diff --git a/jolt-core/clojure/core/00-syntax.clj b/jolt-core/clojure/core/00-syntax.clj
index 4a7af14..ed85a2d 100644
--- a/jolt-core/clojure/core/00-syntax.clj
+++ b/jolt-core/clojure/core/00-syntax.clj
@@ -445,3 +445,13 @@
 
 (defmacro lazy-cat [& colls]
   `(concat ~@(map (fn [c] `(lazy-seq ~c)) colls)))
+
+;; not= here (not 20-coll): the kernel tier uses it, and the kernel
+;; bootstrap-compiles right after this file loads. Canonical Clojure arities.
+(defn not=
+  ([x] false)
+  ([x y] (not (= x y)))
+  ([x y & more] (not (apply = x y more))))
+
+;; unreduced here: the seq tier's reduce machinery unwraps with it.
+(defn unreduced [x] (if (reduced? x) (deref x) x))
diff --git a/jolt-core/clojure/core/20-coll.clj b/jolt-core/clojure/core/20-coll.clj
index 293f937..a0717ce 100644
--- a/jolt-core/clojure/core/20-coll.clj
+++ b/jolt-core/clojure/core/20-coll.clj
@@ -6,6 +6,23 @@
 ;; Same migration rule as the seq tier (see 10-seq.clj): not in core-renames, no
 ;; internal Janet callers, not used by the self-hosted compiler.
 
+;; Tiny leaves first — fns below in this tier (and 25-sorted) use them.
+(defn identity [x] x)
+
+(defn constantly [x] (fn [& args] x))
+
+;; neg? throws on non-numbers via <, as Clojure's Numbers.isNeg does.
+(defn neg? [x] (< x 0))
+
+;; even?/odd? accept any integral number (jolt has one number type, so 2.0
+;; counts) and throw otherwise — Clojure's IllegalArgumentException wording.
+(defn even? [n]
+  (if (integer? n)
+    (zero? (rem n 2))
+    (throw (str "Argument must be an integer: " n))))
+
+(defn odd? [n] (not (even? n)))
+
 ;; Base is (hash-map), not the {} literal: a literal map is a struct that doesn't
 ;; canonicalize collection keys across representations (a {:a 1} literal vs
 ;; (hash-map :a 1) key), whereas a PHM does — so counting/grouping by collection
@@ -373,6 +390,17 @@
   ([keyfn comp coll]
    (sort (fn [x y] (comp (keyfn x) (keyfn y))) coll)))
 
