .collect::<Vec<_>>()
+                            .join(", ")
+                    ),
+                    other => format!("{key}={other}"),
+                })
+                .collect::<Vec<_>>()
+                .join(" "),
+            other => other.to_string(),
+        }
+    };
+    match value {
+        Value::Object(fields) => {
+            if let (Some(Value::String(algorithm)), Some(params)) =
+                (fields.get("algorithm"), fields.get("params"))
+            {
+                let params = params
+                    .as_object()
+                    .and_then(|p| p.values().next())
+                    .map(compact)
+                    .unwrap_or_default();
+                details.push(format!("{algorithm}({params})"));
+                return;
+            }
+            for (key, field) in fields {
+                match key.as_str() {
+                    "schema" | "input_schema" | "output_schema" | "predicates" | "cols" => {}
+                    "query" => details.push(compact(field)),
+                    // An aggregate's measures, e.g. `quantile(q=0.5)`.
+                    "measures" => {
+                        for measure in field.as_array().into_iter().flatten() {
+                            let Some(kind) = measure.get("kind").and_then(Value::as_str) else {
+                                continue;
+                            };
+                            let params: Vec<_> = measure
+                                .as_object()
+                                .into_iter()
+                                .flatten()
+                                .filter(|(key, value)| {
+                                    *key != "kind" && (value.is_number() || value.is_string())
+                                })
+                                .map(|(key, value)| format!("{key}={value}"))
+                                .collect();
+                            details.push(format!("{kind}({})", params.join(", ")));
+                        }
+                    }
+                    "range" | "window" => details.push(format!("{key}={field}")),
+                    _ => find_details(field, details, depth + 1),
+                }
+            }
+        }
+        Value::Array(items) => {
+            for item in items {
+                find_details(item, details, depth + 1);
+            }
+        }
+        _ => {}
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/devtools/src/planning_stages.rs b/crates/devtools/src/planning_stages.rs
index fee1040fc..366b7c013 100644
--- a/crates/devtools/src/planning_stages.rs
+++ b/crates/devtools/src/planning_stages.rs
@@ -7,7 +7,7 @@ use asap_logical_asap_optimization::per_computation_candidates::PerComputationCa
 pub use asap_logical_asap_optimization::workload_candidates::Pass2Candidate;
 use asap_physical_asap_optimization::PhysicalWorkloadPlan;
 use asap_plan_selection::pass::{run_stage1_to_stage3_with, Stage1ToStage3Search};
-pub use asap_plan_selection::pass::{LogicalCandidate, PrunedCandidate};
+pub use asap_plan_selection::pass::{LogicalCandidate, MemoSteps, PrunedCandidate};
 use asap_plan_selection::PlanningModels;
 use asap_plan_selection::{Selection, SelectionError};
 use asap_types::ir::schema::schema_support::with_promql_series_identity;
@@ -29,6 +29,8 @@ pub struct PlanningStagesRun {
     pub stage2_physical_asap_optimization: Vec<PhysicalWorkloadPlan>,
     pub stage2_pruned: Vec<PrunedCandidate>,
     pub stage3_plan_selection: Result<Selection, SelectionError>,
+    /// The memo after each step and the selected plan's choice over it.
+    pub memo_steps: Option<MemoSteps>,
 }
 
 /// Lower a PromQL workload, each series' identity as a column (the row
@@ -205,6 +207,7 @@ pub fn run_search_over(
         },
         stage2_pruned: run.stage2_pruned,
         stage3_plan_selection: run.stage3_plan_selection,
+        memo_steps: run.memo_steps,
     })
 }
 
