@@ -20,7 +20,9 @@
 //     the queries as written and, when Pass 2's identical-expression rule
 //     merges something, again with identical sub-DAGs shared ("· shared
 //     input"), and, when the summary-capability rule applies, again with
-//     one summary sized for its strictest consumer ("· shared summary"); in
+//     one summary sized for its strictest consumer ("· shared summary"),
+//     and, when queries read windows of one scan on a common grid, again
+//     with one summary per shared segment ("· shared segments"); in
 //     enumeration order, only those with a written physical candidate. A
 //     repeating query's mergeable alternatives also come in tumbling panes
 //     (Pass 2's window-composition rule), e.g. "Q1 Kll · tumbling 1m panes";
@@ -267,6 +269,7 @@ fn stage_pipeline(
             Sharing::Independent => "",
             Sharing::IdenticalExpressions => " · shared input",
             Sharing::SummaryCapability => " · shared summary",
+            Sharing::WindowSegments => " · shared segments",
         };
         let written = candidate
             .physical
 
@@ -183,13 +183,15 @@ fn example3b_lists_tumbling_candidates() {
     }
 }
 
-/// Example 4, Pattern A repeated monthly: the same 486 candidates as the ad
-/// hoc batch (3a), and none maintained at ingestion time. The windows (1–5 y)
-/// are longer than the month between runs and no pane width fits, so
-/// nothing is maintainable. The selected plan is 3a's, now amortized over
-/// monthly runs instead of one run per hour of horizon.
+/// Example 4, Pattern A repeated monthly: the same 487 logical candidates
+/// as the ad hoc batch (3a), 486 independent or sharing input plus the one
+/// sharing 1-year segments (Q60). The windows (1–5 y) are longer than the
+/// month between runs and no pane width fits, so only the shared segments
+/// can be maintained at ingestion time (Q61): 488 plans. The selected plan
+/// is 3a's, now amortized over monthly runs instead of one run per hour of
+/// horizon.
 #[test]
-fn example4a_repeats_monthly_with_nothing_maintainable() {
+fn example4a_repeats_monthly_with_only_segments_maintainable() {
     let once = generate(&[
         "--example",
         "planner-layering-3a",
@@ -205,10 +207,14 @@ fn example4a_repeats_monthly_with_nothing_maintainable() {
     let physical = monthly["stage2_physical_asap"]["candidates"]
         .as_array()
         .unwrap();
-    assert_eq!(physical.len(), 486);
-    assert!(physical
+    assert_eq!(physical.len(), 488);
+    let maintained: Vec<_> = physical
         .iter()
-        .all(|p| !p["label"].as_str().unwrap().contains("ingestion time")));
+        .map(|p| p["label"].as_str().unwrap())
+        .filter(|label| label.contains("ingestion time"))
+        .collect();
+    assert_eq!(maintained.len(), 1, "{maintained:?}");
+    assert!(maintained[0].ends_with("shared segments · ingestion time: Kll ×5 panes"));
     let selected = |d: &Value| {
         d["stage3_selection"]["selected"]
             .as_str()
 
@@ -575,6 +575,17 @@ pub fn query_option(
     }
 }
 
+/// Whether `dag` shares a summary build across queries: Pass 2's
+/// shared-segment rule (Q60), whose segments several queries merge.
+pub fn shares_segments(dag: &impl ExportedDag, query_roots: &[LogicalASAPNodeId]) -> bool {
+    cross_query_nodes(dag, query_roots).into_iter().any(|id| {
+        matches!(
+            dag.payload(id),
+            LogicalASAPOperatorPayload::SummaryAgg { .. }
+        )
+    })
+}
+
 /// Nodes reachable from more than one query root.
 pub fn cross_query_nodes(
     dag: &impl ExportedDag,
 
@@ -158,13 +158,17 @@ fn stage1_a_keeps_five_independent_klls() {
     assert_eq!(sizes.len(), 1, "one ε, one KLL size: {sizes:?}");
 }
 
-/// The identical-expression rule shares only raw input (scan, range, shift), never a quantile or summary, and keeps the unshared variant.
+/// The identical-expression rule shares only raw input (scan, range, shift), never a quantile or summary, and keeps the unshared variant. (The shared-segment candidate shares its segments; see below.)
 #[test]
 fn stage1_a_identical_expression_rule_shares_only_raw_input() {
     let run = run_a();
     assert!(run.logical.iter().any(|c| c.shared_input));
     assert!(run.logical.iter().any(|c| !c.shared_input));
-    for c in &run.logical {
+    for c in run
+        .logical
+        .iter()
+        .filter(|c| !shares_segments(&c.dag, &c.query_roots))
+    {
         for id in cross_query_nodes(&c.dag, &c.query_roots) {
             let kind = relational(c.dag.payload(id));
             assert!(
@@ -176,24 +180,35 @@ fn stage1_a_identical_expression_rule_shares_only_raw_input() {
     }
 }
 
