mk: pythagorean triples search — intarith showcase

Finds all (a, b, c) with a, b, c in [1..10], a <= b, a^2 + b^2 = c^2.
Result: ((3 4 5) (6 8 10)) — the two smallest Pythagorean triples
within the domain.

Demonstrates the enumerate-then-filter pattern:
  (ino a dom) (ino b dom) (ino c dom) — generate
  (lteo-i a b) — symmetry break
  (*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) — squares
  (pluso-i a-sq b-sq sum) (== sum c-sq) — Pythagorean equation

288/288 cumulative.

lib/minikanren/tests/pythag.sx

@@ -0,0 +1,36 @@
+;; lib/minikanren/tests/pythag.sx — Pythagorean triple search.
+;;
+;; Uses ino + intarith goals to find triples (a, b, c) with
+;; a, b, c ∈ [1..N], a ≤ b, a² + b² = c². With intarith escapes
+;; the search runs at host-arithmetic speed.
+
+(define
+  digits-1-10
+  (list
+    1
+    2
+    3
+    4
+    5
+    6
+    7
+    8
+    9
+    10))
+
+(mk-test
+  "pythag-triples-1-to-10"
+  (let
+    ((triples (run* q (fresh (a b c a-sq b-sq sum c-sq) (ino a digits-1-10) (ino b digits-1-10) (ino c digits-1-10) (lteo-i a b) (*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) (pluso-i a-sq b-sq sum) (== sum c-sq) (== q (list a b c))))))
+    (and
+      (= (len triples) 2)
+      (and
+        (some
+          (fn (t) (= t (list 3 4 5)))
+          triples)
+        (some
+          (fn (t) (= t (list 6 8 10)))
+          triples))))
+  true)
+
+(mk-tests-run!)

plans/minikanren-on-sx.md

@@ -173,6 +173,11 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **Pythagorean triples (intarith showcase)**: search for
+  (a, b, c) ∈ [1..10]³, a ≤ b, a² + b² = c² via `ino + lteo-i + *o-i +
+  pluso-i + ==`. Finds exactly `(3 4 5)` and `(6 8 10)`. Demonstrates the
+  enumerate-then-filter pattern with intarith escape into host arithmetic.
+  1 new test, 288/288 cumulative.
 - **2026-05-08** — **intarith.sx — fast ground-only integer arithmetic**:
   pluso-i / minuso-i / *o-i / lto-i / lteo-i / neqo-i wrap host arithmetic
   via `project`. They are not relational like Peano `pluso` (require args