diff --git a/crates/devtools/tests/stage_pipeline.rs b/crates/devtools/tests/stage_pipeline.rs
index 794d82cd9..d181f544c 100644
--- a/crates/devtools/tests/stage_pipeline.rs
+++ b/crates/devtools/tests/stage_pipeline.rs
@@ -1362,7 +1362,7 @@ fn workload_examples_preserve_data_and_valid_materialized_views() {
         .iter()
         .filter(|e| e.get("workload").is_some())
         .collect();
-    assert_eq!(workload_examples.len(), 9);
+    assert_eq!(workload_examples.len(), 10);
     // Each production search has a wall-clock budget. Bound fixture
     // concurrency so this acceptance test does not starve its own solvers.
     for batch in workload_examples.chunks(2) {
@@ -2206,3 +2206,169 @@ fn a_classic_histogram_quantile_gets_a_selected_plan() {
         assert!(selection["selected"].is_string(), "{query}: {selection}");
     }
 }
+
+/// The issue's example workload (#1003): one ratio of per-series quantiles,
+/// every minute, ε = 0.01, δ = 0.001.
+const MEMO_RATIO_OF_QUANTILES: &str =
+    "../../tools/dag-viewer/memo-examples/promql/ratio-of-quantiles-5m.json";
+
+/// The `memo` section: the memo after each step, the selected choice and
+/// the enumeration, on the issue's example.
+#[test]
+fn memo_section_lists_each_step_the_selected_choice_and_the_enumeration() {
+    let out = std::env::temp_dir().join(format!(
+        "stage_pipeline_{}_memo_ratio.json",
+        std::process::id()
+    ));
+    let status = Command::new(env!("CARGO_BIN_EXE_stage_pipeline"))
+        .args(["--workload", MEMO_RATIO_OF_QUANTILES, "--out"])
+        .arg(&out)
+        .status()
+        .unwrap();
+    assert!(status.success());
+    let document: Value = serde_json::from_str(&std::fs::read_to_string(&out).unwrap()).unwrap();
+    std::fs::remove_file(out).unwrap();
+    let memo = &document["memo"];
+    let steps = memo["steps"].as_array().unwrap();
+    let names: Vec<_> = steps.iter().map(|s| s["step"].as_str().unwrap()).collect();
+    assert_eq!(names, ["stage0", "pass1", "pass2", "concrete_states"]);
+    let candidates = |step: &Value| -> u64 {
+        step["groups"]
+            .as_array()
+            .unwrap()
+            .iter()
+            .map(|g| g["candidate_count"].as_u64().unwrap())
+            .sum()
+    };
+    // The PromQL frontend gives each series its identity as a column, so the
+    // two `quantile_over_time(0.5, data[5m])` have a unique key and share one
+    // group: 7 groups (scan, range, two quantile groups, ratio, sum, avg),
+    // 7 + 7 + 5 Pass 1 candidates, 7 × 7 candidate DAGs.
+    assert_eq!(steps[0]["groups"].as_array().unwrap().len(), 7);
+    assert_eq!(candidates(&steps[0]), 0);
+    assert_eq!(steps[1]["groups"].as_array().unwrap().len(), 7);
+    assert_eq!(candidates(&steps[1]), 19);
+    let per_step = &memo["enumeration"]["per_step"];
+    assert_eq!(
+        per_step["stage0"],
+        serde_json::json!({"count": 1, "complete": true})
+    );
+    assert_eq!(
+        per_step["pass1"],
+        serde_json::json!({"count": 49, "complete": true})
+    );
+    // The listed step is the last one enumerated completely within 200
+    // choices (Stage 0 has no candidates to choose), else the last step.
+    let listed = ["pass1", "pass2", "concrete_states"]
+        .into_iter()
+        .rfind(|step| {
+            per_step[step]["complete"] == true && per_step[step]["count"].as_u64().unwrap() <= 200
+        })
+        .unwrap_or("concrete_states");
+    assert_eq!(memo["enumeration"]["step"], listed);
+    if listed != "concrete_states" {
+        assert_eq!(
+            memo["enumeration"]["choices"].as_array().unwrap().len() as u64,
+            per_step[listed]["count"].as_u64().unwrap()
+        );
+    }
+    // Every group's DAG and every listed candidate's DAG is a valid FlatDag,
+    // and each boundary names one of the candidate's child groups.
+    for step in steps {
+        for group in step["groups"].as_array().unwrap() {
+            validated_dag(&group["dag"], 1);
+            for candidate in group["candidates"].as_array().unwrap() {
+                validated_dag(&candidate["dag"], 1);
+                let children = candidate["children"].as_array().unwrap();
+                for child in candidate["group_of_node"].as_object().unwrap().values() {
+                    assert!(children.contains(child));
+                }
+            }
+        }
+    }
+    // Every candidate of the selected choice exists in the last step.
+    let last = steps.last().unwrap()["groups"].as_array().unwrap();
+    let choice = memo["selected_choice"].as_object().unwrap();
+    assert!(!choice.is_empty());
+    for (group, index) in choice {
+        let group = &last[group.parse::<usize>().unwrap()];
+        assert!(index.as_u64().unwrap() < group["candidate_count"].as_u64().unwrap());
+    }
+    let enumeration = &memo["enumeration"];
+    let choices = enumeration["choices"].as_array().unwrap();
+    assert!(!choices.is_empty() && choices.len() <= 200);
+    for choice in choices {
+        validated_dag(&choice["dag"], 1);
+    }
+    // `--no-memo` leaves the section out.
+    let out = std::env::temp_dir().join(format!(
+        "stage_pipeline_{}_no_memo_ratio.json",
+        std::process::id()
+    ));
+    let status = Command::new(env!("CARGO_BIN_EXE_stage_pipeline"))
+        .args(["--workload", MEMO_RATIO_OF_QUANTILES, "--no-memo", "--out"])
+        .arg(&out)
+        .status()
+        .unwrap();
+    assert!(status.success());
+    let document: Value = serde_json::from_str(&std::fs::read_to_string(&out).unwrap()).unwrap();
+    std::fs::remove_file(out).unwrap();
+    assert!(document.get("memo").is_none());
+}
+
+/// Composing the selected choice over the last step's memo gives the
+/// selected plan's Stage 1 DAG, on the issue's example and #509 Example 1.
+/// Stage 1's DAG is rebuilt from the candidates' operator implementations
+/// (`implement_candidate_operators`: an exact top-k becomes
+/// `Project(Limit(Sort))`), so the composed query DAGs are compared after
+/// the same implementation.
+#[test]
+fn composed_selected_choice_is_the_selected_stage1_dag() {
+    use asap_devtools::planning_stages::run_default_search_over;
+    use asap_logical_asap_optimization::memo::enumeration::compose;
+    use asap_logical_asap_optimization::per_computation_candidates::recompose_guarantees;
+    use asap_types::ir::flat::flatten;
+    let ratio: PlanningWorkload =
+        serde_json::from_str(&std::fs::read_to_string(MEMO_RATIO_OF_QUANTILES).unwrap()).unwrap();
+    for workload in [ratio, example1()] {
+        let roots = lower_promql_roots(&workload).unwrap();
+        let entries: Vec<_> = workload.query_workload.entries().collect();
+        let data = workload.data_workload.clone().unwrap_or_default();
+        let run = run_default_search_over(
+            roots,
+            &entries,
+            &data,
+            asap_plan_selection::PlanningModels::builtin(),
+        )
+        .unwrap();
+        let steps = run.memo_steps.as_ref().unwrap();
+        let choice = steps.selected_choice.as_ref().unwrap();
+        let memo = &steps.concrete_states;
+        let composed = compose(memo, choice).unwrap();
+        let composed: Vec<_> = (0..entries.len())
+            .map(|query| {
+                let (_, node) = composed
+                    .iter()
+                    .find(|(group, _)| memo.groups[group.0 as usize].roots_of.contains(&query))
+                    .unwrap();
+                QueryRoot::Operator(
+                    asap_physical_asap_optimization::implement_candidate_operators(node, &[])
+                        .unwrap(),
+                )
+            })
+            .collect::<Vec<_>>();
+        // As reconstruction does, over the implemented operators.
+        let composed = recompose_guarantees(&composed).unwrap();
+        let [selected] = &run.stage1_logical_asap_optimization[..] else {
+            panic!("the default search keeps the selected Stage 1 candidate")
+        };
+        let selected = selected.roots.as_ref().unwrap();
+        assert_eq!(composed.len(), selected.len());
+        for (composed, selected) in composed.into_iter().zip(selected) {
+            assert_eq!(
+                serde_json::to_value(flatten(&[composed]).0).unwrap(),
+                serde_json::to_value(flatten(std::slice::from_ref(selected)).0).unwrap()
+            );
+        }
+    }
+}
diff --git a/crates/integration-tests/src/lib.rs b/crates/integration-tests/src/lib.rs
index fe7e5981d..17789eec6 100644
--- a/crates/integration-tests/src/lib.rs
+++ b/crates/integration-tests/src/lib.rs
@@ -648,6 +648,7 @@ pub mod planning {
             stage3_selected: Some(selected),
             stage1_selected: Some(selected_logical),
             stage3_plan_selection: Ok(selection),
+            memo_steps: None,
         }
     }
 }
diff --git a/crates/integration-tests/tests/memo_enumeration.rs b/crates/integration-tests/tests/memo_enumeration.rs
index eeeb30d96..f822d67b6 100644
--- a/crates/integration-tests/tests/memo_enumeration.rs
+++ b/crates/integration-tests/tests/memo_enumeration.rs
@@ -193,3 +193,53 @@ fn expanded_memo_enumeration_stops_at_the_limit_and_every_candidate_composes() {
         }
     }
 }
+
+/// Candidates may read each other: a coarse quantile's rollup reads the finer
+/// grouping, whose candidates may read the coarse one. A choice taking both
+/// composes no DAG: `compose` says so, and `enumerate` leaves it out.
+#[test]
+fn choices_whose_candidates_read_each_other_are_left_out() {
+    let queries = [
+        "quantile_over_time(0.5, data[1m])",
+        "quantile_over_time(0.9, data[5m])",
+        "quantile by (host, job) (0.5, data)",
+        "quantile by (job) (0.5, data)",
+    ];
+    let entry = QueryWorkloadEntry {
+        query: Default::default(),
+        requirements: QueryRequirements {
+            accuracy: approximate(),
+            max_latency_ms: None,
+        },
+        predictability: Default::default(),
+        recurrence: QueryRecurrence::Repeated(RepeatedDemand::FixedInterval(RepetitionInterval(
+            10_000,
+        ))),
+        range_evaluation: None,
+    };
+    let memo = expanded_memo(roots(&queries), &vec![entry; queries.len()]);
+    let mutual = (0..memo.groups.len())
+        .flat_map(|group| (0..memo.candidates[group].len()).map(move |index| (group, index)))
+        .find_map(|(group, index)| {
+            memo.candidates[group][index]
+                .children
+                .iter()
+                .find_map(|&child| {
+                    memo.candidates[child.0 as usize]
+                        .iter()
+                        .position(|c| c.children.contains(&MemoGroupId(group as u32)))
+                        .map(|back| (child, back))
+                })
+                .map(|(child, back)| [(MemoGroupId(group as u32), index), (child, back)])
+        })
+        .expect("a pair of groups whose candidates read each other");
+    assert!(matches!(
+        compose(&memo, &mutual.into()),
+        Err(asap_logical_asap_optimization::memo::enumeration::ComposeError::Cycle { .. })
+    ));
+    let enumeration = enumerate(&memo, 2_000);
+    assert!(!enumeration.choices.is_empty());
+    for choice in &enumeration.choices {
+        compose(&memo, choice).unwrap();
+    }
+}
diff --git a/crates/logical-asap-optimization/src/memo/enumeration.rs b/crates/logical-asap-optimization/src/memo/enumeration.rs
index 23c8a6115..9beb27c3c 100644
--- a/crates/logical-asap-optimization/src/memo/enumeration.rs
+++ b/crates/logical-asap-optimization/src/memo/enumeration.rs
@@ -11,10 +11,12 @@
 //! that differ only in what recomposing guarantees re-derives compose equal
 //! DAGs. Composing checks only that a choice composes; input contracts,
 //! accuracy at the roots, Stage 2 legality and Stage 3 cost stay with the
-//! validator and the later stages. The memo must be acyclic, as every memo
-//! step builds it.
+//! validator and the later stages. The memo's groups are acyclic, as every
+//! memo step builds them, but candidates may read each other (a rollup of
+//! a finer grouping whose candidate reads the coarser one): a choice taking
+//! such candidates together composes no DAG and is not enumerated.
 