-/// One Exponential Histogram of KLLs over [T − 5y, T] serves all five queries, each through its own merge and p99 estimate.
+/// The windows' boundaries lie on a 1-year grid, so one set of five 1-year
+/// KLL segments over [T − 5y, T] serves all five queries (Q60, in place of
+/// the spec's Exponential Histogram): each query merges the segments its
+/// range covers and estimates p99 from its merge.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram"]
-fn stage1_a_window_composition_adds_one_eh_for_all_five() {
+fn stage1_a_shared_segments_serve_all_five() {
     let run = run_a();
-    let found = run.logical.iter().find(|c| {
-        windowed_builds(c).iter().any(|(_, a, form, readers)| {
-            *a == SketchAlgorithm::Kll
-                && matches!(form, WindowForm::ExponentialHistogram { horizon_ms } if *horizon_ms >= 5 * YEAR_MS)
-                && readers.len() == 5
-        })
-    });
-    let c = found.expect("a candidate with one EH of KLLs read by all five queries");
-    let (eh, ..) = windowed_builds(c)
-        .into_iter()
-        .find(|(_, _, form, _)| matches!(form, WindowForm::ExponentialHistogram { .. }))
-        .unwrap();
-    let estimates = estimates_of(&c.dag, eh);
+    let c = run
+        .logical
+        .iter()
+        .find(|c| shares_segments(&c.dag, &c.query_roots))
+        .expect("a candidate sharing window segments");
+    let segments = windowed_builds(c);
+    assert_eq!(segments.len(), 5, "{}", c.id);
+    for (_, algorithm, form, _) in &segments {
+        assert_eq!(*algorithm, SketchAlgorithm::Kll);
+        assert_eq!(*form, WindowForm::Tumbling { length_ms: YEAR_MS });
+    }
+    let read: BTreeSet<usize> = segments.iter().flat_map(|(.., r)| r.clone()).collect();
+    assert_eq!(read, (0..5).collect());
+    // Each query merges as many segments as its range has years.
+    for (q, (_, lookback, _)) in PATTERN_A.iter().enumerate() {
+        let covering = segments.iter().filter(|(.., r)| r.contains(&q)).count() as u64;
+        assert_eq!(covering, lookback / YEAR_MS, "q{}", q + 1);
+    }
+    let estimates: std::collections::BTreeMap<_, _> = segments
+        .iter()
+        .flat_map(|(build, ..)| estimates_of(&c.dag, *build))
+        .collect();
     assert_eq!(estimates.len(), 5, "one estimate per query");
     for (estimate, statistic) in estimates {
         assert_eq!(statistic, SketchStatistic::Quantile { q: 0.99 });
@@ -211,16 +226,14 @@ fn stage1_a_window_composition_adds_one_eh_for_all_five() {
     }
 }
 
-/// The shared EH candidate is added next to the independent KLL candidates, not instead of them.
+/// The shared-segment candidate is added next to the independent KLL candidates, not instead of them.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram"]
 fn stage1_a_keeps_independent_and_shared_window_summaries() {
     let run = run_a();
-    let shared = run.logical.iter().any(|c| {
-        windowed_builds(c).iter().any(|(_, _, f, r)| {
-            matches!(f, WindowForm::ExponentialHistogram { .. }) && r.len() == 5
-        })
-    });
+    let shared = run
+        .logical
+        .iter()
+        .any(|c| shares_segments(&c.dag, &c.query_roots));
     let independent = run.logical.iter().any(|c| {
         let builds = windowed_builds(c);
         builds.len() == 5
@@ -233,7 +246,7 @@ fn stage1_a_keeps_independent_and_shared_window_summaries() {
 
 /// Pass 2 adds a candidate for each way of grouping two queries onto one shared window summary.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): partial groupings"]
+#[ignore = "partial and pairwise groupings are not generated, only all-shared segments (Q62)"]
 fn stage1_a_window_composition_groups_every_pair() {
     let run = run_a();
     let groups: BTreeSet<_> = run
@@ -282,7 +295,11 @@ fn stage3_a_shared_scan_is_not_costlier() {
     };
     let cost = |c: &Logical| run.cost(&run.physical_of(c).next().unwrap().id);
     let mut compared = 0;
-    for shared in run.logical.iter().filter(|c| c.shared_input) {
+    for shared in run
+        .logical
+        .iter()
+        .filter(|c| c.shared_input && !shares_segments(&c.dag, &c.query_roots))
+    {
         let separate = run
             .logical
             .iter()
 
