diff --git a/lib/kernel/runtime.sx b/lib/kernel/runtime.sx
index 03480b32..38841c8a 100644
--- a/lib/kernel/runtime.sx
+++ b/lib/kernel/runtime.sx
@@ -391,6 +391,45 @@
             (error (str name ": expects 2 arguments")))
           (:else (f (first args) (nth args 1))))))))
 
+;; Variadic left-fold helper. ZERO-RES is the identity (`(+)` → 0);
+;; ONE-FN handles single-arg case (`(- x)` negates; `(+ x)` returns x).
+(define knl-fold-step
+  (fn (f acc rest-args)
+    (cond
+      ((or (nil? rest-args) (= (length rest-args) 0)) acc)
+      (:else
+        (knl-fold-step f (f acc (first rest-args)) (rest rest-args))))))
+
+(define knl-fold-app
+  (fn (name f zero-res one-fn)
+    (kernel-make-primitive-applicative
+      (fn (args)
+        (cond
+          ((= (length args) 0) zero-res)
+          ((= (length args) 1) (one-fn (first args)))
+          (:else (knl-fold-step f (first args) (rest args))))))))
+
+;; Variadic n-ary chained comparison: `(< 1 2 3)` ≡ `(< 1 2)` AND `(< 2 3)`.
+(define knl-chain-step
+  (fn (cmp prev rest-args)
+    (cond
+      ((or (nil? rest-args) (= (length rest-args) 0)) true)
+      (:else
+        (let ((next (first rest-args)))
+          (cond
+            ((cmp prev next)
+              (knl-chain-step cmp next (rest rest-args)))
+            (:else false)))))))
+
+(define knl-chain-cmp
+  (fn (name cmp)
+    (kernel-make-primitive-applicative
+      (fn (args)
+        (cond
+          ((< (length args) 2)
+            (error (str name ": expects at least 2 arguments")))
+          (:else (knl-chain-step cmp (first args) (rest args))))))))
+
 ;; ── list / pair primitives ──────────────────────────────────────
 
 (define
@@ -657,14 +696,18 @@
         env
         "get-current-environment"
         kernel-get-current-env-operative)
-      (kernel-env-bind! env "+" (knl-bin-app "+" (fn (a b) (+ a b))))
-      (kernel-env-bind! env "-" (knl-bin-app "-" (fn (a b) (- a b))))
-      (kernel-env-bind! env "*" (knl-bin-app "*" (fn (a b) (* a b))))
-      (kernel-env-bind! env "/" (knl-bin-app "/" (fn (a b) (/ a b))))
-      (kernel-env-bind! env "<" (knl-bin-app "<" (fn (a b) (< a b))))
-      (kernel-env-bind! env ">" (knl-bin-app ">" (fn (a b) (> a b))))
-      (kernel-env-bind! env "<=?" (knl-bin-app "<=?" (fn (a b) (<= a b))))
-      (kernel-env-bind! env ">=?" (knl-bin-app ">=?" (fn (a b) (>= a b))))
+      (kernel-env-bind! env "+"
+        (knl-fold-app "+" (fn (a b) (+ a b)) 0 (fn (x) x)))
+      (kernel-env-bind! env "-"
+        (knl-fold-app "-" (fn (a b) (- a b)) 0 (fn (x) (- 0 x))))
+      (kernel-env-bind! env "*"
+        (knl-fold-app "*" (fn (a b) (* a b)) 1 (fn (x) x)))
+      (kernel-env-bind! env "/"
+        (knl-fold-app "/" (fn (a b) (/ a b)) 1 (fn (x) (/ 1 x))))
+      (kernel-env-bind! env "<"   (knl-chain-cmp "<"   (fn (a b) (< a b))))
+      (kernel-env-bind! env ">"   (knl-chain-cmp ">"   (fn (a b) (> a b))))
+      (kernel-env-bind! env "<=?" (knl-chain-cmp "<=?" (fn (a b) (<= a b))))
+      (kernel-env-bind! env ">=?" (knl-chain-cmp ">=?" (fn (a b) (>= a b))))
       (kernel-env-bind! env "=?" kernel-eq?-applicative)
       (kernel-env-bind! env "equal?" kernel-equal?-applicative)
       (kernel-env-bind! env "eq?" kernel-eq?-applicative)
diff --git a/lib/kernel/tests/standard.sx b/lib/kernel/tests/standard.sx
index ee70ea58..c637f02e 100644
--- a/lib/kernel/tests/standard.sx
+++ b/lib/kernel/tests/standard.sx
@@ -337,4 +337,30 @@
 (ks-test "or: middle truthy"
   (ks-eval "($or? #f 42 nope)") 42)
 
