diff --git a/lib/check.ml b/lib/check.ml
index 1691019..0e4b2f9 100644
--- a/lib/check.ml
+++ b/lib/check.ml
@@ -854,8 +854,19 @@ let rec resolve env ?(seen = []) (t : Ast.texpr) : Types.t =
      | "Map", _ -> fail loc "(Map K V) takes exactly two types"
      | "Result", _ -> unimplemented loc "(Result T E)" 6
      | _ ->
+       (* Not generics, which are here: a *function* is generic over [$t] and
+          instantiated per call site. This is a parameterised named type —
+          [(Pair i32 f64)] — and that is a different thing and is not built.
+          [Types.Named] is a bare string with no parameters, so there is
+          nowhere to put the arguments, and giving it some is a change to
+          [Types.t] and therefore to the layout calculator, both backends,
+          [Render] and the DWARF path. docs/SPIKE-GENERICS.md, question 4,
+          prices it and leaves it out. *)
        fail loc
-         "%s takes no type arguments — generics are milestone 5" name)
+         "%s takes no type arguments. A generic *function* is written with \
+          [$t] in its parameter vector and copied per call site; a generic \
+          *type* — (%s ...) — is not there yet"
+         name name)
 
 (* One edit away from a type that exists — a substitution, an insertion, a
    deletion or a transposition of neighbours. Bounded at one, because two edits
@@ -951,12 +962,26 @@ and resolve_name env ~seen loc n =
       | _ when near_miss env n <> None ->
         Loc.failk "check/unknown-type" loc "unknown type %s — did you mean %s?" n
           (Option.get (near_miss env n))
-      (* Lowercase is a type variable, Capitalized is concrete — no sigil
-         (plan.org, Types). A variable parses, but nothing at milestone 2 can
-         give a value one, so it is rejected here rather than later. *)
+      (* An unknown lowercase name, and the sentence it gets used to be that
+         generics were milestone 5 work. They are not: [$t] binds a type
+         variable and bare [t] uses one, and [resolve_name] has already
+         consulted [env.tyvars] and [env.subst] before anything reaches here.
+         So a lowercase name arriving at this arm is one of exactly two
+         things, and the message names both rather than sending somebody to a
+         schedule.
+
+         Either it is a typo too far from any type to be guessed at — the
+         near-miss arm above catches the one-edit ones — or it is a type
+         variable that was never introduced, which is the sigil's whole
+         purpose to notice: without the binding site a mistyped type name
+         silently became a type parameter and made the signature more
+         permissive than it was written to be. *)
       | _ when n <> "" && n.[0] = Char.lowercase_ascii n.[0] ->
-        unimplemented loc
-          (Printf.sprintf "generic code over the type variable %s" n) 5
+        Loc.failk "check/unknown-type" loc
+          "unknown type %s. A lowercase name is a type variable only where a \
+           defn signature introduced it — write $%s in the parameter vector \
+           to introduce one, and %s reads it from there"
+          n n n
       | _ -> Loc.failk "check/unknown-type" loc "unknown type %s" n
 
 and array_len env loc = function
@@ -5651,7 +5676,17 @@ and named_call ctx ~want loc name args =
     in
     let a, b = binary ctx name loc ~want:(numeric_want want) [ x; y ] in
     (* [min] and [max] are [<] with a pick, so [ordered?] is what they want —
-       not [numeric?]. A generic that declares [ordered?] gets both. *)
+       not [numeric?]. A generic that declares [ordered?] gets both.
+
+       They stay builtins now that generics could express them, and the reason
+       is the two lines above rather than the type system: they are variadic,
+       and each step puts both of its sides in slots so that every operand is
+       evaluated exactly once. A prelude [(defn min [a $t b $t] $t ...)] would
+       be binary and would have to be nested at the call site, which is where
+       the double evaluation this arm exists to prevent would come back. The
+       generic half is already theirs — [ordered?] admits them inside any
+       body that declares it — so collapsing them would cost the arity and
+       the evaluation rule and buy nothing. *)
     unconstrained ctx.env loc name ~needs:"ordered?" a.Tast.ty;
     if not (Types.is_numeric a.Tast.ty || generic_ty a.Tast.ty) then
       not_numeric name "numbers" a;
@@ -7409,8 +7444,9 @@ and ordinary_call ctx ~want loc name args =
                the fork the form fell down. *)
             Loc.failk "check/unknown-function" loc
               "unknown function %s. A capitalised name is a type, and a type \
-               given type arguments — (%s ...) — is generic code, which is \
-               milestone 5"
+               given type arguments — (%s ...) — is a generic type, which is \
+               not there yet. A generic *function* is: it is written with \
+               [$t] in its parameter vector and copied per call site"
               name name
           else Loc.failk "check/unknown-function" loc "unknown function %s" name
 
diff --git a/lib/prelude.ml b/lib/prelude.ml
index 16c3062..76c4cb7 100644
--- a/lib/prelude.ml
+++ b/lib/prelude.ml
@@ -467,6 +467,44 @@ let source = {flan|
         (push v (at s i))))
     v))
 