@@ -98,6 +98,22 @@ fn eh_options(run: &Run) -> BTreeMap<Materialization, (String, PhysicalASAPNodeI
     options_of(run, None, 5)
 }
 
+/// The physical candidates of the shared-segment candidate (Q60), keyed by
+/// the materialization of its segments, with the newest segment's id.
+fn segment_options(run: &Run) -> BTreeMap<Materialization, (String, LogicalASAPNodeId)> {
+    let logical = run
+        .logical
+        .iter()
+        .find(|c| shares_segments(&c.dag, &c.query_roots))
+        .expect("a candidate sharing window segments");
+    run.physical_of(logical)
+        .map(|p| {
+            let (segment, ..) = sketch_builds(&p.dag)[0];
+            (materialization(p, segment), (p.id.clone(), segment))
+        })
+        .collect()
+}
+
 fn tumbling() -> Option<WindowForm> {
     Some(WindowForm::Tumbling {
         length_ms: PATTERN_B_INTERVAL_MS,
@@ -165,7 +181,7 @@ fn stage2_materialized_output_covers_its_consumers() {
 
 /// The shared EH candidate yields A1 (query time, kept), A2 (ingestion time) and A3 (not materialized).
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram; and A3, not materialized for several consumers (Q44)"]
+#[ignore = "shared segments (Q60) are not kept for one batch, and A3 is not generated (Q44); a one-off batch has no ingestion-time option (Q61)"]
 fn stage2_a_shared_eh_has_three_materialization_options() {
     let found: BTreeSet<_> = eh_options(&run_promql(&once())).into_keys().collect();
     assert_eq!(
@@ -176,43 +192,53 @@ fn stage2_a_shared_eh_has_three_materialization_options() {
 
 /// With data at rest, A2 is not generated; A1 and A3 remain.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram"]
+#[ignore = "shared segments (Q60) are not kept for one batch, and A3 is not generated (Q44)"]
 fn stage2_a_at_rest_drops_the_ingestion_time_option() {
     let found: BTreeSet<_> = eh_options(&run_promql(&at_rest())).into_keys().collect();
     assert_eq!(found, BTreeSet::from([QueryTimeKept, NotMaterialized]));
 }
 
-/// A materialized shared EH is one build node read by all five queries, charged once.
+/// The shared segments (Q60, in place of the spec's EH) are five builds,
+/// each built once, read by all five queries through their merges and
+/// charged once, in every materialization: at query time for the one-off
+/// batch, and also at ingestion time when it repeats monthly (Q61).
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram"]
-fn stage2_a_materialized_eh_is_built_once_for_all_consumers() {
-    let run = run_promql(&once());
-    for (m, (id, build)) in eh_options(&run) {
-        if m == NotMaterialized {
-            continue;
+fn stage2_a_segments_are_built_once_for_all_consumers() {
+    for (workload, expected) in [
+        (once(), BTreeSet::from([NotMaterialized])),
+        (monthly(), BTreeSet::from([IngestionTime, NotMaterialized])),
+    ] {
+        let run = run_promql(&workload);
+        let options = segment_options(&run);
+        assert_eq!(options.keys().copied().collect::<BTreeSet<_>>(), expected);
+        for (id, _) in options.values() {
+            let p = run.physical(id);
+            let segments = sketch_builds(&p.dag);
+            assert_eq!(segments.len(), 5, "{id}");
+            let read: BTreeSet<usize> = segments
+                .iter()
+                .flat_map(|(b, ..)| readers(&p.dag, &p.query_roots, *b))
+                .collect();
+            assert_eq!(read.len(), 5, "{id}");
+            let merges = p
+                .dag
+                .nodes
+                .iter()
+                .filter(|n| matches!(n.payload, LogicalASAPOperatorPayload::SummaryMerge))
+                .count();
+            assert_eq!(merges, 5, "{id}");
+            if let Some(cost) = run.selection.costs.get(id) {
+                for (b, ..) in &segments {
+                    assert!(cost.per_node.contains_key(b), "{id}");
+                }
+            }
         }
-        let p = run.physical(&id);
-        let ehs = sketch_builds(&p.dag)
-            .into_iter()
-            .filter(|(b, ..)| {
-                matches!(
-                    window_form(&p.dag, *b),
-                    WindowForm::ExponentialHistogram { .. }
-                )
-            })
-            .count();
-        assert_eq!(ehs, 1, "{id}");
-        assert_eq!(readers(&p.dag, &p.query_roots, build).len(), 5, "{id}");
-        assert!(
-            run.selection.costs[&id].per_node.contains_key(&build),
-            "{id}"
-        );
     }
 }
 
