diff --git a/lib/check.ml b/lib/check.ml
index e350325..87f2457 100644
--- a/lib/check.ml
+++ b/lib/check.ml
@@ -1674,6 +1674,69 @@ let unbox loc (want : Types.t) (e : Tast.expr) : Tast.expr =
           then "f64" else "i64"))
   | _ -> no_dyn_yet loc ~into:false want ""
 
+(* ── A numeric cast written on a dyn, FIX.org 2026-09-20 ───────────────
+ *
+   [(f64 d)] where [d] is dyn. Until this, the only place in the language
+   that opened a box was a typed parameter, which is why a program that
+   wanted a number out of a dyn had to define a one-line function whose
+   parameter slot did the unboxing and call *that*. A cast is already the
+   operator for "convert this to that", so it is the spelling that should
+   have worked, and now does.
+
+   What is built is a branch on the box's tag, not a call that converts:
+
+       (let ([s d])
+         (if (= (flan_dyn_cast_kind s "file:1:2" "u32" 0) 1)
+             (u32 (flan_dyn_need_f64 s))
+             (u32 (flan_dyn_need_i64 s))))
+
+   Each arm is an ordinary [Cast] over an ordinary [need], so the conversion
+   is *the same node* a typed operand of that type would have produced.
+   That is the point of this shape rather than a coercing runtime entry point
+   that answers the finished number: [(i64 2.5)] is not a bare [fptosi] in
+   this compiler — [Emit.check_cast] range-checks it first and signals
+   ArithError when the value will not fit, and the x86 backend does the same
+   — so a C function returning an [int64_t] would have had to grow its own
+   second opinion about range and NaN, in a second place, for two backends.
+   Here there is nothing to keep in step: [(i64 float-box)] *is* [(i64 x)]
+   with an unbox in front of it, which is exactly what the semantics say.
+
+   [need_f64] and [need_i64] are the trapping entry points, and neither can
+   trap here: each is reached only on the arm where the tag has already been
+   read as its own. The trap that can happen is the runtime's, for a box
+   holding a non-number, and [flan_dyn_cast_kind] owns that sentence — bool
+   included, which is what [flan_dyn_need_i64] already does with a bool at a
+   typed parameter. The cross-kind case does not trap: it converts and warns
+   once for the site, the author's call, recorded in FIX.org.
+
+   The slot exists because the value is read three times — once for the tag,
+   once on whichever arm runs — and the argument may be an arbitrary
+   expression. [unbox_option] above builds the same shape for the same
+   reason. *)
+let cast_dyn ctx loc (target : Types.t) (got : Tast.expr) : Tast.expr =
+  let s = fresh_slot ctx Types.Dyn in
+  let sv = mk loc Types.Dyn (Tast.Local s) in
+  let want_float = match target with Types.Float _ -> 1 | _ -> 0 in
+  let kind =
+    rt loc (Types.Int Types.I32) "flan_dyn_cast_kind"
+      [ sv; here loc;
+        mk loc Types.String (Tast.Str (Types.to_string target));
+        mk loc (Types.Int Types.I32) (Tast.Int (Int64.of_int want_float, Types.I32)) ]
+  in
+  let is_float =
+    mk loc Types.Bool
+      (Tast.Prim (Tast.Eq,
+                  [ kind;
+                    mk loc (Types.Int Types.I32) (Tast.Int (1L, Types.I32)) ]))
+  in
+  let arm sym ty = widen loc target (rt loc ty sym [ sv ]) in
+  mk loc target
+    (Tast.Let ([ (s, got) ],
+               [ mk loc target
+                   (Tast.If (is_float,
+                             arm "flan_dyn_need_f64" dyn_f64,
+                             arm "flan_dyn_need_i64" dyn_i64)) ]))
+
 (* nil is written [nil] and nothing else produces it, so this is the whole of
    "the checker can see a nil reaching here" — a name, not a dataflow fact.
    There is no propagation through a [let] or a call in this checker (see
@@ -6123,9 +6186,16 @@ and named_call ctx ~want loc name args =
     let a = check ctx (List.hd args) in
     (match a.Tast.ty with
      | Types.Enum _ -> ()
+     (* A dyn opens here — [cast_dyn], FIX.org 2026-09-20. Only on this arm:
+        the generic one above casts to a type *variable*, whose [where] clause
+        says the operand is numeric, and a dyn is not what a [numeric?] bound
+        admits. *)
+     | Types.Dyn -> ()
      | t when Types.is_numeric t -> ()
      | t -> fail loc "%s converts a number, found %s" name (Types.to_string t));
-    prim (Tast.Cast target) target [ a ]
+    (match a.Tast.ty with
+     | Types.Dyn -> cast_dyn ctx loc target a
+     | _ -> prim (Tast.Cast target) target [ a ])
 