+;; ── The sign questions, over every numeric type at once ───────────────
+;;
+;; The family the whole of generics was asked for. Three questions about a
+;; number's sign, one body each, answering at i8 through u64 and at both
+;; float widths — where without a type variable they would be three functions
+;; per width, which is why they were never written at all.
+;;
+;; What makes them writable is not the type variable on its own: it is that a
+;; written 0 may stand where $t stands. That needs the {:where (numeric? $t)}
+;; clause and nothing weaker, because the bound is what promises the literal
+;; has a meaning at every type the variable can become. An unconstrained
+;; variable is refused, and so is [ordered?] — it admits an enum, which holds
+;; no number.
+;;
+;; The comparison is the clause's too: [numeric?] entails [ordered?], so one
+;; predicate on the line gives the body both the < it writes and the 0 it
+;; writes it against.
+;;
+;; **The unsigned instantiations are not mistakes.** (neg? (u8 3)) is false at
+;; every u8 and the copy is a constant, which a reader may find odd in the
+;; emitted code and which is exactly right: a generic is copied per written
+;; type, and the body says what it says at each of them. Refusing the copy
+;; would mean a bound that spells "signed", and there is no such predicate.
+(defn pos? [x $t] bool
+  {:where (numeric? $t)}
+  (> x 0))
+
+(defn neg? [x $t] bool
+  {:where (numeric? $t)}
+  (< x 0))
+
+;; Named zero? rather than =0 because it reads as the question it is. The
+;; float instantiations answer true for both zeros, since -0.0 = 0.0 is what
+;; IEEE says and this does not second-guess it.
+(defn zero? [x $t] bool
+  {:where (numeric? $t)}
+  (= x 0))
+
 ;; ── The per-type layer that stays ─────────────────────────────────────
 ;;
 ;; sum is the one shape a type variable cannot express, and it is worth being
@@ -947,9 +985,24 @@ let source = {flan|
 (declare cbrt-f32 [x f32] f32 "cbrtf")
 (declare cbrt-f64 [x f64] f64 "cbrt")
 
-;; Integer magnitude, one per width because there are no generics over the
-;; numeric types and min and max are builtins rather than functions, so a
-;; single abs is not expressible today.
+;; Integer magnitude, one per width, and the reason it stays that way changed
+;; when generics landed. The old one — no generics over the numeric types —
+;; is not true any more: (defn abs [x $t] $t {:where (numeric? $t)} (if (< x
+;; 0) (- 0 x) x)) checks and runs at every integer width, and the literal 0
+;; stands there because the clause admits it.
+;;
+;; **What stops it is the float half of its own bound.** numeric? is the only
+;; predicate that admits a written 0, and it admits f32 and f64 too — so a
+;; generic abs would be instantiated at them, and the body above is the wrong
+;; abs for a float: (< -0.0 0) is false, so it hands back a negative zero
+;; from a function named abs. The float pair below is libm's for exactly that
+;; reason, a sign-bit clear rather than a negation, and a generic that shadows
+;; it at f32 would be a quiet wrong answer rather than a tidier prelude.
+;;
+;; So the collapse waits on a bound that spells "an integer type" — an
+;; integer? predicate, which is language surface and not this file's call.
+;; FIX.org, "Generics and implicit widening", records it as the candidate.
+;; Two functions is the honest price until then.
 ;;
 ;; The most negative value of each width has no positive counterpart, and this
 ;; does not special-case it: the subtraction is the same subtraction written
diff --git a/test/programs/generics.flan b/test/programs/generics.flan
index 12ddee7..78944a8 100644
--- a/test/programs/generics.flan
+++ b/test/programs/generics.flan
@@ -51,21 +51,25 @@
   (min (max x lo) hi))
 
