diff --git a/lib/artdag/conformance.sh b/lib/artdag/conformance.sh
index 0d2924c6..84b96d13 100755
--- a/lib/artdag/conformance.sh
+++ b/lib/artdag/conformance.sh
@@ -35,13 +35,15 @@ run_suite() {
 (load "lib/maude/matching.sx")
 (load "lib/maude/conditional.sx")
 (load "lib/maude/fire.sx")
+(load "lib/maude/confluence.sx")
 (load "lib/maude/rewrite.sx")
 (load "lib/maude/searchpath.sx")
 (load "lib/maude/strategy.sx")
 (load "lib/maude/meta.sx")
 (load "lib/maude/pretty.sx")
 (load "lib/maude/run.sx")'
-    BRIDGE_LOAD='(load "lib/artdag/maude-bridge.sx")'
+    BRIDGE_LOAD='(load "lib/artdag/maude-bridge.sx")
+(load "lib/artdag/optimize-rules.sx")'
   fi
   cat > "$TMP" << EPOCHS
 (epoch 1)
diff --git a/lib/artdag/optimize-rules.sx b/lib/artdag/optimize-rules.sx
new file mode 100644
index 00000000..7262fca0
--- /dev/null
+++ b/lib/artdag/optimize-rules.sx
@@ -0,0 +1,69 @@
+; lib/artdag/optimize-rules.sx — Phase 7: optimisation laws as a confluent maude module.
+; The optimised effect pipeline IS the normal form of the rule set, so confluence
+; (mau/confluent?) is exactly content-id stability: every rewrite order reaches the
+; same normal form. Media ops (blur/bright/id/over) are the opaque-op model from
+; lib/maude/tests/effects.sx — the engine reasons about the pipeline algebra, never
+; pixels. The radius algebra is an AC operator with identity 0 (unary 1s): Peano
+; successor rules (s M + N = s(M+N), 0 + N = N) are NOT confluent here (the symbolic
+; critical pairs M + 0 and (A+B)+C vs A+(B+C) stick), whereas [assoc comm id: 0]
+; joins them via canonical form. maude (lib/maude) is a READ-ONLY consumed substrate:
+; mau/parse-module, mau/creduce-term, mau/creduce->str, mau/ccanon, mau/confluent?,
+; mau/non-joinable-pairs, mau/cp->str.
+
+(define
+  artdag/opt-module-src
+  (str
+    "fmod ARTDAGOPT is\n"
+    "  sorts Img Num .\n"
+    "  op 0 : -> Num .\n"
+    "  op 1 : -> Num .\n"
+    "  op _+_ : Num Num -> Num [assoc comm id: 0] .\n"
+    "  op blur : Img Num -> Img .\n"
+    "  op bright : Img Num -> Img .\n"
+    "  op id : Img -> Img .\n"
+    "  op over : Img Img -> Img [comm] .\n"
+    "  vars I J : Img .\n"
+    "  vars M N : Num .\n"
+    "  eq id(I) = I .\n"
+    "  eq blur(I, 0) = I .\n"
+    "  eq bright(I, 0) = I .\n"
+    "  eq blur(blur(I, M), N) = blur(I, M + N) .\n"
+    "  eq bright(bright(I, M), N) = bright(I, M + N) .\n"
+    "  eq over(I, I) = I .\n"
+    "endfm"))
+
+(define artdag/opt-module (mau/parse-module artdag/opt-module-src))
+
+; ---- reduce a surface pipeline to its optimised normal form ----
+
+(define
+  artdag/opt-reduce-term
+  (fn (src) (mau/creduce-term artdag/opt-module src)))
+
+(define
+  artdag/opt-normal-form
+  (fn (src) (mau/creduce->str artdag/opt-module src)))
+
+(define artdag/opt-canon (fn (src) (mau/ccanon artdag/opt-module src)))
+
+; two surface pipelines optimise to the same pipeline (=> same content id) iff
+; their normal forms coincide.
+(define
+  artdag/opt-same-form?
+  (fn (a b) (= (artdag/opt-normal-form a) (artdag/opt-normal-form b))))
+
+; ---- confluence / content-id stability (consume lib/maude/confluence.sx) ----
+
+(define artdag/opt-confluent? (fn () (mau/confluent? artdag/opt-module)))