+;; parse-uuid: nil unless s is a canonical 8-4-4-4-12 hex UUID string; throws
+;; on a non-string (Clojure 1.11). __make-uuid is the host constructor for the
+;; tagged value (overlay source can't write :jolt/type map literals — the
+;; reader treats them as tagged forms).
+(defn parse-uuid [s]
+  (if (string? s)
+    (when (re-matches
+           #"[0-9a-fA-F]{8}-[0-9a-fA-F]{4}-[0-9a-fA-F]{4}-[0-9a-fA-F]{4}-[0-9a-fA-F]{12}" s)
+      (__make-uuid s))
+    (throw (str "parse-uuid requires a string, got: " s))))
+
 ;; Version-4 UUID (RFC 4122): zero-padded hex groups 8-4-4-4-12, version
 ;; nibble 4, variant 8-b — built over rand-int and validated by parse-uuid.
 (defn random-uuid []
@@ -882,3 +910,65 @@
 ;; num: Clojure coerces to java.lang.Number; jolt just checks.
 (defn num [x]
   (if (number? x) x (throw (str "num requires a number, got: " x))))
+
+;; == numeric equality: 1-arity is trivially true without inspecting the value
+;; (Clojure's shape); 2+ args must be numbers, as Numbers.equiv throws.
+(defn ==
+  ([x] true)
+  ([x y]
+   (if (and (number? x) (number? y))
+     (= x y)
+     (throw (str "Cannot cast to number: " (if (number? x) y x)))))
+  ([x y & more]
+   (if (== x y)
+     (apply == y more)
+     false)))
+
+;; ensure-reduced / halt-when: canonical Clojure. halt-when smuggles the halt
+;; value through reduce in a ::halt-keyed map and unwraps it in the completion
+;; arity, so the halt REPLACES the whole reduction result.
+(defn ensure-reduced [x] (if (reduced? x) x (reduced x)))
+
+(defn halt-when
+  ([pred] (halt-when pred nil))
+  ([pred retf]
+   (fn [rf]
+     (fn
+       ([] (rf))
+       ([result]
+        (if (and (map? result) (contains? result ::halt))
+          (get result ::halt)
+          (rf result)))
+       ([result input]
+        (if (pred input)
+          (reduced (hash-map ::halt (if retf (retf (rf result) input) input)))
+          (rf result input)))))))
+
+;; parse-boolean: exact "true"/"false" only; nil on anything else, throw on a
+;; non-string (Clojure 1.11).
+(defn parse-boolean [s]
+  (if (string? s)
+    (cond (= s "true") true (= s "false") false :else nil)
+    (throw (str "parse-boolean requires a string, got: " s))))
+
+(defn newline [] (print "\n") nil)
+
+;; seque: jolt is single-threaded eager here — the queue is a no-op and the
+;; coll passes through.
+(defn seque
+  ([s] s)
+  ([n-or-q s] s))
+
+(defn array-seq [arr & _] (seq arr))
+
+(defn to-array-2d [coll] (to-array (map to-array coll)))
+
+;; Masking integer coercions (not aliases): byte/short wrap to their width.
+;; unchecked-char keeps jolt's historical NUMBER result (Clojure returns a
+;; char) — the char wrapper is a different value type here. int handles chars,
+;; so (unchecked-byte \a) works as on the JVM.
+(defn unchecked-byte [x] (bit-and (int x) 0xff))
+(defn unchecked-short [x] (bit-and (int x) 0xffff))
+(defn unchecked-char [x] (bit-and (int x) 0xffff))
+(defn unchecked-float [x] (double x))
+(defn unchecked-double [x] (double x))
diff --git a/jolt-core/clojure/core/30-macros.clj b/jolt-core/clojure/core/30-macros.clj
index 8747a09..2fd1be6 100644
--- a/jolt-core/clojure/core/30-macros.clj
+++ b/jolt-core/clojure/core/30-macros.clj
@@ -407,3 +407,10 @@
 ;; loads — so the macro must be registered BEFORE those tiers, else (lazy-seq …)
 ;; compiles as a call to the macro-as-function and leaks its expansion at runtime
 ;; (jolt-r81). They only need seed fns (make-lazy-seq/coll->cells/concat).
+
+;; memfn: a fn wrapping a method call, (memfn toUpperCase) => #(.toUpperCase %).
+;; The method symbol is rewritten to jolt's .method call sugar; extra arg names
+;; become fn params, as in Clojure.
+(defmacro memfn [method-name & args]
+  `(fn [target# ~@args]
+     (~(symbol (str "." (name method-name))) target# ~@args)))
diff --git a/src/jolt/core.janet b/src/jolt/core.janet
index 0e4ccbf..f4cb37f 100644
--- a/src/jolt/core.janet
+++ b/src/jolt/core.janet
@@ -231,9 +231,7 @@
 
 (defn core-zero? [x] (= (need-num x "zero?") 0))
 (defn core-pos? [x] (> (need-num x "pos?") 0))
-(defn core-neg? [x] (< (need-num x "neg?") 0))
-(defn core-even? [n] (= 0 (% (need-int n "even?") 2)))
-(defn core-odd? [n] (not= 0 (% (need-int n "odd?") 2)))
+# neg? / even? / odd? live in the Clojure collection tier (core/20-coll.clj).
 
 # Finite integral number: NaN and the infinities are NOT integers (floor of
 # inf is inf, so the naive floor check wrongly accepted them).
@@ -401,7 +399,7 @@
         (++ i))
       ok)))
 
-(defn core-not= [& args] (not (apply core-= args)))
+# not= lives in the syntax tier (core/00-syntax.clj) — the kernel uses it.
 
 # Comparisons are variadic: (< a b c) means a < b < c.
 (defn- chain-cmp [op opname xs]
@@ -818,7 +816,7 @@
 
 (defn core-reduced [x] @{:jolt/type :jolt/reduced :val x})
 (defn core-reduced? [x] (and (table? x) (= :jolt/reduced (x :jolt/type))))
-(defn core-unreduced [x] (if (core-reduced? x) (x :val) x))
+# unreduced lives in the syntax tier (core/00-syntax.clj) over reduced?/deref.
 (defn- ensure-reduced [x] (if (core-reduced? x) x (core-reduced x)))
 
 (defn td-map [f]
@@ -1402,9 +1400,7 @@
 # Higher-order functions
 # ============================================================
 
-(def core-identity (fn [x] x))
-
-(def core-constantly (fn [x] (fn [& _] x)))
+# identity / constantly live in the Clojure collection tier (core/20-coll.clj).
 
