diff --git a/lib/artdag/conformance.sh b/lib/artdag/conformance.sh
index 63c902ec..cb59c336 100755
--- a/lib/artdag/conformance.sh
+++ b/lib/artdag/conformance.sh
@@ -13,7 +13,7 @@ if [ ! -x "$SX_SERVER" ]; then
   exit 1
 fi
 
-SUITES=(dag analyze)
+SUITES=(dag analyze plan)
 
 OUT_JSON="lib/artdag/scoreboard.json"
 OUT_MD="lib/artdag/scoreboard.md"
@@ -38,6 +38,7 @@ run_suite() {
 (load "lib/datalog/api.sx")
 (load "lib/artdag/dag.sx")
 (load "lib/artdag/analyze.sx")
+(load "lib/artdag/plan.sx")
 (epoch 2)
 (eval "(define artdag-test-pass 0)")
 (eval "(define artdag-test-fail 0)")
diff --git a/lib/artdag/plan.sx b/lib/artdag/plan.sx
new file mode 100644
index 00000000..c0dde7a8
--- /dev/null
+++ b/lib/artdag/plan.sx
@@ -0,0 +1,100 @@
+; lib/artdag/plan.sx — Phase 3: schedule a DAG (or its dirty subset) into
+; topological batches under a max-parallelism cap. A batch is a set of nodes
+; whose deps are all satisfied by earlier batches, so they run in parallel.
+; cap <= 0 means unlimited width. Depends on dag.sx and analyze.sx.
+
+; inputs of id that also lie inside the scheduled set (out-of-set deps are
+; treated as already satisfied — e.g. clean cache hits in an incremental plan).
+(define
+  artdag/-deps-in
+  (fn
+    (dag id sset)
+    (filter
+      (fn (in) (artdag/member? in sset))
+      (artdag/node-inputs (artdag/dag-get dag id)))))
+
+(define
+  artdag/-ready-in
+  (fn
+    (dag sset placed)
+    (filter
+      (fn
+        (id)
+        (and
+          (not (artdag/member? id placed))
+          (artdag/all-in? (artdag/-deps-in dag id sset) placed)))
+      (artdag/sort-strings sset))))
+
+(define
+  artdag/-batch-loop
+  (fn
+    (dag sset placed batches)
+    (if
+      (= (len placed) (len sset))
+      batches
+      (let
+        ((wave (artdag/-ready-in dag sset placed)))
+        (artdag/-batch-loop
+          dag
+          sset
+          (concat placed wave)
+          (concat batches (list wave)))))))
+
+; split a wave into consecutive chunks of at most n (sorted order preserved).
+(define
+  artdag/-chunk
+  (fn
+    (xs n)
+    (if
+      (<= (len xs) n)
+      (list xs)
+      (cons
+        (slice xs 0 n)
+        (artdag/-chunk (slice xs n (len xs)) n)))))
+
+(define
+  artdag/-cap-split
+  (fn
+    (batches cap)
+    (if
+      (<= cap 0)
+      batches
+      (reduce
+        (fn (acc b) (concat acc (artdag/-chunk b cap)))
+        (list)
+        batches))))
+
+; schedule an explicit set of node-ids into capped topological batches.
+(define
+  artdag/plan-subset
+  (fn
+    (dag node-ids cap)
+    (artdag/-cap-split (artdag/-batch-loop dag node-ids (list) (list)) cap)))
+
+; full plan over every node in the dag.
+(define
+  artdag/plan
+  (fn (dag cap) (artdag/plan-subset dag (keys (artdag/dag-nodes dag)) cap)))
+
+; incremental plan: schedule only the dirty closure of the changed nodes.
+(define
+  artdag/plan-dirty
+  (fn
+    (dag changed cap)
+    (artdag/plan-subset dag (artdag/dirty-closure dag changed) cap)))
+
+; ---- plan inspection ----
+
+(define artdag/plan-batches (fn (plan) (len plan)))
+
+(define
+  artdag/plan-width
+  (fn
+    (plan)
+    (reduce (fn (m b) (if (> (len b) m) (len b) m)) 0 plan)))
+
+(define
+  artdag/plan-flatten
+  (fn (plan) (reduce (fn (acc b) (concat acc b)) (list) plan)))
+
+(define artdag/plan-size (fn (plan) (len (artdag/plan-flatten plan))))
diff --git a/lib/artdag/scoreboard.json b/lib/artdag/scoreboard.json
index 46d9d6e8..cb0b8677 100644
--- a/lib/artdag/scoreboard.json
+++ b/lib/artdag/scoreboard.json
@@ -1,9 +1,10 @@
 {
   "suites": {
     "dag": {"pass": 20, "fail": 0},
-    "analyze": {"pass": 16, "fail": 0}
+    "analyze": {"pass": 16, "fail": 0},
+    "plan": {"pass": 18, "fail": 0}
   },
-  "total_pass": 36,
+  "total_pass": 54,