   (* ── ordinary calls ────────────────────────────────────────────── *)
   (* A local or a parameter holding a function value, called by the name it is
diff --git a/lib/emit.ml b/lib/emit.ml
index 3eeaecb..f6261c7 100644
--- a/lib/emit.ml
+++ b/lib/emit.ml
@@ -3653,6 +3653,11 @@ declare void @flan_dyn_print(i64)
 declare i64 @flan_dyn_need_i64(i64)
 declare double @flan_dyn_need_f64(i64)
 declare i32 @flan_dyn_need_bool(i64)
+; A numeric cast written on a dyn answers which numeric tag the box holds;
+; check.ml's [cast_dyn] branches on it and each arm is an ordinary need plus
+; the ordinary cast. The two slices are the site's location and the target's
+; name, each crossing as ptr+len.
+declare i32 @flan_dyn_cast_kind(i64, ptr, i64, ptr, i64, i32)
 ; nil <-> None at an (Option T) boundary, and (Some nil)'s run-time half —
 ; M2 queue item 4, check.ml's [box_option]/[unbox_option] and the [Some]
 ; builtin.
diff --git a/runtime/flan_dyn.c b/runtime/flan_dyn.c
index 9cfd605..8e13dd4 100644
--- a/runtime/flan_dyn.c
+++ b/runtime/flan_dyn.c
@@ -1139,6 +1139,92 @@ uint8_t flan_dyn_need_bool(flan_dyn v) {
   return (uint8_t)(dyn_payload(v) ? 1 : 0);
 }
 
+/* ── A numeric cast opening a box, FIX.org 2026-09-20 ───────────────────
+ *
+ * [(f64 d)] on a dyn. The *conversion* is not done here: [check.ml] lowers
+ * such a cast to a branch on this function's answer, and each arm is the
+ * ordinary [flan_dyn_need_i64]/[flan_dyn_need_f64] followed by the cast the
+ * emitter already emits for a typed argument of that type. So this function
+ * decides one thing — which of the two numeric tags the box holds — and
+ * everything about the arithmetic (the fptosi range check, NaN, the
+ * narrowing rule) stays where it already was, identical in both backends and
+ * identical to the typed spelling of the same cast.
+ *
+ * Answers 1 for a float box, 0 for an int box. Every other tag traps, with
+ * the same [trap1] sentence the typed boundary's own refusals use — bool
+ * included, which mirrors [flan_dyn_need_i64] refusing a bool today rather
+ * than inventing a new rule for casts.
+ *
+ * [want_float] is what the *target* type is: 1 for f32/f64, 0 for the
+ * integer widths. When it disagrees with the box, the cast still happens —
+ * the author's call, "just coerce it with a warning" — and the warning below
+ * is the whole of what the disagreement costs. A cast is already a
+ * conversion operator, [(f64 5)] converts a typed integer, so converting
+ * across the box is the cast doing its job; the warning exists because the
+ * box's kind was not what the program apparently expected.
+ *
+ * Once per *site*, not per value. These casts sit in per-cell-per-frame
+ * loops — sand.flan runs at 120fps — and a per-occurrence line would be a
+ * flood rather than a diagnostic. The site is the [loc] text [check.ml]
+ * passes in, and the table below is keyed on its *bytes* rather than its
+ * address: the two backends emit their own constants for it and neither
+ * promises that two mentions of one site share one pointer.
+ *
+ * The table is fixed and small because it is only ever as large as the
+ * number of cross-kind cast sites a program has, which is a handful in the
+ * programs this was written for. A program with more than [SITE_MAX] of them
+ * stops deduplicating for the overflow — it still warns, every time, which
+ * is the noisy failure rather than the silent one. Not thread-safe, and
+ * deliberately: a duplicated or dropped line under a race is a diagnostic
+ * that came out twice, and the alternative is a lock on a path that runs per
+ * cast in a frame loop. */
+
+#define SITE_MAX 64
+
+static struct { const uint8_t *ptr; int64_t len; } warned_sites[SITE_MAX];
+static int warned_count;
+
+static int site_first_time(const uint8_t *loc, int64_t loc_len) {
+  for (int i = 0; i < warned_count; i++)
+    if (warned_sites[i].len == loc_len &&
+        memcmp(warned_sites[i].ptr, loc, (size_t)loc_len) == 0)
+      return 0;
+  if (warned_count < SITE_MAX) {
+    warned_sites[warned_count].ptr = loc;
+    warned_sites[warned_count].len = loc_len;
+    warned_count++;
+  }
+  return 1;
+}
+
+int32_t flan_dyn_cast_kind(flan_dyn v, const uint8_t *loc, int64_t loc_len,
+                           const uint8_t *target, int64_t target_len,
+                           int32_t want_float) {
+  int32_t tag = flan_dyn_tag(v);
+  if (tag != FLAN_DYN_TAG_INT && tag != FLAN_DYN_TAG_FLOAT) {
+    /* [trap1] takes the operation as a C string and the target is a Flan
+     * slice, so it is copied out. Every cast name is two or three bytes; the
+     * clamp is for a caller this file cannot see. */
+    char name[8];
+    size_t n = (size_t)target_len < sizeof name - 1 ? (size_t)target_len
+                                                    : sizeof name - 1;
+    memcpy(name, target, n);
+    name[n] = '\0';
+    trap1(TYPE_TRAP, name, "a number was wanted", v);
+  }
+  int32_t is_float = tag == FLAN_DYN_TAG_FLOAT ? 1 : 0;
+  if (is_float != (want_float ? 1 : 0) && site_first_time(loc, loc_len)) {
+    fflush(stdout);
+    fprintf(stderr,
+            "flan %.*s: (%.*s x) found a dyn holding %s, and converted it to "
+            "%.*s — warned once for this site\n",
+            (int)loc_len, (const char *)loc, (int)target_len,
+            (const char *)target, tag_of(v), (int)target_len,
+            (const char *)target);
+  }
+  return is_float;
+}
+
 /* nil <-> None at an (Option T) boundary. Cannot trap — every dyn value
  * answers this one way or the other. */
 int32_t flan_dyn_is_nil(flan_dyn v) {
diff --git a/runtime/flan_dyn.h b/runtime/flan_dyn.h
index 6a82133..2f95b6b 100644
--- a/runtime/flan_dyn.h
+++ b/runtime/flan_dyn.h
@@ -144,6 +144,21 @@ int64_t flan_dyn_need_i64(flan_dyn v);
 double  flan_dyn_need_f64(flan_dyn v);
 uint8_t flan_dyn_need_bool(flan_dyn v);
 