-use std::collections::{BTreeMap, HashMap};
+use std::collections::{BTreeMap, HashMap, HashSet};
 use std::rc::Rc;
 
 use asap_types::ir::{OperatorNode, QueryRoot};
@@ -52,13 +54,18 @@ pub enum ComposeError {
         candidate: usize,
         child: MemoGroupId,
     },
+    /// The chosen candidates read each other in a cycle (e.g. a coarse
+    /// group's rollup reads a finer group whose chosen candidate reads it).
+    #[error("group {group:?} reads itself through the chosen candidates")]
+    Cycle { group: MemoGroupId },
     /// Re-deriving the composed nodes' schemas and guarantees failed.
     #[error("recomposing the composed DAG: {0}")]
     Recompose(#[from] PerComputationCandidateError),
 }
 
 /// Every choice of one candidate per needed group, starting from the query
-/// roots, stopping after `limit` choices.
+/// roots, stopping after `limit` choices. A choice whose candidates read
+/// each other in a cycle composes no DAG and is left out.
 pub fn enumerate(memo: &CandidateMemo, limit: usize) -> MemoEnumeration {
     fn walk(
         memo: &CandidateMemo,
@@ -81,6 +88,15 @@ pub fn enumerate(memo: &CandidateMemo, limit: usize) -> MemoEnumeration {
             }
         };
         for (index, candidate) in memo.candidates[group.0 as usize].iter().enumerate() {
+            // A candidate reading a group that already reads this one closes
+            // a cycle; every edge is checked as its group is chosen.
+            if candidate
+                .children
+                .iter()
+                .any(|&child| reaches(memo, choice, child, group))
+            {
+                continue;
+            }
             choice.insert(group, index);
             let mut next = pending.clone();
             next.extend(candidate.children.iter().rev());
@@ -113,10 +129,14 @@ pub fn compose(
         group: MemoGroupId,
         choice: &MemoChoice,
         done: &mut HashMap<MemoGroupId, Rc<OperatorNode>>,
+        composing: &mut HashSet<MemoGroupId>,
     ) -> Result<Rc<OperatorNode>, ComposeError> {
         if let Some(found) = done.get(&group) {
             return Ok(Rc::clone(found));
         }
+        if !composing.insert(group) {
+            return Err(ComposeError::Cycle { group });
+        }
         let index = choice.get(&group).copied().unwrap_or(0);
         let candidate =
             memo.candidates[group.0 as usize]
@@ -125,7 +145,7 @@ pub fn compose(
                     group,
                     candidate: index,
                 })?;
-        let own_nodes: std::collections::HashSet<_> = OperatorNode::reachable(&candidate.node)
+        let own_nodes: HashSet<_> = OperatorNode::reachable(&candidate.node)
             .iter()
             .map(Rc::as_ptr)
             .collect();
@@ -139,18 +159,22 @@ pub fn compose(
                     child,
                 });
             }
-            replacements.insert(Rc::as_ptr(old), composed(memo, child, choice, done)?);
+            replacements.insert(
+                Rc::as_ptr(old),
+                composed(memo, child, choice, done, composing)?,
+            );
         }
         let node = replace(&candidate.node, &replacements);
         done.insert(group, Rc::clone(&node));
         Ok(node)
     }
     let mut done = HashMap::new();
+    let mut composing = HashSet::new();
     let (groups, roots): (Vec<_>, Vec<_>) = root_groups(memo)
         .map(|group| {
             Ok((
                 group,
-                QueryRoot::Operator(composed(memo, group, choice, &mut done)?),
+                QueryRoot::Operator(composed(memo, group, choice, &mut done, &mut composing)?),
             ))
         })
         .collect::<Result<Vec<_>, ComposeError>>()?
@@ -167,6 +191,24 @@ pub fn compose(
         .collect())
 }
 
+/// Whether `from` is `to` or reads it through the candidates `choice` names.
+fn reaches(memo: &CandidateMemo, choice: &MemoChoice, from: MemoGroupId, to: MemoGroupId) -> bool {
+    let mut pending = vec![from];
+    let mut seen = HashSet::new();
+    while let Some(group) = pending.pop() {
+        if group == to {
+            return true;
+        }
+        if !seen.insert(group) {
+            continue;
+        }
+        if let Some(&index) = choice.get(&group) {
+            pending.extend(&memo.candidates[group.0 as usize][index].children);
+        }
+    }
+    false
+}
+
 fn root_groups(memo: &CandidateMemo) -> impl DoubleEndedIterator<Item = MemoGroupId> + '_ {
     memo.groups
         .iter()
diff --git a/crates/plan-selection/src/lib.rs b/crates/plan-selection/src/lib.rs
index 890baa6fa..3f7ff498c 100644
--- a/crates/plan-selection/src/lib.rs
+++ b/crates/plan-selection/src/lib.rs
@@ -297,7 +297,7 @@ pub mod search;
 pub use search as pass;
 pub use search::{
     optimize, run_stage1_to_stage3, run_stage1_to_stage3_with, ExecutorCompileCheck,
-    ExecutorCompileError, OptimizationInput, OptimizationInputError, OptimizationPass,
+    ExecutorCompileError, MemoSteps, OptimizationInput, OptimizationInputError, OptimizationPass,
     OptimizeError, PassNameConflict, PassRegistry, PlanOutput, PlanningModels, QueryPlan,
     Stage1ToStage3Pass, Stage1ToStage3Run, Stage1ToStage3Search,
 };
diff --git a/crates/plan-selection/src/search/candidates/factoring.rs b/crates/plan-selection/src/search/candidates/factoring.rs
index 1e9359fe1..4ecc28828 100644
--- a/crates/plan-selection/src/search/candidates/factoring.rs
+++ b/crates/plan-selection/src/search/candidates/factoring.rs
@@ -80,8 +80,12 @@ impl CompatibilityMemo {
 /// certified_price checks every supplied producer; template-based proposal
 /// prices remain advisory. Execution and accuracy are recomputed from selected
 /// suppliers, never from the representative template's child witness.
+///
+/// `memo_candidate_roots` (root IDs, by memo group and candidate) is mapped
+/// to the new IDs without removing duplicates.
 pub(super) fn factor_terminal_readers(
     inventory: &mut super::inventory::CandidateInventory,
+    memo_candidate_roots: &mut [Vec<PhysicalCandidateId>],
     deadline: Option<std::time::Instant>,
 ) -> Result<usize, super::inventory::CandidateInventoryError> {
     use super::inventory::CandidateInventoryError;
@@ -231,6 +235,9 @@ pub(super) fn factor_terminal_readers(
     for group in &mut inventory.group_candidates {
         remap(group);
     }
+    for id in memo_candidate_roots.iter_mut().flatten() {
+        *id = new_ids[id.0];
+    }
     inventory.graph.candidates = candidates;
     inventory.templates = templates;
     inventory
@@ -336,7 +343,10 @@ mod tests {
         for assignment in [[0, 0], [0, 1], [1, 0], [1, 1]] {
             let original = with_scopes(terminal_fixture());
             let mut factored = terminal_fixture();
-            assert_eq!(factor_terminal_readers(&mut factored, None).unwrap(), 1);
+            assert_eq!(
+                factor_terminal_readers(&mut factored, &mut [], None).unwrap(),
+                1
+            );
             assert_eq!(factored.graph.candidates.len(), 3);
             let compressed = with_scopes(factored);
             assert!(
@@ -383,7 +393,10 @@ mod tests {
         };
         let original = with_scopes(build());
         let mut compact = build();
-        assert_eq!(factor_terminal_readers(&mut compact, None).unwrap(), 1);
+        assert_eq!(
+            factor_terminal_readers(&mut compact, &mut [], None).unwrap(),
+            1
+        );
         let compact = with_scopes(compact);
         let counts = |graph: &super::super::graph::CandidateDependencyGraph| {
             (
@@ -409,17 +422,26 @@ mod tests {
         let mut other = (**accuracy.templates[3].as_ref().unwrap()).clone();
         other.guarantee = Some(AccuracyGuarantee::exact("different proof contract"));
         accuracy.templates[3] = Some(Rc::new(other));
-        assert_eq!(factor_terminal_readers(&mut accuracy, None).unwrap(), 0);
+        assert_eq!(
+            factor_terminal_readers(&mut accuracy, &mut [], None).unwrap(),
+            0
+        );
         let mut eligibility = terminal_fixture();
         eligibility.graph.query_roots[1].compatible_candidates = vec![PhysicalCandidateId(3)];
-        assert_eq!(factor_terminal_readers(&mut eligibility, None).unwrap(), 0);
+        assert_eq!(
+            factor_terminal_readers(&mut eligibility, &mut [], None).unwrap(),
+            0
+        );
         let mut internal = terminal_fixture();
         internal.graph.candidates[0]
             .producer_requirements
             .push(ProducerRequirement {
                 compatible_producers: vec![PhysicalCandidateId(2)].into(),
             });
-        assert_eq!(factor_terminal_readers(&mut internal, None).unwrap(), 0);
+        assert_eq!(
+            factor_terminal_readers(&mut internal, &mut [], None).unwrap(),
+            0
+        );
     }
 