   "total_fail": 0,
-  "total": 36
+  "total": 54
 }
diff --git a/lib/artdag/scoreboard.md b/lib/artdag/scoreboard.md
index 43f3868d..30ab2fc4 100644
--- a/lib/artdag/scoreboard.md
+++ b/lib/artdag/scoreboard.md
@@ -6,4 +6,5 @@ _Generated by `lib/artdag/conformance.sh`_
 |-------|-----:|-----:|------:|
 | dag | 20 | 0 | 20 |
 | analyze | 16 | 0 | 16 |
-| **Total** | **36** | **0** | **36** |
+| plan | 18 | 0 | 18 |
+| **Total** | **54** | **0** | **54** |
diff --git a/lib/artdag/tests/plan.sx b/lib/artdag/tests/plan.sx
new file mode 100644
index 00000000..100155c6
--- /dev/null
+++ b/lib/artdag/tests/plan.sx
@@ -0,0 +1,122 @@
+; Phase 3 — Plan: topological batches under a parallelism cap, incremental plan.
+
+; diamond:  a -> b, a -> c, (b,c) -> d
+(define
+  pl-D
+  (artdag/build
+    (list
+      (list "a" "load" (list) {})
+      (list "b" "f" (list "a") {})
+      (list "c" "g" (list "a") {})
+      (list "d" "add" (list "b" "c") {} true))))
+(define pl-a (artdag/dag-id pl-D "a"))
+(define pl-b (artdag/dag-id pl-D "b"))
+(define pl-c (artdag/dag-id pl-D "c"))
+(define pl-d (artdag/dag-id pl-D "d"))
+
+; wide:  a -> b, c, e, f  (four independent dependents)
+(define
+  pl-W
+  (artdag/build
+    (list
+      (list "a" "load" (list) {})
+      (list "b" "f" (list "a") {})
+      (list "c" "g" (list "a") {})
+      (list "e" "h" (list "a") {})
+      (list "f" "k" (list "a") {}))))
+
+; ---- full plan, unlimited width ----
+
+(artdag-test
+  "full plan: batch count"
+  (artdag/plan-batches (artdag/plan pl-D 0))
+  3)
+
+(artdag-test
+  "full plan: schedules every node"
+  (artdag/plan-size (artdag/plan pl-D 0))
+  4)
+
+(artdag-test
+  "full plan: first batch is the leaf"
+  (first (artdag/plan pl-D 0))
+  (list pl-a))
+
+(artdag-test
+  "full plan: middle batch runs b,c in parallel"
+  (first (rest (artdag/plan pl-D 0)))
+  (artdag/sort-strings (list pl-b pl-c)))
+
+(artdag-test
+  "full plan: last batch is the sink"
+  (first (rest (rest (artdag/plan pl-D 0))))
+  (list pl-d))
+
+(artdag-test
+  "full plan: max width is 2"
+  (artdag/plan-width (artdag/plan pl-D 0))
+  2)
+
+; ---- parallelism cap ----
+
+(artdag-test
+  "cap 1: width never exceeds 1"
+  (artdag/plan-width (artdag/plan pl-D 1))
+  1)
+
+(artdag-test
+  "cap 1: serializes into one node per batch"
+  (artdag/plan-batches (artdag/plan pl-D 1))
+  4)
+
+(artdag-test
+  "cap larger than widest wave is a no-op"
+  (artdag/plan pl-D 10)
+  (artdag/plan pl-D 0))
+
+(artdag-test
+  "wide cap 2: width capped at 2"
+  (artdag/plan-width (artdag/plan pl-W 2))
+  2)
+
+(artdag-test
+  "wide cap 2: leaf wave then two capped sub-batches"
+  (artdag/plan-batches (artdag/plan pl-W 2))
+  3)
+
+(artdag-test
+  "wide cap 2: still schedules all five nodes"
+  (artdag/plan-size (artdag/plan pl-W 2))
+  5)
+
+(artdag-test
+  "wide unlimited: single wave of four after leaf"
+  (artdag/plan-width (artdag/plan pl-W 0))
+  4)
+
+; ---- incremental (dirty-only) plan ----
+
+(artdag-test
+  "dirty plan: schedules only the dirty closure"
+  (artdag/plan-size (artdag/plan-dirty pl-D (list pl-b) 0))
+  2)
+
+(artdag-test
+  "dirty plan: b then d"
+  (artdag/plan-dirty pl-D (list pl-b) 0)
+  (list (list pl-b) (list pl-d)))
+
+(artdag-test
+  "dirty plan: clean deps treated as satisfied"
+  (first (artdag/plan-dirty pl-D (list pl-b) 0))
+  (list pl-b))
+
+(artdag-test
+  "dirty plan: leaf change replans whole graph"
+  (artdag/plan-size (artdag/plan-dirty pl-D (list pl-a) 0))
+  4)
+
+(artdag-test
+  "dirty plan: sink change is a single batch"
+  (artdag/plan-dirty pl-D (list pl-d) 0)
+  (list (list pl-d)))
diff --git a/plans/artdag-on-sx.md b/plans/artdag-on-sx.md
index 0ce869c1..4d8ab8e7 100644
--- a/plans/artdag-on-sx.md
+++ b/plans/artdag-on-sx.md
@@ -30,7 +30,7 @@ edges.
 