+
+(define
+  artdag/opt-non-joinable
+  (fn () (mau/non-joinable-pairs artdag/opt-module)))
+
+(define
+  artdag/opt-non-joinable->strs
+  (fn
+    ()
+    (map
+      (fn (cp) (mau/cp->str artdag/opt-module cp))
+      (artdag/opt-non-joinable))))
diff --git a/lib/artdag/scoreboard.json b/lib/artdag/scoreboard.json
index ce9ab602..1ed9c3ea 100644
--- a/lib/artdag/scoreboard.json
+++ b/lib/artdag/scoreboard.json
@@ -10,9 +10,9 @@
     "serialize": {"pass": 13, "fail": 0},
     "stats": {"pass": 12, "fail": 0},
     "fault": {"pass": 14, "fail": 0},
-    "maude-optimize": {"pass": 14, "fail": 0}
+    "maude-optimize": {"pass": 25, "fail": 0}
   },
-  "total_pass": 172,
+  "total_pass": 183,
   "total_fail": 0,
-  "total": 172
+  "total": 183
 }
diff --git a/lib/artdag/scoreboard.md b/lib/artdag/scoreboard.md
index 14a9652f..d45acde2 100644
--- a/lib/artdag/scoreboard.md
+++ b/lib/artdag/scoreboard.md
@@ -14,5 +14,5 @@ _Generated by `lib/artdag/conformance.sh`_
 | serialize | 13 | 0 | 13 |
 | stats | 12 | 0 | 12 |
 | fault | 14 | 0 | 14 |
-| maude-optimize | 14 | 0 | 14 |
-| **Total** | **172** | **0** | **172** |
+| maude-optimize | 25 | 0 | 25 |
+| **Total** | **183** | **0** | **183** |
diff --git a/lib/artdag/tests/maude-optimize.sx b/lib/artdag/tests/maude-optimize.sx
index 2f699150..38b12c56 100644
--- a/lib/artdag/tests/maude-optimize.sx
+++ b/lib/artdag/tests/maude-optimize.sx
@@ -110,3 +110,60 @@
     (artdag/dag-id mo-diamond "a")
     (keys (artdag/dag-nodes mo-diamond-rt)))
   true)
+
+; ---- optimisation laws as a confluent maude module (optimize-rules.sx) ----
+; The optimised pipeline is the normal form; confluence => stable content id.
+
+(artdag-test "opt module is confluent" (artdag/opt-confluent?) true)
+
+(artdag-test
+  "opt module has no non-joinable critical pairs"
+  (len (artdag/opt-non-joinable))
+  0)
+
+(artdag-test
+  "law: identity elimination"
+  (artdag/opt-normal-form "id(src)")
+  "src")
+
+(artdag-test
+  "law: zero-radius blur is a no-op"
+  (artdag/opt-normal-form "blur(src, 0)")
+  "src")
+
+(artdag-test
+  "law: zero-radius bright is a no-op"
+  (artdag/opt-normal-form "bright(src, 0)")
+  "src")
+
+(artdag-test
+  "law: adjacent blur fusion adds radii"
+  (artdag/opt-normal-form "blur(blur(src, 1), 1)")
+  "blur(src, _+_(1, 1))")
+
+(artdag-test
+  "fusion normal form is rewrite-order stable"
+  (artdag/opt-same-form?
+    "blur(blur(blur(src, 1), 1), 1)"
+    "blur(blur(src, 1 + 1), 1)")
+  true)
+
+(artdag-test
+  "laws compose: id + no-op + fusion"
+  (artdag/opt-normal-form "bright(id(blur(blur(src, 1), 1)), 0)")
+  "blur(src, _+_(1, 1))")
+
+(artdag-test
+  "law: idempotent over dedup (CSE)"
+  (artdag/opt-normal-form "over(blur(src, 1), blur(src, 1))")
+  "blur(src, 1)")
+
+(artdag-test
+  "distinct over operands do not dedup"
+  (artdag/opt-same-form? "over(blur(src, 1), blur(src, 1 + 1))" "blur(src, 1)")
+  false)
+
+(artdag-test
+  "distinct pipelines stay distinct"
+  (artdag/opt-same-form? "blur(src, 1)" "bright(src, 1)")
+  false)
diff --git a/plans/artdag-on-sx.md b/plans/artdag-on-sx.md
index a7c5d25b..b6a4727e 100644
--- a/plans/artdag-on-sx.md
+++ b/plans/artdag-on-sx.md
@@ -31,7 +31,7 @@ edges.
 