     // Logical ownership (including window semantics), closedness and required
diff --git a/crates/plan-selection/src/search/candidates/inventory.rs b/crates/plan-selection/src/search/candidates/inventory.rs
index 8085fa641..d3947a13f 100644
--- a/crates/plan-selection/src/search/candidates/inventory.rs
+++ b/crates/plan-selection/src/search/candidates/inventory.rs
@@ -62,14 +62,17 @@ pub(in crate::search) fn build_candidate_inventory(
     node_local_cost: impl FnMut(&OperatorNode) -> Result<f64, String>,
 ) -> Result<CandidateInventory, CandidateInventoryError> {
     build_candidate_inventory_before(memo, output_groups, node_local_cost, None)
+        .map(|(inventory, _)| inventory)
 }
 
+/// The inventory, and the root ID of each memo candidate, indexed like
+/// `CandidateMemo::candidates` (factoring may give several the same ID).
 pub(in crate::search) fn build_candidate_inventory_before(
     memo: &CandidateMemo,
     output_groups: &[MemoGroupId],
     node_local_cost: impl FnMut(&OperatorNode) -> Result<f64, String>,
     deadline: Option<std::time::Instant>,
-) -> Result<CandidateInventory, CandidateInventoryError> {
+) -> Result<(CandidateInventory, Vec<Vec<PhysicalCandidateId>>), CandidateInventoryError> {
     let mut inventory = build_with_compatibility_memo(
         memo,
         output_groups,
@@ -77,8 +80,13 @@ pub(in crate::search) fn build_candidate_inventory_before(
         deadline,
         &mut CompatibilityMemo::default(),
     )?;
-    crate::search::candidates::factoring::factor_terminal_readers(&mut inventory, deadline)?;
-    Ok(inventory)
+    let mut memo_candidate_roots = inventory.group_candidates.clone();
+    crate::search::candidates::factoring::factor_terminal_readers(
+        &mut inventory,
+        &mut memo_candidate_roots,
+        deadline,
+    )?;
+    Ok((inventory, memo_candidate_roots))
 }
 
 fn build_with_compatibility_memo(
diff --git a/crates/plan-selection/src/search/mod.rs b/crates/plan-selection/src/search/mod.rs
index e561b6f3e..1d7f0ba75 100644
--- a/crates/plan-selection/src/search/mod.rs
+++ b/crates/plan-selection/src/search/mod.rs
@@ -42,7 +42,8 @@ use asap_logical_asap_optimization::per_computation_candidates::PerComputationCa
 
 pub use pipeline::{
     run_stage1_to_stage3, run_stage1_to_stage3_from_pass1, run_stage1_to_stage3_with,
-    LogicalCandidate, PrunedCandidate, Stage1ToStage3Pass, Stage1ToStage3Run, Stage1ToStage3Search,
+    LogicalCandidate, MemoSteps, PrunedCandidate, Stage1ToStage3Pass, Stage1ToStage3Run,
+    Stage1ToStage3Search,
 };
 
 static BUILTIN_ACCURACY_MODEL: BuiltinAccuracyModel = BuiltinAccuracyModel;
diff --git a/crates/plan-selection/src/search/pipeline.rs b/crates/plan-selection/src/search/pipeline.rs
index 1d5eb59a4..50740665a 100644
--- a/crates/plan-selection/src/search/pipeline.rs
+++ b/crates/plan-selection/src/search/pipeline.rs
@@ -6,6 +6,8 @@
 
 use std::rc::Rc;
 
+use asap_logical_asap_optimization::memo::candidates::CandidateMemo;
+use asap_logical_asap_optimization::memo::enumeration::MemoChoice;
 use asap_logical_asap_optimization::memo::LogicalMemo;
 
 use asap_types::ir::schema::schema_support::with_promql_series_identity;
@@ -38,6 +40,24 @@ pub struct LogicalCandidate {
     pub pass2: Option<Pass2Candidate>,
 }
 
+/// The memo after each step of the planning round whose plan was selected
+/// (or of the last round when none was), as the search built it.
+#[derive(Debug, Clone)]
+pub struct MemoSteps {
+    /// After hash-consing the frontends' roots: groups, no candidates.
+    pub stage0: CandidateMemo,
+    /// After Pass 1 (per-computation candidates, then accuracy-scoped sizes).
+    pub pass1: CandidateMemo,
+    /// After local window composition (pane candidates).
+    pub pass2: CandidateMemo,
+    /// After concrete summary-state group expansion: the memo the search
+    /// selects from.
+    pub concrete_states: CandidateMemo,
+    /// The selected plan's candidate for each group of `concrete_states` it
+    /// uses, or why there is none.
+    pub selected_choice: Result<MemoChoice, String>,
+}
+
 /// A composed logical candidate that physical ASAP-aware optimization could
 /// not implement, with the reason.
 #[derive(Debug, Clone, PartialEq)]
@@ -78,6 +98,9 @@ pub struct Stage1ToStage3Run<Id> {
     /// implements, with its roots as Stage 1 composed them (before Stage 3
     /// sized them): what Stage 2 implemented.
     pub stage1_selected: Option<LogicalCandidate>,
+    /// The memo after each step, and the selected plan's choice over it;
+    /// `None` when the search built no memo.
+    pub memo_steps: Option<MemoSteps>,
 }
 
 impl<Id> Stage1ToStage3Run<Id> {
@@ -236,6 +259,7 @@ fn run_with_initial_memo<Id: Clone + std::fmt::Debug>(
     run.stage1_logical_asap_optimization = archive.logical;
     run.stage2_physical_asap_optimization = archive.physical;
     run.stage2_pruned = archive.pruned;
+    run.memo_steps = archive.memo_steps;
     run
 }
 
@@ -280,6 +304,7 @@ fn memo_run<Id: Clone + std::fmt::Debug>(
                 roots: Ok(roots),
                 pass2: None,
             }),
+        memo_steps: None,
     }
 }
 
diff --git a/crates/plan-selection/src/search/route.rs b/crates/plan-selection/src/search/route.rs
index eff451fcd..8847645c2 100644
--- a/crates/plan-selection/src/search/route.rs
+++ b/crates/plan-selection/src/search/route.rs
@@ -1,6 +1,8 @@
 //! Driver integration for the explicit, bounded candidate-connection search.
 use crate::{CostModel, PlanningModels, SelectionError, Stage1ToStage3Search};
-use asap_logical_asap_optimization::memo::LogicalMemo;
+use asap_logical_asap_optimization::memo::candidates::CandidateMemo;
+use asap_logical_asap_optimization::memo::enumeration::MemoChoice;
+use asap_logical_asap_optimization::memo::{LogicalMemo, MemoGroupId};
 use asap_logical_asap_optimization::per_computation_candidates::PerComputationCandidates;
 use asap_types::ir::{OperatorNode, QueryRoot};
 use asap_types::workload::{DataWorkload, QueryWorkloadEntry};
@@ -19,6 +21,8 @@ pub(crate) struct CandidateArchive {
     pub logical: Vec<crate::search::pipeline::LogicalCandidate>,
     pub physical: Vec<asap_physical_asap_optimization::PhysicalWorkloadPlan>,
     pub pruned: Vec<crate::search::pipeline::PrunedCandidate>,
+    /// The memo steps of the round whose plan was selected, else the last round's.
+    pub memo_steps: Option<crate::search::pipeline::MemoSteps>,
 }
 