+;; ── variadic arithmetic ─────────────────────────────────────────
+(ks-test "+: zero args = 0"    (ks-eval "(+)") 0)
+(ks-test "+: one arg = arg"    (ks-eval "(+ 7)") 7)
+(ks-test "+: two args"         (ks-eval "(+ 3 4)") 7)
+(ks-test "+: five args"        (ks-eval "(+ 1 2 3 4 5)") 15)
+
+(ks-test "*: zero args = 1"    (ks-eval "(*)") 1)
+(ks-test "*: one arg"          (ks-eval "(* 7)") 7)
+(ks-test "*: four args"        (ks-eval "(* 1 2 3 4)") 24)
+
+(ks-test "-: one arg negates"  (ks-eval "(- 10)") -10)
+(ks-test "-: two args"         (ks-eval "(- 10 3)") 7)
+(ks-test "-: four args fold"   (ks-eval "(- 100 1 2 3)") 94)
+
+(ks-test "/: two args"         (ks-eval "(/ 20 5)") 4)
+(ks-test "/: three args fold"  (ks-eval "(/ 100 2 5)") 10)
+
+;; ── variadic chained comparison ─────────────────────────────────
+(ks-test "<: chained ascending"  (ks-eval "(< 1 2 3 4 5)") true)
+(ks-test "<: not strict"          (ks-eval "(< 1 2 2 3)") false)
+(ks-test "<: anti-monotonic"      (ks-eval "(< 5 3)") false)
+(ks-test ">: chained descending" (ks-eval "(> 5 4 3 2 1)") true)
+(ks-test "<=? ascending equals"   (ks-eval "(<=? 1 1 2 3 3)") true)
+(ks-test "<=? violation"          (ks-eval "(<=? 1 2 1)") false)
+(ks-test ">=? descending equals" (ks-eval "(>=? 3 3 2 1)") true)
+
 (define ks-tests-run! (fn () {:total (+ ks-test-pass ks-test-fail) :passed ks-test-pass :failed ks-test-fail :fails ks-test-fails}))
diff --git a/plans/kernel-on-sx.md b/plans/kernel-on-sx.md
index cffb4885..6643d0ab 100644
--- a/plans/kernel-on-sx.md
+++ b/plans/kernel-on-sx.md
@@ -160,6 +160,7 @@ The motivation is that SX's host `make-env` family is registered only in HTTP/si
 
 ## Progress log
 
+- 2026-05-11 — Variadic `+ - * /` and chained `< > <=? >=?`. `(+ 1 2 3)` = 6, `(+)` = 0, `(+ 7)` = 7. `(- 10 1 2 3)` = 4 (left fold); single-arg `-` negates. `(* 1 2 3 4)` = 24, `(*)` = 1. Chained comparison: `(< 1 2 3)` ≡ `(< 1 2) ∧ (< 2 3)`. Implementation: `knl-fold-app` for n-ary fold with zero-arity identity and one-arity special-case; `knl-chain-cmp` for chained boolean. 19 new tests. chisel: nothing (mechanical extension of existing arithmetic primitives). 279 tests total.
 - 2026-05-11 — `$let*` sequential let. Each binding evaluated in scope where earlier bindings are visible, so `($let* ((x 1) (y (+ x 1))) y)` returns 2. Implemented by nesting envs one per binding — `knl-let*-step` recursively builds the env chain. `$let` and `$let*` now both accept multi-expression bodies (`knl-eval-body` re-used). 8 new tests in `tests/hygiene.sx`. chisel: nothing (a standard derived form). 260 tests total.
 - 2026-05-11 — `$and?` / `$or?` short-circuit booleans. Operatives (not applicatives) so untaken arguments are NOT evaluated. Identity values: `$and?` empty = true, `$or?` empty = false. Returns the last evaluated value (Kernel convention — not coerced to bool). 10 new tests including the short-circuit verification (`($and? #f nope)` returns false without evaluating `nope`). chisel: shapes-reflective. Sketched `lib/guest/reflective/short-circuit.sx` API; the protocol is identical across reflective Lisps because short-circuit FORCES operative semantics — an applicative variant would defeat the purpose. 252 tests total.
 - 2026-05-11 — `$cond` / `$when` / `$unless`. Standard Kernel control flow added: `$cond` walks clauses in order, evaluates first truthy test, runs that clause's body in sequence; `else` is the catch-all symbol; empty cond and no-match cond return nil. `$when` and `$unless` are simple conditional execution. All three preserve hygiene (clauses not taken are NOT evaluated). 12 new tests in `tests/standard.sx`. chisel: nothing. 242 tests total. (Third `nothing` in a row but allowable here — these are textbook Kernel idioms with no novel reflective angle.)