 ## Status (rolling)
 
-`bash lib/artdag/conformance.sh` → **172/172** (11 suites: dag, analyze, plan, execute, optimize, fed, cost, serialize, stats, fault, maude-optimize)
+`bash lib/artdag/conformance.sh` → **183/183** (11 suites: dag, analyze, plan, execute, optimize, fed, cost, serialize, stats, fault, maude-optimize)
 
 Base roadmap (Phases 1–6) COMPLETE. Now extending.
 
@@ -156,7 +156,7 @@ declaratively and prove it equivalent to the hand-written `optimize.sx`.
 - [ ] Equivalence: assert the maude-optimised DAG == `optimize.sx`'s output on
   the existing fixtures (same nodes, same content ids) — the rule set must cover
   at least the hand-written passes.
-- [ ] Confluence / CID-stability check: **consume `mau/confluent?` from
+- [x] Confluence / CID-stability check: **consume `mau/confluent?` from
   `lib/maude/confluence.sx`** — do NOT build your own checker. Assert the
   optimisation rule module is confluent (`(mau/confluent? rules-module)` is
   true) so different rewrite orders reach the same normal form and the optimised
@@ -184,6 +184,26 @@ be an op token.
 
 ## Progress log
 
+- **2026-06-19 Phase 7 — optimisation laws + confluence** (maude-optimize 25/25,
+  total 183/183). `lib/artdag/optimize-rules.sx`: the effect-pipeline optimisation
+  passes as a maude module `ARTDAGOPT` — `id(I)=I`, `blur(I,0)=I`, `bright(I,0)=I`,
+  adjacent fusion `blur(blur(I,M),N)=blur(I,M+N)` (+bright), idempotent
+  `over(I,I)=I`. Key result: the radius algebra is `_+_ [assoc comm id: 0]` (unary
+  `1`s), NOT Peano successor rules — the Peano version is non-confluent (6
+  non-joinable critical pairs: `M+0` sticks, `(A+B)+C` vs `A+(B+C)` doesn't join),
+  whereas AC+id makes `(mau/confluent? artdag/opt-module)` true (0 non-joinable
+  pairs) by joining those overlaps via canonical form. So the optimised pipeline's
+  normal form — and hence its content id — is stable under any rewrite order.
+  `artdag/opt-normal-form`/`opt-reduce-term`/`opt-canon` reduce a surface pipeline;
+  `opt-same-form?` decides content-id equality; `opt-confluent?`/`opt-non-joinable`
+  /`opt-non-joinable->strs` consume `lib/maude/confluence.sx` (loaded into the
+  maude-optimize suite). Tests: confluence holds, every law fires, fusion is
+  rewrite-order stable, laws compose, dedup vs no-dedup, distinct pipelines stay
+  distinct. Gotcha: compare reduced *strings* (`mau/creduce->str`) — canon term
+  objects compare unequal under `=` even when the printed normal form is identical.
+  Remaining Phase 7: bridge the maude normal form back to a runnable DAG +
+  equivalence-with-`optimize.sx`.
+
 - **2026-06-07 Phase 7 — maude-bridge** (maude-optimize suite 14/14, total 172/172).
   `lib/artdag/maude-bridge.sx`: lossless adapter between an artdag effect DAG and a
   maude term. `artdag/dag->term dag id` walks from a sink, emitting `(mau/app op