 ## Status (rolling)
 
-`bash lib/artdag/conformance.sh` → **36/36** (2 suites: dag, analyze)
+`bash lib/artdag/conformance.sh` → **54/54** (3 suites: dag, analyze, plan)
 
 ## Ground rules
 
@@ -97,10 +97,10 @@ lib/artdag/optimize.sx                  lib/artdag/federation.sx
 
 ## Phase 3 — Plan
 
-- [ ] `lib/artdag/plan.sx` — schedule into topological **batches** (each batch's
+- [x] `lib/artdag/plan.sx` — schedule into topological **batches** (each batch's
   nodes have all deps satisfied → run in parallel); respect a max-parallelism limit
-- [ ] plan over the *dirty* subset only (incremental plan)
-- [ ] `lib/artdag/tests/plan.sx` — batch correctness, parallelism cap, dirty-only plan
+- [x] plan over the *dirty* subset only (incremental plan)
+- [x] `lib/artdag/tests/plan.sx` — batch correctness, parallelism cap, dirty-only plan
 - [ ] (optional/later) miniKanren constraint scheduling — flag, don't block on it
 
 ## Phase 4 — Execute (incremental + memoized)
@@ -136,6 +136,15 @@ lib/artdag/optimize.sx                  lib/artdag/federation.sx
 
 ## Progress log
 
+- **Phase 3 — Plan** (plan suite 18/18, total 54/54). `lib/artdag/plan.sx`:
+  `artdag/plan` schedules a dag into Kahn-wave topological batches — each batch's
+  nodes have all in-scope deps satisfied by earlier batches, so they run in parallel.
+  A `cap` (>0) splits any wave wider than the cap into consecutive sub-batches;
+  `cap<=0` is unlimited. `artdag/plan-dirty` schedules only the dirty closure: deps
+  outside the scheduled set (clean cache hits) count as already satisfied, so a
+  mid-node change yields just `[[changed]…[downstream]]`. Inspection helpers
+  `plan-batches`/`plan-width`/`plan-size`/`plan-flatten`.
+
 - **Phase 2 — Analyze on Datalog** (analyze suite 16/16, total 36/36).
   `lib/artdag/analyze.sx`: `artdag/edge-facts` projects each `(input-id, node-id)`
   pair to an `(edge ...)` fact; `artdag/analyze` builds a `dl-program-data` db with