artdag: Phase 7 non-vacuous confluence gate regression + 2 tests

Assert mau/confluent? actually discriminates: the Peano-arithmetic variant of the
optimisation laws is flagged non-confluent with named non-joinable pairs, so the green
'opt module is confluent' is real evidence rather than a rubber stamp. maude-optimize
40/40, total 198/198.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

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": 38, "fail": 0}
+    "maude-optimize": {"pass": 40, "fail": 0}
   },
-  "total_pass": 196,
+  "total_pass": 198,
   "total_fail": 0,
-  "total": 196
+  "total": 198
 }

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 | 38 | 0 | 38 |
-| **Total** | **196** | **0** | **196** |
+| maude-optimize | 40 | 0 | 40 |
+| **Total** | **198** | **0** | **198** |

lib/artdag/tests/maude-optimize.sx

@@ -301,3 +301,45 @@
   "opt-cheaper?: untouched DAG keeps equal cost (never a pessimisation)"
   (artdag/opt-cheaper? mo-plain mo-plain-id artdag/const-cost)
   true)
+
+; ---- the confluence gate is meaningful, not vacuous ----
+; the Peano-arithmetic variant of the same laws is KNOWN non-confluent (M+0 sticks,
+; (A+B)+C vs A+(B+C) don't join). Assert the checker actually catches it, so the
+; green "opt module is confluent" above is real evidence, not a checker that passes
+; everything.
+
+(define
+  mo-peano-module
+  (mau/parse-module
+    (str
+      "fmod ARTDAGPEANO is\n"
+      "  sorts Img Num .\n"
+      "  op src : -> Img .\n"
+      "  op 0 : -> Num .\n"
+      "  op s_ : Num -> Num .\n"
+      "  op _+_ : Num Num -> Num .\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 0 + N = N .\n"
+      "  eq s M + N = s (M + N) .\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")))
+
+(artdag-test
+  "confluence gate is real: Peano variant is flagged non-confluent"
+  (mau/confluent? mo-peano-module)
+  false)
+
+(artdag-test
+  "confluence gate is real: Peano variant names its non-joinable pairs"
+  (> (len (mau/non-joinable-pairs mo-peano-module)) 0)
+  true)

plans/artdag-on-sx.md

@@ -31,7 +31,7 @@ edges.
 
 ## Status (rolling)
 
-`bash lib/artdag/conformance.sh` → **196/196** (11 suites: dag, analyze, plan, execute, optimize, fed, cost, serialize, stats, fault, maude-optimize)
+`bash lib/artdag/conformance.sh` → **198/198** (11 suites: dag, analyze, plan, execute, optimize, fed, cost, serialize, stats, fault, maude-optimize)
 
 Base roadmap (Phases 1–6) COMPLETE. Now extending.
 
@@ -191,6 +191,13 @@ be an op token.
 
 ## Progress log
 
+- **2026-06-19 Phase 7 — confluence gate is non-vacuous** (maude-optimize 40/40, total
+  198/198). Added a regression proving `mau/confluent?` actually discriminates: the
+  Peano-arithmetic variant of the same laws (`0 + N = N`, `s M + N = s(M+N)` instead of
+  `_+_ [assoc comm id: 0]`) is asserted **non-confluent** with named non-joinable pairs,
+  so the green "opt module is confluent" is real evidence, not a checker that rubber-stamps
+  everything. Documents the exact AC-vs-Peano design choice as an executable contrast.
+
 - **2026-06-19 Phase 7 — cost-directed: optimisation is never a pessimisation**
   (maude-optimize 38/38, total 196/196). `artdag/opt-improvement dag id cost-fn` compares
   the original output cone (`artdag/dce` to `id`) against the maude-reduced DAG under an