 # complement now lives in the Clojure collection tier (core/20-coll.clj).
 
@@ -1686,7 +1682,7 @@
   (prin "\n")
   nil)
 
-(defn core-newline [] (prin "\n") nil)
+# newline lives in the Clojure collection tier (core/20-coll.clj).
 
 # Clojure 1.11 string->scalar parsers: nil on malformed input, throw on a
 # non-string. Validation is strict (scan-number alone accepts 0x10 etc.).
@@ -1717,9 +1713,7 @@
       (def pat (peg/compile ~(sequence (opt (set "+-")) (choice (sequence (some :d) (opt (sequence "." (any :d)))) (sequence "." (some :d))) (opt (sequence (set "eE") (opt (set "+-")) (some :d))) -1)))
       (if (peg/match pat str*) (scan-number str*) nil))))
 
-(defn core-parse-boolean [s]
-  (def str* (parse-arg-str s "parse-boolean"))
-  (case str* "true" true "false" false nil))
+# parse-boolean lives in the Clojure collection tier (core/20-coll.clj).
 
 # Host time source for the `time` macro (monotonic, milliseconds).
 (defn core-current-time-ms [] (* 1000 (os/clock :monotonic)))
@@ -1933,8 +1927,7 @@
 
 (defn core-to-array [coll]
   (def arr @[]) (each x (realize-for-iteration coll) (array/push arr x)) arr)
-(defn core-to-array-2d [coll]
-  (def arr @[]) (each row (realize-for-iteration coll) (array/push arr (core-to-array row))) arr)
+# to-array-2d lives in the Clojure collection tier (core/20-coll.clj).
 
 # Array-element casts — identity on arrays; `bytes` coerces to a byte buffer.
 (defn core-bytes [x] (if (buffer? x) x (core-byte-array x)))
@@ -1949,11 +1942,8 @@
 # Scalar numeric coercions
 (defn core-byte [x] (let [b (band (math/trunc x) 0xff)] (if (>= b 128) (- b 256) b)))
 (defn core-short [x] (let [s (band (math/trunc x) 0xffff)] (if (>= s 0x8000) (- s 0x10000) s)))
-(defn core-unchecked-byte [x] (band (math/trunc x) 0xff))
-(defn core-unchecked-short [x] (band (math/trunc x) 0xffff))
-(defn core-unchecked-char [x] (band (math/trunc x) 0xffff))
-(defn core-unchecked-float [x] (* 1.0 x))
-(defn core-unchecked-double [x] (* 1.0 x))
+# The masking unchecked-byte/short/char and float/double coercions live in
+# the Clojure collection tier (core/20-coll.clj).
 
 # 64-bit integers (Janet int/s64 — C-backed)
 (defn core-bigint [x] (int/s64 x))
@@ -1982,8 +1972,7 @@
 # reader-conditional? now lives in the Clojure collection tier (tagged-value predicate).
 # sorted-map-by / sorted-set-by (and all other sorted-coll constructors and
 # semantics) now live in the Clojure sorted tier (core/25-sorted.clj).
-(defn core-array-seq [arr & _] (core-seq arr))
-(defn core-seque [& args] (in args (- (length args) 1)))
+# array-seq / seque live in the Clojure collection tier (core/20-coll.clj).
 # supers now lives in the Clojure collection tier (no class hierarchy: #{}).
 (defn core-class [x]
   (cond
@@ -2429,13 +2418,8 @@
 (defn core-proxy-call-with-super [f proxy meth] (f))
 (defn core-proxy-mappings [proxy] {})
 (defn core-update-proxy [proxy mappings] proxy)
-(defn core-numeric= [& args]
-  (if (< (length args) 2) true
-    (do (var ok true) (var i 0)
-      (while (and ok (< i (dec (length args))))
-        (unless (= (in args i) (in args (+ i 1))) (set ok false)) (++ i))
-      ok)))
-(defn core-memfn [& args] (error "memfn: JVM method handles are not supported in Jolt"))
+# == lives in the Clojure collection tier (core/20-coll.clj); memfn is an
+# overlay macro (core/30-macros.clj) over the .method call sugar.
 (defn core-eduction [& args]
   # (eduction xform* coll): apply the composed transducers eagerly to coll
   (let [n (length args)
@@ -2505,17 +2489,8 @@
 (defn core-deliver [p v] (core-reset! p v) p)
 