 // The driver reports price search and lexicographic/Pareto search uniformly,
@@ -52,6 +56,13 @@ struct DomainProgress {
     refinements: usize,
     report: Option<crate::CandidateConnectionReport>,
     local_memo: Option<asap_logical_asap_optimization::memo::candidates::CandidateMemo>,
+    /// The memo after Stage 0 and after Pass 1, kept with `local_memo`.
+    pass1_steps: Option<(
+        asap_logical_asap_optimization::memo::candidates::CandidateMemo,
+        asap_logical_asap_optimization::memo::candidates::CandidateMemo,
+    )>,
+    /// This round's memo steps, with its selected plan's ID when it has one.
+    memo_steps: Option<(Option<String>, crate::search::pipeline::MemoSteps)>,
     previous_domain:
         Option<asap_logical_asap_optimization::memo::state_configurations::PaneWidthDomain>,
 }
@@ -102,16 +113,29 @@ pub(crate) fn candidate_connection_search<Id: Clone>(
         && total_ms as f64 - prior_ms >= 1_000.0
         && search.max_evaluations.unwrap_or(128) >= 4;
     if !seed_enabled {
-        return search_domain(
+        let mut progress = DomainProgress::default();
+        let result = search_domain(
             initial,
             context,
             search,
             local_candidate_generation_ms,
             archive,
             PaneWidthDomain::Complete,
-            &mut DomainProgress::default(),
+            &mut progress,
         );
+        archive.memo_steps = progress.memo_steps.map(|(_, steps)| steps);
+        return result;
     }
+    // Each round's memo steps, with its selected plan's namespaced ID; the
+    // archive keeps the last round's for a search that ends without a plan.
+    let mut memo_rounds = Vec::new();
+    let mut record_round =
+        |archive: &mut CandidateArchive, progress: &mut DomainProgress, namespace: &str| {
+            if let Some((plan, steps)) = progress.memo_steps.take() {
+                archive.memo_steps = Some(steps.clone());
+                memo_rounds.push((plan.map(|id| format!("{namespace}{id}")), steps));
+            }
+        };
     let seed_ms = (((total_ms as f64 - prior_ms) / 4.0) as u64).min(5_000);
     let mut seed_progress = DomainProgress::default();
     let mut seed_archive = CandidateArchive::default();
@@ -129,6 +153,7 @@ pub(crate) fn candidate_connection_search<Id: Clone>(
         &mut seed_progress,
     )
     .map(|plan| namespace_round(plan, "seed-"));
+    record_round(archive, &mut seed_progress, "seed-");
     let seed_elapsed = started.elapsed();
     if seed.is_err() && !seed_progress.budget_stopped && !seed_progress.infeasible {
         return seed;
@@ -137,6 +162,7 @@ pub(crate) fn candidate_connection_search<Id: Clone>(
     let full_started = Instant::now();
     let mut full_progress = DomainProgress {
         local_memo: seed_progress.local_memo.take(),
+        pass1_steps: seed_progress.pass1_steps.take(),
         previous_domain: seed_progress.previous_domain,
         ..Default::default()
     };
@@ -199,6 +225,7 @@ pub(crate) fn candidate_connection_search<Id: Clone>(
         let complete = domain == PaneWidthDomain::Complete;
         let mut round_progress = DomainProgress {
             local_memo: full_progress.local_memo.take(),
+            pass1_steps: full_progress.pass1_steps.take(),
             previous_domain: full_progress.previous_domain,
             ..Default::default()
         };
@@ -224,7 +251,13 @@ pub(crate) fn candidate_connection_search<Id: Clone>(
             &mut round_progress,
         )
         .map(|plan| namespace_round(plan, &format!("pane-round-{}-", rounds.len() - 1)));
+        record_round(
+            archive,
+            &mut round_progress,
+            &format!("pane-round-{}-", rounds.len() - 1),
+        );
         full_progress.local_memo = round_progress.local_memo.take();
+        full_progress.pass1_steps = round_progress.pass1_steps.take();
         full_progress.previous_domain = round_progress.previous_domain;
         full_progress.refinements += round_progress.refinements;
         completed_full_domain = complete && round_progress.catalog_completed;
@@ -412,6 +445,20 @@ pub(crate) fn candidate_connection_search<Id: Clone>(
     }
     result.0.search.candidates_checked =
         (seed_progress.refinements + full_progress.refinements) as u64;
+    // A record only: a plan whose round recorded no memo keeps the last one,
+    // marked as not the selected plan's.
+    match memo_rounds
+        .into_iter()
+        .find(|(plan, _)| plan.as_ref() == Some(&result.1.id))
+    {
+        Some((_, steps)) => archive.memo_steps = Some(steps),
+        None => {
+            if let Some(steps) = &mut archive.memo_steps {
+                steps.selected_choice =
+                    Err("the selected plan's planning round is not recorded".into());
+            }
+        }
+    }
     Ok(result)
 }
 
@@ -818,6 +865,10 @@ fn search_domain<Id: Clone>(
     let mut memo = match progress.local_memo.take() {
         Some(memo) => memo,
         None => {
+            let stage0 = CandidateMemo {
+                candidates: vec![Vec::new(); initial.groups.len()],
+                groups: initial.groups.clone(),
+            };
             let mut memo = try_populate_pass1(
                 initial,
                 &pruned.as_ref().expect("first round pruned").inventory,
@@ -830,6 +881,7 @@ fn search_domain<Id: Clone>(
                 Instant::now().checked_add(remaining()),
             )
             .map_err(|error| unsupported(&error))?;
+            progress.pass1_steps = Some((stage0, memo.clone()));
             memo
         }
     };
@@ -858,16 +910,31 @@ fn search_domain<Id: Clone>(
             unsupported(&error.to_string())
         })?
         .memo;
+    progress.memo_steps = progress.pass1_steps.as_ref().map(|(stage0, pass1)| {
+        (
+            None,
+            crate::search::pipeline::MemoSteps {
+                stage0: stage0.clone(),
+                pass1: pass1.clone(),
+                pass2: progress.local_memo.clone().expect("kept above"),
+                concrete_states: memo.clone(),
+                selected_choice: Err("no plan was selected".into()),
+            },
+        )
+    });
     let memo_expansion_ms = started.elapsed().as_secs_f64() * 1000.0;
     check_budget("memo rule expansion", progress)?;
     let groups = memo.groups.len();
     let logical_candidates = memo.candidates.iter().map(Vec::len).sum();
     let started = Instant::now();
-    let source = build_candidate_inventory_before(&memo, &output_groups, |_| Ok(0.0), deadline)
-        .map_err(|error| {
-            progress.budget_stopped = matches!(error, CandidateInventoryError::DeadlineExceeded(_));
-            unsupported(&error.to_string())
-        })?;
+    let (source, memo_candidate_roots) =
+        build_candidate_inventory_before(&memo, &output_groups, |_| Ok(0.0), deadline).map_err(
+            |error| {
+                progress.budget_stopped =
+                    matches!(error, CandidateInventoryError::DeadlineExceeded(_));
+                unsupported(&error.to_string())
+            },
+        )?;
     let immediate_candidates = source.graph.candidates.len();
 
     let mut configured = enumerate_candidate_configurations_before(
@@ -1106,11 +1173,103 @@ fn search_domain<Id: Clone>(
         .ok_or_else(|| unsupported("validated plan has no selected graph"))?;
     let logical = selected_logical_roots(&configured, selected, &roots)
         .map_err(|error| unsupported(&error))?;
+    if let Some((plan, steps)) = &mut progress.memo_steps {
+        *plan = Some(physical.id.clone());
+        steps.selected_choice = selected_memo_choice(
+            &steps.concrete_states,
+            &source,
+            &memo_candidate_roots,
+            &configured,
+            selected,
+        );
+    }
     selection.search.candidates_checked = result.refinements as u64;
     selection.search.candidate_connections = Some(report);
     Ok((selection, physical, logical))
 }
 
