diff --git a/lib/prolog/runtime.sx b/lib/prolog/runtime.sx
index 596f051f..816bc84a 100644
--- a/lib/prolog/runtime.sx
+++ b/lib/prolog/runtime.sx
@@ -309,6 +309,12 @@
             (nth (pl-args g) 1)
             trail
             k))
+        ((and (pl-compound? g) (= (pl-fun g) "is") (= (len (pl-args g)) 2))
+          (pl-solve-eq!
+            (first (pl-args g))
+            (list "num" (pl-eval-arith (nth (pl-args g) 1)))
+            trail
+            k))
         ((and (pl-compound? g) (= (pl-fun g) ",") (= (len (pl-args g)) 2))
           (pl-solve!
             db
@@ -429,6 +435,47 @@
           (str (pl-fun w) "(" (pl-format-args (pl-args w)) ")"))
         (true (str w))))))
 
+(define
+  pl-eval-arith
+  (fn
+    (t)
+    (let
+      ((w (pl-walk-deep t)))
+      (cond
+        ((pl-num? w) (pl-num-val w))
+        ((pl-compound? w)
+          (let
+            ((f (pl-fun w)) (args (pl-args w)))
+            (cond
+              ((and (= f "+") (= (len args) 2))
+                (+
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "-") (= (len args) 2))
+                (-
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "-") (= (len args) 1))
+                (- 0 (pl-eval-arith (first args))))
+              ((and (= f "*") (= (len args) 2))
+                (*
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "/") (= (len args) 2))
+                (/
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "mod") (= (len args) 2))
+                (mod
+                  (pl-eval-arith (first args))
+                  (pl-eval-arith (nth args 1))))
+              ((and (= f "abs") (= (len args) 1))
+                (let
+                  ((v (pl-eval-arith (first args))))
+                  (cond ((< v 0) (- 0 v)) (true v))))
+              (true 0))))
+        (true 0)))))
+
 (define
   pl-solve-not-eq!
   (fn
diff --git a/lib/prolog/tests/solve.sx b/lib/prolog/tests/solve.sx
index 59257757..f043c729 100644
--- a/lib/prolog/tests/solve.sx
+++ b/lib/prolog/tests/solve.sx
@@ -495,4 +495,124 @@
     pl-output-buffer)
   "hi\n")
 
+(define pl-s-env-arith1 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, 42)" pl-s-env-arith1)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, 42) binds X to 42"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith1 "X")))
+  42)
+
+(define pl-s-env-arith2 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, +(2, 3))" pl-s-env-arith2)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, +(2, 3)) binds X to 5"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith2 "X")))
+  5)
+
+(define pl-s-env-arith3 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, *(2, 3))" pl-s-env-arith3)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, *(2, 3)) binds X to 6"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith3 "X")))
+  6)
+
+(define pl-s-env-arith4 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, -(10, 3))" pl-s-env-arith4)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, -(10, 3)) binds X to 7"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith4 "X")))
+  7)
+
+(define pl-s-env-arith5 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, /(10, 2))" pl-s-env-arith5)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, /(10, 2)) binds X to 5"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith5 "X")))
+  5)
+
+(define pl-s-env-arith6 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, mod(10, 3))" pl-s-env-arith6)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, mod(10, 3)) binds X to 1"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith6 "X")))
+  1)
+
+(define pl-s-env-arith7 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, abs(-(0, 5)))" pl-s-env-arith7)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, abs(-(0, 5))) binds X to 5"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith7 "X")))
+  5)
+
+(define pl-s-env-arith8 {})
+
+(pl-solve-once!
+  pl-s-empty-db
+  (pl-s-goal "is(X, +(2, *(3, 4)))" pl-s-env-arith8)
+  (pl-mk-trail))
+
+(pl-s-test!
+  "is(X, +(2, *(3, 4))) binds X to 14 (nested)"
+  (pl-num-val (pl-walk-deep (dict-get pl-s-env-arith8 "X")))
+  14)
+
+(pl-s-test!
+  "is(5, +(2, 3)) succeeds (LHS num matches)"
+  (pl-solve-once!
+    pl-s-empty-db
+    (pl-s-goal "is(5, +(2, 3))" {})
+    (pl-mk-trail))
+  true)
+
+(pl-s-test!
+  "is(6, +(2, 3)) fails (LHS num mismatch)"
+  (pl-solve-once!
+    pl-s-empty-db
+    (pl-s-goal "is(6, +(2, 3))" {})
+    (pl-mk-trail))
+  false)
+
+(pl-s-test!
+  "is propagates bound vars on RHS"
+  (pl-solve-once!
+    pl-s-empty-db
+    (pl-s-goal "=(Y, 4), is(X, +(Y, 1)), =(X, 5)" {})
+    (pl-mk-trail))
+  true)
+
 (define pl-solve-tests-run! (fn () {:failed pl-s-test-fail :passed pl-s-test-pass :total pl-s-test-count :failures pl-s-test-failures}))
diff --git a/plans/prolog-on-sx.md b/plans/prolog-on-sx.md
index 336d7e39..5cf35264 100644
--- a/plans/prolog-on-sx.md
+++ b/plans/prolog-on-sx.md
@@ -54,7 +54,7 @@ Representation choices (finalise in phase 1, document here):
 - [x] Solver: DFS with choice points backed by delimited continuations (`lib/callcc.sx`). On goal entry, capture; per matching clause, unify head + recurse body; on failure, undo trail, try next — first cut: trail-based undo + CPS k (no shift/reset yet, per briefing gotcha). Built-ins so far: `true/0`, `fail/0`, `=/2`, `,/2`. Refactor to delimited conts later.
 - [x] Cut (`!`): cut barrier at current choice-point frame; collapse all up to barrier — two-cut-box scheme: each `pl-solve-user!` creates a fresh inner-cut-box (set by `!` in this predicate's body) AND snapshots the outer-cut-box state on entry. After body fails, abandon clause alternatives if (a) inner was set or (b) outer transitioned false→true during this call. Lets post-cut goals backtrack normally while blocking pre-cut alternatives. 6 cut tests cover bare cut, clause-commit, choice-commit, cut+fail, post-cut backtracking, nested-cut isolation.
 - [x] Built-ins: `=/2`, `\\=/2`, `true/0`, `fail/0`, `!/0`, `,/2`, `;/2`, `->/2` inside `;`, `call/1`, `write/1`, `nl/0` — all 11 done. `write/1` and `nl/0` use a global `pl-output-buffer` string + `pl-output-clear!` for testability; `pl-format-term` walks deep then renders atoms/nums/strs/compounds/vars (var → `_<id>`). Note: cut-transparency via `;` not testable yet without operator support — `;(,(a,!), b)` parser-rejects because `,` is body-operator-only; revisit in phase 4.
-- [ ] Arithmetic `is/2` with `+ - * / mod abs`
+- [x] Arithmetic `is/2` with `+ - * / mod abs` — `pl-eval-arith` walks deep, recurses on compounds, dispatches on functor; binary `+ - * / mod`, binary AND unary `-`, unary `abs`. `is/2` evaluates RHS, wraps as `("num" v)`, unifies via `pl-solve-eq!`. 11 tests cover each op + nested + ground LHS match/mismatch + bound-var-on-RHS chain.
 - [ ] Classic programs in `lib/prolog/tests/programs/`:
   - [ ] `append.pl` — list append (with backtracking)
   - [ ] `reverse.pl` — naive reverse
@@ -88,6 +88,7 @@ Representation choices (finalise in phase 1, document here):
 