 /// A3 rebuilds the EH for each of the five queries, so it costs more than A1, which builds it once.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram; and A3 (Q44)"]
+#[ignore = "A3, not materialized for several consumers, is not generated (Q44)"]
 fn stage3_a_rebuilding_per_query_costs_more_than_building_once() {
     let run = run_promql(&once());
     let options = eh_options(&run);
@@ -227,7 +253,7 @@ fn stage3_a_rebuilding_per_query_costs_more_than_building_once() {
 
 /// As given (run once, ad hoc), A1 is the cheapest of the three: A2 maintains years of history for one batch.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram"]
+#[ignore = "a one-off batch has no ingestion-time option (Q61), and A3 is not generated (Q44)"]
 fn stage3_a_once_adhoc_prefers_the_query_time_eh() {
     let run = run_promql(&once());
     let options = eh_options(&run);
@@ -239,7 +265,7 @@ fn stage3_a_once_adhoc_prefers_the_query_time_eh() {
 
 /// Repeated monthly and predictable, A2's maintenance is shared by many batches, so A2 gains on A1.
 #[test]
-#[ignore = "needs Pass 2 window composition (#580): Exponential Histogram, maintainable over a monthly window"]
+#[ignore = "a one-off batch has no ingestion-time option to compare with (Q61)"]
 fn stage3_a_monthly_amortizes_ingestion_time_maintenance() {
     let ratio = |workload: PlanningWorkload| {
         let run = run_promql(&workload);
 
@@ -697,7 +697,10 @@ fn realize(
     };
     let state = match window {
         WindowForm::Whole => build(child)?,
-        WindowForm::Tumbling { pane_ms } => tumbling_state(&child, pane_ms, build)?,
+        WindowForm::Tumbling { pane_ms }
+        | WindowForm::Segments {
+            segment_ms: pane_ms,
+        } => tumbling_state(&child, pane_ms, build)?,
     };
     let evaluation = match query {
         Some(query) => ASAPOp::SummaryEstimate {
 
@@ -16,7 +16,7 @@ use asap_types::ir::{OperatorNode, QueryRoot};
 use asap_types::workload::{MetricType, RootDemand};
 
 use super::summary_capability::share_summary_capability;
-use super::window_composition::add_window_forms;
+use super::window_composition::{add_window_forms, share_window_segments};
 use crate::pass1::logical_candidates::{
     enumerate_local_logical_candidates, LocalLogicalCandidates, LogicalCandidateError,
 };
@@ -34,6 +34,11 @@ pub enum Sharing {
     /// are sized for their strictest consumer, so composition builds
     /// identical producers, which are merged.
     SummaryCapability,
+    /// The shared-segment rule on top of the identical-expression rule
+    /// ([`share_window_segments`]): queries over windows of one scan merge
+    /// one shared summary per segment, and the identical segments are merged
+    /// after composition.
+    WindowSegments,
 }
 
 impl Sharing {
@@ -56,7 +61,9 @@ pub struct SharingVariant<Id> {
 /// last is skipped when it would repeat the identical-expression variant.
 /// In every variant, the window-composition rule adds tumbling forms of
 /// mergeable alternatives for repeating queries (`demand[i]` is the demand
-/// of `roots[i]`; a root without one gets none).
+/// of `roots[i]`; a root without one gets none). Last, the shared-segment
+/// variant when windows of one scan can share segments: only that form, not
+/// the tumbling forms, for the targets it groups.
 pub fn stage1_logical_candidates<Id: Clone>(
     roots: Vec<(Id, QueryRoot)>,
     metric_types: &BTreeMap<String, MetricType>,
@@ -74,6 +81,7 @@ pub fn stage1_logical_candidates<Id: Clone>(
         });
     }
     let base = &variants.last().expect("the independent variant").inventory;
+    let segments = share_window_segments(base, demand)?;
     if let Some(capability) = share_summary_capability(base)? {
         if capability.resized || variants.len() == 1 {
             variants.push(SharingVariant {
@@ -85,6 +93,12 @@ pub fn stage1_logical_candidates<Id: Clone>(
     for variant in &mut variants {
         add_window_forms(&mut variant.inventory, demand);
     }
+    if let Some(inventory) = segments {
+        variants.push(SharingVariant {
+            sharing: Sharing::WindowSegments,
+            inventory,
+        });
+    }
     Ok(variants)
 }
 
 
@@ -2,7 +2,8 @@
 //! strictest accuracy requirement of its readers. The stage pipeline applies
 //! the identical-expression rule ([`identical_expressions`]), the
 //! summary-capability rule ([`summary_capability`]) and the
-//! window-composition rule's tumbling windows ([`window_composition`]).
+//! window-composition rule's tumbling windows and shared segments
+//! ([`window_composition`]).
 
 pub mod identical_expressions;
 pub mod reconciliation;