+/// The selected plan's memo candidate for each group it uses: the memo
+/// candidate whose root each selected candidate is. Factoring may give several
+/// memo candidates of a group one root (identical terminal readers of
+/// different inputs); the one reading the selected producers' groups is taken.
+fn selected_memo_choice(
+    memo: &CandidateMemo,
+    source: &crate::search::candidates::inventory::CandidateInventory,
+    memo_candidate_roots: &[Vec<crate::search::candidates::graph::PhysicalCandidateId>],
+    configured: &crate::search::candidates::configurations::CandidateConfigurationInventory,
+    selected: &crate::search::candidates::graph::SelectedCandidateGraph,
+) -> Result<MemoChoice, String> {
+    use std::collections::HashMap;
+    let mut memo_candidates_of = HashMap::<_, Vec<(MemoGroupId, usize)>>::new();
+    for (group, roots) in memo_candidate_roots.iter().enumerate() {
+        for (index, &root) in roots.iter().enumerate() {
+            memo_candidates_of
+                .entry(root)
+                .or_default()
+                .push((MemoGroupId(group as u32), index));
+        }
+    }
+    let source_of = |id: crate::search::candidates::graph::PhysicalCandidateId| {
+        configured.configurations[id.0].source_candidate
+    };
+    let mut producer_groups = HashMap::<_, Vec<MemoGroupId>>::new();
+    for connection in &selected.connections {
+        producer_groups
+            .entry(connection.consumer)
+            .or_default()
+            .push(source.graph.candidates[source_of(connection.producer).0].group);
+    }
+    let mut choice = MemoChoice::new();
+    for &id in &selected.selected_candidates {
+        let Some(options) = memo_candidates_of.get(&source_of(id)) else {
+            continue; // a candidate's private node
+        };
+        let reads = |&&(group, index): &&(MemoGroupId, usize)| {
+            producer_groups.get(&id).is_none_or(|read| {
+                read.iter().all(|&child| {
+                    child == group
+                        || memo.candidates[group.0 as usize][index]
+                            .children
+                            .contains(&child)
+                })
+            })
+        };
+        let &(group, index) = options.iter().find(reads).ok_or_else(|| {
+            format!(
+                "selected candidate {} reads groups none of its memo candidates read",
+                id.0
+            )
+        })?;
+        if let Some(previous) = choice.insert(group, index) {
+            if previous != index {
+                return Err(format!(
+                    "the selected plan implements group {} with two candidates, {previous} and {index}",
+                    group.0
+                ));
+            }
+        }
+    }
+    // Every group the chosen candidates need, from the query roots, is chosen.
+    let mut pending: Vec<_> = (0..memo.groups.len())
+        .filter(|&group| !memo.groups[group].roots_of.is_empty())
+        .map(|group| MemoGroupId(group as u32))
+        .collect();
+    let mut seen = std::collections::HashSet::new();
+    while let Some(group) = pending.pop() {
+        if !seen.insert(group) {
+            continue;
+        }
+        let index = choice.get(&group).ok_or_else(|| {
+            format!(
+                "the selected plan uses group {} but no candidate of it is selected",
+                group.0
+            )
+        })?;
+        pending.extend(&memo.candidates[group.0 as usize][*index].children);
+    }
+    Ok(choice)
+}
+
 fn selected_logical_roots(
     configured: &crate::search::candidates::configurations::CandidateConfigurationInventory,
     selected: &crate::search::candidates::graph::SelectedCandidateGraph,
diff --git a/tools/dag-viewer/README.md b/tools/dag-viewer/README.md
index 7ddde540f..c6fb938ef 100644
--- a/tools/dag-viewer/README.md
+++ b/tools/dag-viewer/README.md
@@ -319,6 +319,23 @@ are ignored, `stage_pipeline`'s default.
   candidates they come from.
 - When Pass 1 fails, Stage 1 has `error` and no candidates. When selection
   fails, `selected` is null, with the rejections or with `error`.
+- `memo` (left out with `--no-memo`) is the memo the search built, from
+  the planning round whose plan was selected: `steps`, one per memo step
+  (`stage0`, `pass1`, `pass2`: local window composition, `concrete_states`:
+  the Pass 2 memo rules and the concrete summary-state groups), each with
+  its groups (`id`, `label`, `children`, `parents`, `queries`, `roots_of`,
+  `dag`) and their candidates (`candidate_count`,
+  `candidate_count_by_origin`, `candidates_capped`, and the first
+  `--max-memo-candidates`, default 64, under `candidates`: `index`,
+  `implements`, `children`, `origin`, `budget_share`, `added`, `label`,
+  `dag`, `group_of_node`); `selected_choice`, the selected plan's
+  candidate index per group of the last step (null with
+  `selected_choice_unavailable` when it has none); and `enumeration`: each
+  step's number of candidate DAGs up to `--memo-enumeration-limit` (default
+  1000) under `per_step`, and the first `--max-enumerated` (default 200)
+  `choices` of `step` (the last step enumerated completely within that
+  many, else the last step), each composed into its `dag`. The page does
+  not draw it yet. `examples/memo-ratio-of-quantiles.json` has one.
 
 The viewer checks the document before showing it: one root per query, node,
 edge and root references, `scalar_roots` positions, `from_logical`, the Stage 3 ids, costs and
@@ -346,7 +363,7 @@ shown. If a check fails, it shows the problems instead.
   `deployment_capabilities` and `cost_model`) is committed under
   `examples/`. The committed documents are
   `examples/planner-layering-example1.json` and workload-01 of each
-  ASAPQuery set and the six sharing examples. Historical snapshots retain
+  ASAPQuery set, the six sharing examples and the memo example. Historical snapshots retain
   their original plans; `crates/devtools/tests/stage_pipeline.rs` checks input
   consistency and newly generated plan validity and materialized-view linkage.
   Timed searches are not required to reproduce snapshot IDs or prove optimality.
@@ -364,6 +381,9 @@ shown. If a check fails, it shows the problems instead.
   data retained, AWS Fargate prices and accuracy guarantees enforced. Their
   `examples.json` entries name `"search": "candidate-connections"`, which server.py
   passes as `--search`; their documents are committed under `examples/`.
+  `ratio-of-quantiles-5m.json` (one ratio of two equal per-series quantiles
+  plus a third, every minute, ε = 0.01, δ = 0.001) shows the `memo`
+  section: the memo after each step.
 - `cytoscape.min.js`, `dagre.min.js`, `cytoscape-dagre.js`: vendored, so the
   page works offline.
 