 (defn core-tagged-literal [tag form] @{:jolt/type :jolt/tagged-literal :tag tag :form form})
-(defn core-ensure-reduced [x] (if (core-reduced? x) x (core-reduced x)))
-(defn core-halt-when [pred & rest]
-  (let [retf (if (> (length rest) 0) (in rest 0) nil)]
-    (fn [rf]
-      (fn [& a]
-        (case (length a)
-          0 (rf)
-          1 (rf (in a 0))
-          (if (truthy? (pred (in a 1)))
-            (core-reduced (if retf (retf (rf (in a 0)) (in a 1)) (in a 1)))
-            (rf (in a 0) (in a 1))))))))
+# ensure-reduced / halt-when live in the Clojure collection tier
+# (core/20-coll.clj) — halt-when is the canonical ::halt-map version there.
 (defn core-re-groups [m] (error "re-groups: stateful matchers are not supported in Jolt"))
 
 # Transients — real mutable scratch collections backed by Janet's native arrays
@@ -2640,28 +2615,8 @@
 
 
 
-(defn- hex-digit? [c]
-  (or (and (>= c 48) (<= c 57))      # 0-9
-      (and (>= c 97) (<= c 102))     # a-f
-      (and (>= c 65) (<= c 70))))    # A-F
-
-(defn core-parse-uuid
-  "(parse-uuid s) -> the UUID, or nil when s is not a canonical 8-4-4-4-12 hex
-  UUID string. Throws when s is not a string (Clojure 1.11)."
-  [s]
-  (when (not (or (string? s) (buffer? s)))
-    (error (string "parse-uuid requires a string, got " (type s))))
-  (def dash-at {8 true 13 true 18 true 23 true})
-  (if (and (= 36 (length s))
-           (do
-             (var ok true)
-             (for i 0 36
-               (if (get dash-at i)
-                 (when (not= 45 (in s i)) (set ok false))    # 45 = "-"
-                 (when (not (hex-digit? (in s i))) (set ok false))))
-             ok))
-    (make-uuid s)
-    nil))
+# parse-uuid lives in the Clojure collection tier (core/20-coll.clj) over
+# re-matches + the __make-uuid host constructor (types.janet).
 
 (def- core-bindings
   "Map of symbol name → function for all core functions."
@@ -2678,9 +2633,6 @@
     "identical?" core-identical?
     "zero?" core-zero?
     "pos?" core-pos?
-    "neg?" core-neg?
-    "even?" core-even?
-    "odd?" core-odd?
     "integer?" core-integer?
     "list?" core-list?
     "every?" core-every?
@@ -2695,7 +2647,6 @@
     "quot" core-quot
     "rand" core-rand
     "=" core-=
-    "not=" core-not=
     "<" core-<
     ">" core->
     "<=" core-<=
@@ -2733,9 +2684,6 @@
     "future?" core-future?
     "future-cancel" core-future-cancel
     "tagged-literal" core-tagged-literal
-    "ensure-reduced" core-ensure-reduced
-    "unreduced" core-unreduced
-    "halt-when" core-halt-when
     "re-groups" core-re-groups
     "transient" core-transient
     "transient?" core-transient?
@@ -2748,6 +2696,7 @@
     "hash-ordered-coll" core-hash-ordered-coll
     "hash-unordered-coll" core-hash-unordered-coll
     "gensym" gensym
+    "__make-uuid" make-uuid
     "compare" core-compare
     "type" core-type
     "slurp" core-slurp
@@ -2759,10 +2708,7 @@
     "__list-dir" core-list-dir
     "parse-long" core-parse-long
     "parse-double" core-parse-double
-    "parse-boolean" core-parse-boolean
-    "newline" core-newline
     "current-time-ms" core-current-time-ms
-    "parse-uuid" core-parse-uuid
     "mapcat" core-mapcat
     "transduce" core-transduce
     "sequence" core-sequence
@@ -2785,8 +2731,6 @@
     "sort" core-sort
     "partition" core-partition
     "range" core-range
-    "identity" core-identity
-    "constantly" core-constantly
     "vector" core-vector
     "hash-map" core-hash-map
     "array-map" core-array-map
@@ -2845,7 +2789,6 @@
     "make-array" core-make-array
     "into-array" core-into-array
     "to-array" core-to-array
-    "to-array-2d" core-to-array-2d
     "bytes" core-bytes
     "booleans" core-booleans
     "ints" core-ints
@@ -2856,11 +2799,6 @@
     "chars" core-chars
     "byte" core-byte
     "short" core-short
-    "unchecked-byte" core-unchecked-byte
-    "unchecked-short" core-unchecked-short
-    "unchecked-char" core-unchecked-char
-    "unchecked-float" core-unchecked-float
-    "unchecked-double" core-unchecked-double
     "bigint" core-bigint
     "biginteger" core-biginteger
     "chunk-buffer" core-chunk-buffer
@@ -2874,8 +2812,6 @@
     "cat" core-cat
     "disj!" core-disj!
     "reader-conditional" core-reader-conditional
-    "array-seq" core-array-seq
-    "seque" core-seque
     "class" core-class
     "enumeration-seq" core-enumeration-seq
     "iterator-seq" core-iterator-seq
@@ -2886,8 +2822,6 @@
     "proxy-call-with-super" core-proxy-call-with-super
     "proxy-mappings" core-proxy-mappings
     "update-proxy" core-update-proxy
-    "==" core-numeric=
-    "memfn" core-memfn
     "eduction" core-eduction
     "->Eduction" core->Eduction
     "proxy-super" core-proxy-super
diff --git a/test/spec/numbers-spec.janet b/test/spec/numbers-spec.janet
index 38cb1b9..1c83e9a 100644
--- a/test/spec/numbers-spec.janet
+++ b/test/spec/numbers-spec.janet
@@ -192,3 +192,15 @@
   ["num passes a number through" "5"   "(num 5)"]
   ["num on a double"        "5.5" "(num 5.5)"]
   ["num throws on non-number" :throws "(num \"x\")"])
+
+# == is numeric equality: single arg is trivially true (Clojure's 1-arity
+# never inspects the value); 2+ args must be numbers.
+(defspec "numbers / == numeric equality"
+  ["== single arg"          "true"  "(== :a)"]
+  ["== equal"               "true"  "(== 2 2)"]
+  ["== unequal"             "false" "(== 2 3)"]
+  ["== chained"             "true"  "(== 2 2 2)"]
+  ["== chained unequal"     "false" "(== 2 2 3)"]
+  ["== int and double"      "true"  "(== 1 1.0)"]
+  ["== throws on non-number" :throws "(== 1 :a)"]
+  ["== throws on two keywords" :throws "(== :a :a)"])
diff --git a/test/spec/transducers-spec.janet b/test/spec/transducers-spec.janet
index 727581f..2b38908 100644
--- a/test/spec/transducers-spec.janet
+++ b/test/spec/transducers-spec.janet
@@ -28,6 +28,19 @@
   ["eduction"           "[2 3 4]"   "(into [] (eduction (map inc) [1 2 3]))"]
   ["completing"         "9"        "(transduce (map inc) (completing +) 0 [1 2 3])"])
 