+/* A numeric cast written on a dyn — [(f64 d)], [(u32 d)] — FIX.org
+ * 2026-09-20. Unlike the parameter boundary above this one coerces: it
+ * answers which numeric tag the box holds (1 float, 0 int) and the caller
+ * branches, so the conversion itself is the cast the compiler already emits
+ * for a typed operand of that tag. A box holding anything else traps, bool
+ * included, exactly as [flan_dyn_need_i64] refuses one.
+ *
+ * [want_float] says what the target type is, and a disagreement writes one
+ * line to stderr — once per [loc], not once per value, because these casts
+ * run inside frame loops. [loc] and [target] are Flan slices: pointer and
+ * length, not NUL-terminated. */
+int32_t flan_dyn_cast_kind(flan_dyn v, const uint8_t *loc, int64_t loc_len,
+                           const uint8_t *target, int64_t target_len,
+                           int32_t want_float);
+
 /* nil <-> None at an (Option T) boundary, and (Some nil)'s refusal — M2 item
  * 4. [flan_dyn_is_nil] is the tag test the boundary's runtime half needs and
  * does not want to build out of [flan_dyn_tag] and a comparison at every call
diff --git a/runtime/flan_dyn_stub.c b/runtime/flan_dyn_stub.c
index 779f49f..b11cff6 100644
--- a/runtime/flan_dyn_stub.c
+++ b/runtime/flan_dyn_stub.c
@@ -296,6 +296,51 @@ int32_t flan_dyn_need_bool(flan_dyn v) {
   return c->u.b;
 }
 
+/* The cast boundary's tag question — see flan_dyn.h. The stub keeps its own
+ * trap vocabulary, as every function above it does; what it must agree with
+ * the real runtime about is the *answer*, 1 for a float box and 0 for an int
+ * one, because that is what the compiler branches on. The once-per-site
+ * table is the real runtime's word for word: a program built against the
+ * stub that warns twice for one line would be a difference in the
+ * diagnostic, which is the thing this pair exists to keep identical. */
+
+#define STUB_SITE_MAX 64
+
+static struct { const uint8_t *ptr; int64_t len; } stub_warned[STUB_SITE_MAX];
+static int stub_warned_count;
+
+int32_t flan_dyn_cast_kind(flan_dyn v, const uint8_t *loc, int64_t loc_len,
+                           const uint8_t *target, int64_t target_len,
+                           int32_t want_float) {
+  cell *c = as(v);
+  if (c->tag != T_I64 && c->tag != T_F64)
+    dyn_trap("DynExpectedNumber",
+             "a numeric cast was written on this value and it is not a number");
+  int32_t is_float = c->tag == T_F64 ? 1 : 0;
+  if (is_float != (want_float ? 1 : 0)) {
+    int first = 1;
+    for (int i = 0; i < stub_warned_count; i++)
+      if (stub_warned[i].len == loc_len &&
+          memcmp(stub_warned[i].ptr, loc, (size_t)loc_len) == 0)
+        first = 0;
+    if (first) {
+      if (stub_warned_count < STUB_SITE_MAX) {
+        stub_warned[stub_warned_count].ptr = loc;
+        stub_warned[stub_warned_count].len = loc_len;
+        stub_warned_count++;
+      }
+      fflush(stdout);
+      fprintf(stderr,
+              "flan %.*s: (%.*s x) found a dyn holding %s, and converted it "
+              "to %.*s — warned once for this site\n",
+              (int)loc_len, (const char *)loc, (int)target_len,
+              (const char *)target, is_float ? "float" : "int",
+              (int)target_len, (const char *)target);
+    }
+  }
+  return is_float;
+}
+
 /* ── Roots ─────────────────────────────────────────────────────────────
  *
  * Recorded and otherwise ignored. The shadow stack is kept, and its depth