 ;; An integer *literal* where the type variable is wanted, which is what the
-;; author's motivating family needs: one pos? over every numeric type rather
-;; than one per width. The literal is admitted because {:where (numeric? $t)}
-;; is declared, and the bound is what makes it sound rather than optimistic —
-;; every type numeric? admits is an integer or a float, and an untyped integer
-;; constant is usable at all of them, so there is no instantiation at which
-;; this 0 has no meaning. Without the clause it is refused at the definition;
-;; see the rejects in test_flan.ml.
+;; sign family needs: one pos? over every numeric type rather than one per
+;; width. The literal is admitted because {:where (numeric? $t)} is declared,
+;; and the bound is what makes it sound rather than optimistic — every type
+;; numeric? admits is an integer or a float, and an untyped integer constant
+;; is usable at all of them, so there is no instantiation at which this 0 has
+;; no meaning. Without the clause it is refused at the definition; see the
+;; rejects in test_flan.ml.
 ;;
 ;; The literal is never emitted from here. The abstract pass builds a
 ;; placeholder and throws it away with the rest of the body; each copy
 ;; re-checks (> x 0) with $t substituted, and *that* is where the literal is
 ;; built at the concrete width and range-checked.
-(defn pos? [x $t] bool {:where (numeric? $t)} (> x 0))
-(defn neg? [x $t] bool {:where (numeric? $t)} (< x 0))
-(defn zero-p? [x $t] bool {:where (numeric? $t)} (= x 0))
+;;
+;; The -t? suffix is because the prelude now carries pos?/neg?/zero? itself.
+;; These are the same three bodies written in an ordinary program, which is
+;; what says the machinery belongs to the language and not to the prelude.
+(defn pos-t? [x $t] bool {:where (numeric? $t)} (> x 0))
+(defn neg-t? [x $t] bool {:where (numeric? $t)} (< x 0))
+(defn zero-t? [x $t] bool {:where (numeric? $t)} (= x 0))
 
 ;; The same literal in arithmetic rather than comparison, and answering $t
 ;; rather than bool, so the placeholder has to survive being the operand of a
@@ -161,18 +165,25 @@
     ;; The literal-at-a-type-variable family, at six numeric types from three
     ;; written bodies. i32, i64, u8, u16, f32 and f64 all reach the same 0 and
     ;; the same 1.
-    (println (pos? 3))
-    (println (neg? (i8 -3)))
-    (println (zero-p? (u8 0)))
-    (println (zero-p? 0.0))
-    (println (pos? (u16 1)))
-    (println (neg? (f32 -0.5)))
+    (println (pos-t? 3))
+    (println (neg-t? (i8 -3)))
+    (println (zero-t? (u8 0)))
+    (println (zero-t? 0.0))
+    (println (pos-t? (u16 1)))
+    (println (neg-t? (f32 -0.5)))
     (println (next-after 3))
     (println (next-after (i64 10)))
     (println (next-after 2.5))
     (println (next-after (u8 254)))
     (println (plus-300 1))
 
+    ;; And the prelude's own three, which are these bodies under their real
+    ;; names. The -0.0 is the one worth asserting: IEEE says -0.0 = 0.0 and
+    ;; zero? does not second-guess it.
+    (println (pos? (i64 3)))
+    (println (zero? -0.0))
+    (println (neg? (u8 3)))
+
     (show 3)
     (show 4.5)
     (show "text")
diff --git a/test/test_acceptance.ml b/test/test_acceptance.ml
index f84c9e9..1a2dbc0 100644
--- a/test/test_acceptance.ml
+++ b/test/test_acceptance.ml
@@ -2592,10 +2592,14 @@ let () =
        and f64. [255] is next-after at u8 and is the one that would say
        whether the placeholder width the abstract pass builds had leaked into
        a copy; [301] is plus-300 at i32, whose range check belongs to the copy
-       and not to the definition. *)
+       and not to the definition. The [true true false] after them is the
+       prelude's own pos?/zero?/neg? — the same three bodies under their real
+       names — and the middle one is zero? at -0.0, which IEEE says is zero
+       and which this does not second-guess. *)
     let generics_out =
       "3\n4.5\ntrue\n7\n5\n-1\n5\n42\n3\n1\n10\n1\n8\n\
        true\ntrue\ntrue\ntrue\ntrue\ntrue\n4\n11\n3.5\n255\n301\n\
+       true\ntrue\nfalse\n\
        3\n4.5\ntext\n1\n2.5\n9\n36\n2\n2.5\n0\n\
        0\n-1\n2.5\n0\ntrue\nfalse\ntrue\n2\n0\n\
        3\n3\n0\n21\n7\n3\n4.5\n"
diff --git a/test/test_flan.ml b/test/test_flan.ml
index 57b64be..9965aca 100644
--- a/test/test_flan.ml
+++ b/test/test_flan.ml
@@ -1161,12 +1161,15 @@ let () =
       | Some { Tast.params = [ Types.Dyn; Types.Dyn ]; _ } -> ()
       | _ -> check "an unannotated pair is two dyn parameters" false)
    | exception _ -> check "an unannotated pair is two dyn parameters" false);
-  (* A bare lowercase name is still an unimplemented type variable everywhere a
-     type is the only thing a slot can hold. A defn's parameter vector stopped
-     being such a place — a slot there may be a parameter instead — so the rule
-     is exercised where it still decides, at a field. *)
+  (* A bare lowercase name where a type is the only thing a slot can hold. It
+     used to be reported as unimplemented generics; generics are implemented,
+     and a lowercase name is a type variable only where a defn signature
+     introduced one with the sigil — a struct field is not such a place and
+     never will be, since only a signature binds. So the sentence names the
+     sigil rather than a milestone. A defn's parameter vector stopped being a
+     type-only slot, which is why the rule is exercised at a field. *)
   rejects_check "a real type variable" "(defstruct Holder [x elem])"
-    ~needle:"milestone 5";
+    ~needle:"write $elem in the parameter vector";
   rejects_check "an unknown concrete type" "(defn f [x Widget] ())"
     ~needle:"unknown type Widget";
 