diff --git a/tools/dag-viewer/examples.json b/tools/dag-viewer/examples.json
index a4cc4b554..9d25e3d51 100644
--- a/tools/dag-viewer/examples.json
+++ b/tools/dag-viewer/examples.json
@@ -145,5 +145,19 @@
     "search": "candidate-connections",
     "file": "examples/memo-rollupheavy-t11-service-endpoint-5m.json",
     "story": "Sketch rollup: W-RollupHeavy template 11, distinct users over 5 min by (service, endpoint) and by (service); the coarser grouping merges the finer one's KMV states, sized for both."
+  },
+  {
+    "id": "memo-ratio-of-quantiles",
+    "name": "Ratio of quantiles (memo after each step)",
+    "workload": "memo-examples/promql/ratio-of-quantiles-5m.json",
+    "deployment_capabilities": {
+      "raw_data_retained": true,
+      "query_time_results_retained": false
+    },
+    "cost_model": "aws-fargate-us-east-1",
+    "accuracy_guarantees": "enforced",
+    "search": "candidate-connections",
+    "file": "examples/memo-ratio-of-quantiles.json",
+    "story": "The memo through the stages: avg by (job) (quantile_over_time(0.5, data[5m]) / quantile_over_time(0.5, data[5m]) + quantile_over_time(0.9, data[5m])) every minute, within ε = 0.01, δ = 0.001. The two equal quantiles share one group (each series' identity is a unique key); Pass 1 offers 7 candidates for each quantile group (49 candidate DAGs), Pass 2 adds pane candidates, and concrete state groups add one group per pane chain. The document's memo section lists each step's groups and candidates, the selected plan's choice and the enumerated candidate DAGs."
   }
 ]
diff --git a/tools/dag-viewer/examples/memo-ratio-of-quantiles.json b/tools/dag-viewer/examples/memo-ratio-of-quantiles.json
new file mode 100644
index 000000000..b3f54cc32
--- /dev/null
+++ b/tools/dag-viewer/examples/memo-ratio-of-quantiles.json
@@ -0,0 +1,380940 @@
+{
+  "accuracy_guarantees": "enforced",
+  "deployment_capabilities": {
+    "query_time_results_retained": false,
+    "raw_data_retained": true,
+    "supported_summaries": [
+      {
+        "family": "UnivMon",
+        "readouts": [
+          "Total",
+          "Distinct",
+          "FrequencyL2",
+          "FrequencyEntropy"
+        ]
+      },
+      {
+        "family": "Kll",
+        "readouts": [
+          "Quantile"
+        ]
+      },
+      {
+        "family": "Cms",
+        "readouts": [
+          "Total"
+        ]
+      },
+      {
+        "family": "Hll",
+        "readouts": [
+          "Distinct"
+        ]
+      },
+      {
+        "family": "DDSketch",
+        "readouts": [
+          "Quantile"
+        ]
+      },
+      {
+        "family": "CmsWithHeap",
+        "readouts": [
+          "TopK"
+        ]
+      },
+      {
+        "family": "Kmv",
+        "readouts": [
+          "Distinct"
+        ]
+      },
+      {
+        "family": "CountSketchWithHeap",
+        "readouts": [
+          "TopK"
+        ]
+      }
+    ]
+  },
+  "format": "asap-stage-pipeline/v1",
+  "memo": {
+    "enumeration": {
+      "choices": [
+        {
+          "budget_share_1": true,
+          "choice": {
+            "0": 0,
+            "1": 0,
+            "2": 0,
+            "3": 0,
+            "4": 0,
+            "5": 0,
+            "6": 0
+          },
+          "dag": {
+            "nodes": [
+              {
+                "guarantee": {
+                  "provenance": [
+                    {
+                      "kind": "exact",
+                      "reason": "exact over exact inputs"
+                    }
+                  ],
+                  "spec": {
+                    "accuracy_metric": "absolute",
+                    "accuracy_scope": "per_value",
+                    "error": {
+                      "op": "zero"
+                    },
+                    "failure_probability": {
+                      "op": "zero"
+                    }
+                  }
+                },
+                "materialization": "NotMaterialized",
+                "operator": {
+                  "NonASAP": {
+                    "Scan": {
+                      "predicates": [],
+                      "schema": {
+                        "closed": true,
+                        "fields": [
+                          {
+                            "dtype": {
+                              "Plain": "timestamp"
+                            },
+                            "name": "ts",
+                            "nullable": false,
+                            "table": null
+                          },
+                          {
+                            "dtype": {
+                              "Plain": "float64"
+                            },
+                            "name": "value",
+                            "nullable": false,
+                            "table": null
+                          },
+                          {
+                            "dtype": {
+                              "Plain": "utf8"
+                            },
+                            "name": "job",
+                            "nullable": true,
+                            "table": null
+                          },
+                          {
+                            "dtype": {
+                              "Plain": "utf8"
+                            },
+                            "name": "$promql_series_identity",
+                            "nullable": false,
+                            "table": null
+                          }
+                        ],
+                        "time_index": 0,
+                        "unique_keys": [
+                          [
+                            3,
+                            0
+                          ]
+                        ]
+                      },
+                      "source": {
+                        "TimeSeries": {
+                          "metric": "data"
+                        }
+                      }
+                    }
+                  }
+                },
+                "result_kind": "instant_vector",
+                "schema": {
+                  "closed": true,
+                  "fields": [
+                    {
+                      "dtype": {
+                        "Plain": "timestamp"
+                      },
+                      "name": "ts",
+                      "nullable": false,
+                      "table": null
+                    },
+                    {
+                      "dtype": {
+                        "Plain": "float64"
+                      },
+                      "name": "value",
+                      "nullable": false,
+                      "table": null
+                    },
+                    {
+                      "dtype": {
+                        "Plain": "utf8"
+                      },
+                      "name": "job",
+                      "nullable": true,
+                      "table": null
+                    },
+                    {
+                      "dtype": {
+                        "Plain": "utf8"
+                      },
+                      "name": "$promql_series_identity",
+                      "nullable": false,
+                      "table": null
+                    }
+                  ],
+                  "time_index": 0,
+                  "unique_keys": [
+                    [
+                      3,
+                      0
+                    ]
+                  ]
+                },
+                "timing": null
+              },
+              {
+                "guarantee": {
+                  "provenance": [
+                    {
+                      "kind": "exact",
+                      "reason": "exact over exact inputs"
+                    }
+                  ],
+                  "spec": {
+                    "accuracy_metric": "absolute",
+                    "accuracy_scope": "per_value",
+                    "error": {
+                      "op": "zero"
+                    },
+                    "failure_probability": {
+                      "op": "zero"
+                    }
+                  }
+                },
+                "materialization": "NotMaterialized",
+                "operator": {
+                  "NonASAP": {
+                    "TimeRange": {
+                      "child": 0,
+                      "kind": "range",
+                      "range": {
+                        "nanos": 0,
+                        "secs": 300
+                      }
+                    }
+                  }
+                },
+                "result_kind": "range_vector",
+                "schema": {
+                  "closed": true,
+                  "fields": [
+                    {
+                      "dtype": {
+                        "Plain": "timestamp"
+                      },
+                      "name": "ts",
+                      "nullable": false,
+                      "table": null
+                    },
+                    {
+                      "dtype": {
+                        "Plain": "float64"
+                      },
+                      "name": "value",
+                      "nullable": false,
+                      "table": null
+                    },
+                    {
+                      "dtype": {
+                        "Plain": "utf8"
+                      },
+                      "name": "job",
+                      "nullable": true,
+                      "table": null
+                    },
+                    {
+                      "dtype": {
+                        "Plain": "utf8"
+                      },
+                      "name": "$promql_series_identity",
+                      "nullable": false,
+                      "table": null
+                    }
+                  ],
+                  "time_index": 0,
+                  "unique_keys": [
+                    [
+                      3,
+                      0
+                    ]
+                  ]
+                },
+                "timing": null
+              },
+              {
+                "guarantee": {
+                  "provenance": [
+                    {
+                      "kind": "exact",
+                      "reason": "exact over exact inputs"
+                    }
+                  ],
+                  "spec": {
+                    "accuracy_metric": "absolute",
+                    "accuracy_scope": "per_value",
+                    "error": {
+                      "op": "zero"
+                    },
+                    "failure_probability": {
+                      "op": "zero"
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+            "cost_per_second": 1.1244000596263345e-7,
+            "cpu_core_seconds_per_second": 0.01,
+            "detail": "time range 300s: keep 600000000 of 600000000 rows; x 0.0167/s; holds 48 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "TimeRange",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "10": {
+            "cost_per_second": 1.8769813167266545e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "operator: pass 10000 rows; x 0.0167/s; holds 24 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "Project",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "11": {
+            "cost_per_second": 1.8769813167266545e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "operator: pass 10000 rows; x 0.0167/s; holds 24 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "BinaryOp",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "12": {
+            "cost_per_second": 1.8769813167266545e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "operator: pass 10000 rows; x 0.0167/s; holds 24 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "Project",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "2": {
+            "cost_per_second": 8.211830962206423e-7,
+            "cpu_core_seconds_per_second": 0.02,
+            "detail": "hash aggregate 600000000 rows into 10000 groups; x 0.0167/s; holds 4800320000 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "Aggregate",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "3": {
+            "cost_per_second": 1.8799626334533096e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "operator: pass 10000 rows; x 0.0167/s; holds 48 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "BinaryOp",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "4": {
+            "cost_per_second": 8.211830962206423e-7,
+            "cpu_core_seconds_per_second": 0.02,
+            "detail": "hash aggregate 600000000 rows into 10000 groups; x 0.0167/s; holds 4800320000 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "Aggregate",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "5": {
+            "cost_per_second": 1.8799626334533096e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "operator: pass 10000 rows; x 0.0167/s; holds 48 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "BinaryOp",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "6": {
+            "cost_per_second": 7.143805695527792e-11,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "build exact Sum accumulator into 10000 states: 10000 rows x depth 1; x 0.0167/s; holds 560000 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "SummaryAgg",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "7": {
+            "cost_per_second": 1.874e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "finalize 10000 accumulators; x 0.0167/s",
+            "multiplier": 1,
+            "operator": "FinalizeExactAccumulator",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "8": {
+            "cost_per_second": 7.143805695527792e-11,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "build exact Count accumulator into 10000 states: 10000 rows x depth 1; x 0.0167/s; holds 560000 bytes for 6480.1 ms",
+            "multiplier": 1,
+            "operator": "SummaryAgg",
+            "price_source": "analytical",
+            "timing": "query_time"
+          },
+          "9": {
+            "cost_per_second": 1.874e-12,
+            "cpu_core_seconds_per_second": 1.6666666666666665e-7,
+            "detail": "finalize 10000 accumulators; x 0.0167/s",
+            "multiplier": 1,
+            "operator": "FinalizeExactAccumulator",
+            "price_source": "analytical",
+            "timing": "query_time"
+          }
+        },
+        "source": "analytical-cost-v2 (illustrative statistics)",
+        "usage": {
+          "average_memory_bytes": 1037004511.152396,
+          "cpu_ops_per_second": 60001499.99999998,
+          "disk_bytes": 28800000000,
+          "latency_per_query": [
+            {
+              "compaction_ms": 0.0,
+              "query_ms": 6480.09
+            }
+          ],
+          "peak_cpu_cores": 1,
+          "peak_memory_bytes": 9601760264,
+          "scanned_bytes_per_second": 480000000.0
+        }
+      }
+    },
+    "front": [],
+    "materialized_views": [],
+    "pane_retention_ms": {},
+    "rejected": [],
+    "rejected_by_cause": {},
+    "search": {
+      "algorithm": "candidate-connections",
+      "candidate_connections": {
+        "calibration_factor": 1.0,
+        "calibration_scope": "not_required",
+        "catalog_exhausted": false,
+        "catalog_scope": "Pass 1, local panes, shared summary/pane states, exact and sketch rollups, compatible TopK ranking reuse, and scan widening; finite capacity, pane-width, horizon, materialization and execution-scope configurations",
+        "certified_query_cuts": 22,
+        "compatible_connections": 9594,
+        "direct_cost_best_validated_cost": null,
+        "direct_cost_fallback_reasons": [
+          "joint pricing: interface generation exhausted its reserved budget"
+        ],
+        "direct_cost_solve_calls": 0,
+        "direct_cost_validated_plans": 0,
+        "early_query_pruning_counts": {
+          "choices_checked": 0,
+          "choices_removed": 0,
+          "final_choices_retained": 0,
+          "non_summary_choices_retained": 0,
+          "queries_skipped": 1,
+          "shared_producer_choices_retained": 0
+        },
+        "early_query_pruning_examples": [],
+        "early_query_pruning_ms": 0.016875,
+        "evaluation_complete": false,
+        "full_catalog_completed": false,
+        "full_planning_ms": 25118.286811,
+        "groups": 354,
+        "immediate_candidates": 5166,
+        "independent_components": 1,
+        "inventory_construction_ms": 657.100107,
+        "inventory_pane_width_domain": "Expanding { max_parts: 64 }",
+        "joint_price_solve_calls": 0,
+        "local_candidate_generation_ms": 0.285385,
+        "logical_candidates": 1738,
+        "lower_bound": null,
+        "max_refinements": 128,
+        "memo_expansion_ms": 939.9990129999999,
+        "model_construction_ms": 298.499568,
+        "objective": "monetary_cost",
+        "output_references": 1,
+        "pane_width_rounds": [
+          "SeedGrids",
+          "Expanding { max_parts: 4 }",
+          "Expanding { max_parts: 8 }",
+          "Expanding { max_parts: 16 }",
+          "Expanding { max_parts: 32 }",
+          "Expanding { max_parts: 64 }"
+        ],
+        "pane_widths_pending": true,
+        "peak_milp_constraints": 31547,
+        "peak_milp_variables": 21948,
+        "physical_configurations": 6175,
+        "refinements": 28,
+        "relative_gap": null,
+        "rounded_down_cost_bounds": 0,
+        "search_and_validation_ms": 28483.715270999997,
+        "seed_fallback_reason": null,
+        "seed_planning_ms": 5015.112728,
+        "seed_selected": false,
+        "solve_calls": 34,
+        "solver_ms": 23292.61746,
+        "status": "time_or_evaluation_limit_with_validated_incumbent",
+        "stored_supplier_ids": 6172,
+        "structurally_removed_candidates": 3785,
+        "structurally_removed_connections": 5862,
+        "supplier_sets": 3782,
+        "time_limit_ms": 30000,
+        "validation_ms": 56.773236999999995,
+        "validation_rejection_counts": {
+          "no_accuracy_guarantee": 22
+        },
+        "validation_rejection_examples": [
+          "no_accuracy_guarantee: q0: the output has no guarantee, and the deployment has no evidence for it, so it cannot meet target AccuracyTarget { accuracy_metric: None, max_error: 0.01, failure_probability: Some(0.001), accuracy_scope: WholeResult }"
+        ]
+      },
+      "candidates_checked": 28,
+      "incumbent_cost": 2.407114219349679e-6,
+      "runner_up_cost_per_second": null
+    },
+    "search_rejected": [],
+    "selected": "pane-round-5-joint-plan-1"
+  },
+  "workload": {
+    "data_workload": {
+      "arrival": {
+        "ingesting": {
+          "rows_per_second": 2000000.0
+        }
+      },
+      "sources": {
+        "data": {
+          "max_distinct_per_evaluation": null,
+          "metric_type": "gauge",
+          "sample_interval": 5,
+          "series_count": 10000,
+          "stream_norms": null,
+          "values_non_negative": true
+        }
+      }
+    },
+    "queries": [
+      {
+        "id": "q1",
+        "language": "promql",
+        "predictability": {
+          "predictable": {
+            "known_at": null
+          }
+        },
+        "recurrence": {
+          "repeated": {
+            "fixed_interval": 60000
+          }
+        },
+        "requirements": {
+          "accuracy": {
+            "accuracy_scope": "whole_result",
+            "failure_probability": 0.001,
+            "max_error": 0.01
+          },
+          "default_metric": "absolute",
+          "repeat_interval_ms": 60000
+        },
+        "text": "avg by (job) (quantile_over_time(0.5, data[5m]) / quantile_over_time(0.5, data[5m]) + quantile_over_time(0.9, data[5m]))"
+      }
+    ]
+  }
+}
diff --git a/tools/dag-viewer/memo-examples/promql/ratio-of-quantiles-5m.json b/tools/dag-viewer/memo-examples/promql/ratio-of-quantiles-5m.json
new file mode 100644
index 000000000..af180ad3b
--- /dev/null
+++ b/tools/dag-viewer/memo-examples/promql/ratio-of-quantiles-5m.json
@@ -0,0 +1,41 @@
+{
+  "query_workload": {
+    "language": "promql",
+    "query_batch": null,
+    "repeating_queries": [
+      {
+        "query": "avg by (job) (quantile_over_time(0.5, data[5m]) / quantile_over_time(0.5, data[5m]) + quantile_over_time(0.9, data[5m]))",
+        "demand": {
+          "fixed_interval": 60000
+        },
+        "requirements": {
+          "accuracy": {
+            "max_error": 0.01,
+            "failure_probability": 0.001
+          },
+          "max_latency_ms": null
+        },
+        "predictability": {
+          "predictable": {
+            "known_at": null
+          }
+        }
+      }
+    ]
+  },
+  "data_workload": {
+    "arrival": {
+      "ingesting": {
+        "rows_per_second": 2000000.0
+      }
+    },
+    "sources": {
+      "data": {
+        "series_count": 10000,
+        "metric_type": "gauge",
+        "values_non_negative": true,
+        "sample_interval": 5
+      }
+    }
+  }
+}
diff --git a/tools/dag-viewer/stages.test.mjs b/tools/dag-viewer/stages.test.mjs
index 2c80f3721..910aad861 100644
--- a/tools/dag-viewer/stages.test.mjs
+++ b/tools/dag-viewer/stages.test.mjs
@@ -162,6 +162,14 @@ test('a memo-MILP document shows its shared sketch, readers and certified summar
   assert.equal(view.groups.find((g) => g.id === 'G3').chosen, 'Panes · Project · at S1');
 });
 
