diff --git a/.changeset/projection-sync-throw-reaches-readers.md b/.changeset/projection-sync-throw-reaches-readers.md
new file mode 100644
index 000000000..83bc9a7da
--- /dev/null
+++ b/.changeset/projection-sync-throw-reaches-readers.md
@@ -0,0 +1,5 @@
+---
+"@solidjs/signals": patch
+---
+
+A `createProjection` whose re-run throws synchronously (for example, reading an entry that has since failed) now delivers the error to the readers of its fields, so the nearest `<Errored>` shows it instead of the screen keeping the last good value.
diff --git a/packages/signals/src/store/projection.ts b/packages/signals/src/store/projection.ts
index 387eb1ba7..2015a8d99 100644
--- a/packages/signals/src/store/projection.ts
+++ b/packages/signals/src/store/projection.ts
@@ -279,7 +279,9 @@ export function runProjectionComputed<T extends object>(
     // A flight went up (NotReady out of the pass — the derive's own, with
     // the derive as its source): the leaves' readers learn it from here —
     // they do not subscribe to the derive.
-    if (e instanceof NotReadyError && !first) wakeFamily(fam, e);
+    // A synchronous error the same way (#3956: a rerun that finds the
+    // entry failed throws): every live reader re-derives and meets it.
+    if (!first) e instanceof NotReadyError ? wakeFamily(fam, e) : errorFamily(fam);
     throw e;
   }
   // A pass that returned with a flight up (an iterator's sync first yield):
diff --git a/packages/signals/tests/store/projection-sync-throw-3956.test.ts b/packages/signals/tests/store/projection-sync-throw-3956.test.ts
new file mode 100644
index 000000000..ad91561e8
--- /dev/null
+++ b/packages/signals/tests/store/projection-sync-throw-3956.test.ts
@@ -0,0 +1,90 @@
+import { expect, it } from "vitest";
+import {
+  createErrorBoundary,
+  createLoadingBoundary,
+  createProjection,
+  createRenderEffect,
+  createRoot,
+  createSignal,
+  flush
+} from "../../src/index.js";
+
+const settle = async (ms: number) => {
+  const end = Date.now() + ms;
+  while (Date.now() < end) {
+    await new Promise(r => setTimeout(r, 5));
+    flush();
+  }
+};
+
+it("projection: a synchronous throw on a version-bumped rerun reaches Errored (#3956)", async () => {
+  const fetcher = (k: string) =>
+    new Promise<{ items: string[] }>((res, rej) =>
+      setTimeout(() => (k === "bad" ? rej(new Error("refused")) : res({ items: [`row-${k}`] })), 20)
+    );
+  const [key, setKey] = createSignal("good");
+  const [version, setVersion] = createSignal(0, { ownedWrite: true });
+  type E = {
+    status: "pending" | "ok" | "error";
+    p: Promise<{ items: string[] }>;
+    v?: { items: string[] };
+    e?: unknown;
+  };
+  const cache = new Map<string, E>();
+  const entry = (k: string) => {
+    let e = cache.get(k);
+    if (!e) {
+      const ne: E = { status: "pending", p: fetcher(k) };
+      ne.p.then(
+        v => {
+          ne.status = "ok";
+          ne.v = v;
+          setVersion(x => x + 1);
+        },
+        err => {
+          ne.status = "error";
+          ne.e = err;
+          setVersion(x => x + 1);
+        }
+      );
+      cache.set(k, ne);
+      e = ne;
+    }
+    return e;
+  };
+  let screen: unknown;
+  createRoot(() => {
+    const p = createProjection<{ value?: { items: string[] } }>(() => {
+      version();
+      const e = entry(key());
+      if (e.status === "error") throw e.e;
+      if (e.status === "ok") return { value: e.v! } as never;
+      return e.p.then(v => ({ value: v })) as never;
+    }, {});
+    const view = createErrorBoundary(
+      () =>
+        createLoadingBoundary(
+          () => (p.value?.items ?? []).join(","),
+          () => "PENDING"
+        ),
+      () => "ERRORED"
+    );
+    createRenderEffect(
+      () => {
+        let v: any = view();
+        while (typeof v === "function") v = v();
+        return v;
+      },
+      v => {
+        screen = v;
+      }
+    );
+  });
+  flush();
+  await settle(60);
+  expect(screen).toBe("row-good");
+  setKey("bad");
+  flush();
+  await settle(200);
+  expect(screen).toBe("ERRORED");
+});