+# halt-when replaces the WHOLE reduction result with the halting input (or
+# with (retf acc input)) — Clojure's ::halt map protocol, unwrapped by the
+# transducer's completion arity.
+(defspec "transducers / halt-when"
+  ["halt returns the halting input" "7"
+   "(transduce (halt-when (fn [x] (> x 5))) conj [1 2 7 3])"]
+  ["no halt is a plain reduction" "[1 2 3]"
+   "(transduce (halt-when (fn [x] (> x 5))) conj [1 2 3])"]
+  ["retf combines acc and input" "[[1 2] 7]"
+   "(transduce (halt-when (fn [x] (> x 5)) (fn [r i] [r i])) conj [1 2 7 3])"]
+  ["halt-when through into" "3"
+   "(into [] (halt-when odd?) [2 4 3 6])"])
+
 # A `take`/`take-while` transducer returns `reduced`, which must short-circuit
 # the reduction so transducing over an INFINITE seq terminates rather than
 # realizing it eagerly.
diff --git a/test/spec/untested-vars-spec.janet b/test/spec/untested-vars-spec.janet
index db2991c..a9a99ee 100644
--- a/test/spec/untested-vars-spec.janet
+++ b/test/spec/untested-vars-spec.janet
@@ -114,7 +114,11 @@
   ["update-proxy"  "nil" "(update-proxy nil {})"]
   ["proxy-mappings" "{}" "(proxy-mappings nil)"]
   ["proxy-call-with-super calls" "1" "(proxy-call-with-super (fn [] 1) nil \"m\")"]
-  ["memfn throws"  :throws "((memfn count) \"abc\")"]
+  ["memfn upper"   "\"ABC\"" "((memfn toUpperCase) \"abc\")"]
+  ["memfn with args" "2"   "((memfn indexOf needle) \"hello\" \"l\")"]
+  ["memfn length"  "3"     "((memfn length) \"abc\")"]
+  ["array-seq"     "(quote (1 2 3))" "(array-seq (to-array [1 2 3]))"]
+  ["array-seq empty" "nil" "(array-seq (to-array []))"]
   ["proxy-super throws" :throws "(proxy-super count [1])"]
   ["re-groups throws" :throws "(re-groups (re-matcher #\"a\" \"b\"))"]
   ["re-matcher builds" "false" "(nil? (re-matcher #\"a\" \"abc\"))"]