+test('the validator accepts a document with and without its memo section', () => {
+  const doc = memoDoc('ratio-of-quantiles');
+  assert.deepEqual(doc.memo.steps.map((s) => s.step), ['stage0', 'pass1', 'pass2', 'concrete_states']);
+  assert.deepEqual([...call('validateStagePipeline', doc)], []);
+  delete doc.memo;
+  assert.deepEqual([...call('validateStagePipeline', doc)], []);
+});
+
 test('a memo-MILP document shows a sketch rollup, a union schedule and a widened scan', () => {
   const rollup = call('memoSearchView', memoDoc('rollupheavy-t11-service-endpoint-5m'));
   assert.match(rollup.groups.find((g) => g.id === 'G3').chosen, /^Rollup · Project · reads G2, G6 · at S1$/);
diff --git a/tools/dag-viewer/test_viewer.py b/tools/dag-viewer/test_viewer.py
index bf36043ea..5ef731d63 100644
--- a/tools/dag-viewer/test_viewer.py
+++ b/tools/dag-viewer/test_viewer.py
@@ -825,7 +825,7 @@ def test_memo_examples_name_a_search_and_their_own_workload(self):
         """Each memo-search example is planned with `--search candidate-connections`
         from a file under memo-examples/, and server.py passes the search."""
         examples = [e for e in json.loads((HERE / "examples.json").read_text()) if "search" in e]
-        self.assertEqual(len(examples), 6)
+        self.assertEqual(len(examples), 7)
         for example in examples:
             with self.subTest(example["id"]):
                 self.assertTrue(example["workload"].startswith("memo-examples/"))