@@ -2073,9 +2076,16 @@ let () =
   (* [(Pair i32)] in a defvar falls down the value fork now that the third
      element takes either reading, and the generics answer the type fork gave
      it has to be reachable from here too. *)
-  rejects_check "a capitalised call with arguments is generics"
+  (* A capitalised head with arguments is a *type* given type arguments, and
+     that is the half of generics that is not built — Types.Named is a bare
+     string with no room for parameters. The sentence says which half, since
+     generic functions are here and pointing at them is the useful part. *)
+  rejects_check "a capitalised call with arguments is a generic type"
     "(defvar x (Pair i32)) (defn f [] i32 0)"
-    ~needle:"is generic code, which is milestone 5";
+    ~needle:"is a generic type, which is not there yet";
+  accepts "and the generic function it points at is"
+    "(defn pair-fst [a $t  b $u] $t (do b a))\n\
+     (defn main [] () (println (pair-fst 1 true)))";
   rejects_check "defined twice" "(defn f [] ()) (defn f [] ())"
     ~needle:"defined twice";
   accepts "main with no parameters and no return" "(defn main [] ())";
@@ -2895,8 +2905,8 @@ let () =
      defn's body that just answers one says nothing about them. *)
   rejects_check "an fn with nothing to say what it takes"
     "(defn f [] () (fn [x] x))" ~needle:"nothing here says what this fn";
-  rejects_check "type variables are milestone 5" "(defn f [] a 0)"
-    ~needle:"milestone 5";
+  rejects_check "a lowercase return type no signature introduced"
+    "(defn f [] a 0)" ~needle:"write $a in the parameter vector";
   (* The other half: a name in value position now *works*, and the arity is
      checked against the function it names. *)
   rejects_check "a function value at the wrong arity"
@@ -4806,9 +4816,15 @@ let () =
      has no meaning. That is the whole rule, and the four pins below are its
      two halves and its one asymmetry. *)
   accepts "an integer literal stands where a numeric? type variable is wanted"
-    "(defn pos? [x $t] bool {:where (numeric? $t)} (> x 0))";
+    "(defn above-zero? [x $t] bool {:where (numeric? $t)} (> x 0))";
   accepts "and in arithmetic, answering the variable"
     "(defn next [x $t] $t {:where (numeric? $t)} (+ x 1))";
+  (* And the prelude's own three, which are that body under its real name at
+     every numeric type from one definition. *)
+  accepts "the prelude's sign family answers at six numeric types"
+    "(defn main [] () (println (pos? 3) ) (println (neg? (i8 -1))) \
+       (println (zero? (u8 0))) (println (zero? 0.0)) \
+       (println (pos? (u64 1))) (println (neg? (f32 -0.5))))";
   (* [numeric?] is what admits it and nothing weaker does. [ordered?] admits
      an enum, which holds no number, so a literal under it has an
      instantiation at which it means nothing — and the refusal below is what