 _Newest first. Agent appends on every commit._
 
+- 2026-04-25 — `is/2` arithmetic landed. `pl-eval-arith` recursively evaluates ground RHS expressions (binary `+ - * /`, `mod`; binary+unary `-`; unary `abs`); `is/2` wraps the value as `("num" v)` and unifies via `pl-solve-eq!`, so it works in all three modes — bind unbound LHS, check ground LHS for equality, propagate from earlier var bindings on RHS. 11 tests, total 148 (+11). Without operator support, expressions must be written prefix: `is(X, +(2, *(3, 4)))`.
 - 2026-04-25 — `write/1` + `nl/0` landed using global string buffer (`pl-output-buffer` + `pl-output-clear!` + `pl-output-write!`). `pl-format-term` walks deep + dispatches on atom/num/str/compound/var; `pl-format-args` recursively comma-joins. 7 new tests cover atom/num/compound formatting, conjunction order, var-walk, and `nl`. Built-ins box (`=/2`, `\\=/2`, `true/0`, `fail/0`, `!/0`, `,/2`, `;/2`, `->/2`, `call/1`, `write/1`, `nl/0`) now ticked. Total 137 (+7).
 - 2026-04-25 — `->/2` if-then-else landed (both `;(->(C,T), E)` and standalone `->(C, T)` ≡ `(C -> T ; fail)`). `pl-solve-or!` now special-cases `->` in left arg → `pl-solve-if-then-else!`. Cond runs in a fresh local cut-box (ISO opacity for cut inside cond). Then-branch can backtrack, else-branch can backtrack, but cond commits to first solution. 9 new tests covering both forms, both branches, binding visibility, cond-commit, then-backtrack, else-backtrack. Total 130 (+9).
 - 2026-04-25 — Built-ins `\=/2`, `;/2`, `call/1` landed. `pl-solve-not-eq!` (try unify, always undo, succeed iff unify failed). `pl-solve-or!` (try left, on failure check cut and only try right if not cut). `call/1` opens a fresh inner cut-box (ISO opacity: cut inside `call(G)` commits G, not caller). 11 new tests in `tests/solve.sx` cover atoms+vars for `\=`, both branches + count for `;`, and `call/1` against atoms / compounds / bound goal vars. Total 121 (+11). Box not yet ticked — `->/2`, `write/1`, `nl/0` still pending.