diff --git a/.changeset/bloom-union-n-metadata.md b/.changeset/bloom-union-n-metadata.md
new file mode 100644
index 0000000..414cb59
--- /dev/null
+++ b/.changeset/bloom-union-n-metadata.md
@@ -0,0 +1,5 @@
+---
+"distillate": patch
+---
+
+Fix `BloomFilter.union` reporting the wrong `bitsPerKey`/`rate` and breaking `equals`: the result now carries the operand's expected-key count instead of re-deriving it from `m/k` (membership was never affected). `BloomFilter.create` now rejects `n` above `2^32-1` with a `ParamError` instead of silently truncating it into the serialized frame.
diff --git a/packages/distillate/docs/api/bloom/classes/BloomFilter.md b/packages/distillate/docs/api/bloom/classes/BloomFilter.md
index cc03061..0354dce 100644
--- a/packages/distillate/docs/api/bloom/classes/BloomFilter.md
+++ b/packages/distillate/docs/api/bloom/classes/BloomFilter.md
@@ -26,7 +26,7 @@ filter.has("bob"); // false (or a ~1% false positive)
 
 > **new BloomFilter**(`__namedParameters`): `BloomFilter`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:130](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L130)
+Defined in: [packages/distillate/src/bloom/bloom.ts:128](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L128)
 
 Constructs a filter from low-level [BloomParams](../interfaces/BloomParams.md). Prefer
 [BloomFilter.create](#create) unless restoring a specific configuration.
@@ -49,7 +49,7 @@ Constructs a filter from low-level [BloomParams](../interfaces/BloomParams.md).
 
 > **get** **bitsPerKey**(): `number`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:165](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L165)
+Defined in: [packages/distillate/src/bloom/bloom.ts:172](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L172)
 
 Analytic design bits-per-key `m / n`.
 
@@ -65,7 +65,7 @@ Analytic design bits-per-key `m / n`.
 
 > **get** **k**(): `number`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:150](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L150)
+Defined in: [packages/distillate/src/bloom/bloom.ts:157](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L157)
 
 Number of hash probes per key.
 
@@ -81,7 +81,7 @@ Number of hash probes per key.
 
 > **get** **length**(): `number`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:160](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L160)
+Defined in: [packages/distillate/src/bloom/bloom.ts:167](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L167)
 
 Number of bits currently set.
 
@@ -97,7 +97,7 @@ Number of bits currently set.
 
 > **get** **m**(): `number`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:145](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L145)
+Defined in: [packages/distillate/src/bloom/bloom.ts:152](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L152)
 
 Number of bits in the filter.
 
@@ -113,7 +113,7 @@ Number of bits in the filter.
 
 > **get** **seed**(): `number`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:155](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L155)
+Defined in: [packages/distillate/src/bloom/bloom.ts:162](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L162)
 
 Hash seed.
 
@@ -127,7 +127,7 @@ Hash seed.
 
 > **add**(`key`): `void`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:262](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L262)
+Defined in: [packages/distillate/src/bloom/bloom.ts:272](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L272)
 
 Adds a key to the set.
 
@@ -149,7 +149,7 @@ The key to insert, as a string or bytes.
 
 > **equals**(`other`): `boolean`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:207](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L207)
+Defined in: [packages/distillate/src/bloom/bloom.ts:214](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L214)
 
 Tests structural equality: `true` when `other` serializes to identical
 bytes, meaning identical parameters and set bits.
@@ -174,7 +174,7 @@ The filter to compare against.
 
 > **has**(`key`): `boolean`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:273](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L273)
+Defined in: [packages/distillate/src/bloom/bloom.ts:283](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L283)
 
 Tests whether a key is in the set.
 
@@ -198,7 +198,7 @@ The key to test.
 
 > **rate**(): `number`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:176](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L176)
+Defined in: [packages/distillate/src/bloom/bloom.ts:183](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L183)
 
 Estimates the current false-positive rate from the actual fill,
 `(length / m) ** k`. This reflects how full the filter is right now, not
@@ -216,7 +216,7 @@ The estimated false-positive rate, `0` for an empty filter.
 
 > **toBytes**(): `Uint8Array`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:185](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L185)
+Defined in: [packages/distillate/src/bloom/bloom.ts:192](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L192)
 
 Serializes the filter to a portable little-endian byte layout.
 
@@ -232,7 +232,7 @@ The serialized filter, readable by [BloomFilter.fromBytes](#frombytes).
 
 > **toJSON**(): [`FilterJSON`](../interfaces/FilterJSON.md)
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:217](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L217)
+Defined in: [packages/distillate/src/bloom/bloom.ts:224](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L224)
 
 Serializes the filter to a JSON-friendly envelope wrapping the base64 of
 [BloomFilter.toBytes](#tobytes).
@@ -249,7 +249,7 @@ The envelope, readable by [BloomFilter.fromJSON](#fromjson).
 
 > **union**(`other`): `BloomFilter`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:238](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L238)
+Defined in: [packages/distillate/src/bloom/bloom.ts:245](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L245)
 
 Returns a new filter containing the union of this filter and `other`.
 
@@ -307,7 +307,7 @@ A new, empty filter.
 
 > `static` **from**(`keys`, `epsilon`): `BloomFilter`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:88](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L88)
+Defined in: [packages/distillate/src/bloom/bloom.ts:87](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L87)
 
 Builds a filter from `keys`, sized for their count at the target
 false-positive rate. The ergonomic entry point when the key set is already
@@ -339,7 +339,7 @@ A new filter containing every key.
 
 > `static` **fromBytes**(`bytes`): `BloomFilter`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:101](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L101)
+Defined in: [packages/distillate/src/bloom/bloom.ts:100](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L100)
 
 Restores a filter from its [BloomFilter.toBytes](#tobytes) serialization.
 
@@ -363,7 +363,7 @@ The reconstructed filter.
 
 > `static` **fromJSON**(`value`): `BloomFilter`
 
-Defined in: [packages/distillate/src/bloom/bloom.ts:227](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L227)
+Defined in: [packages/distillate/src/bloom/bloom.ts:234](https://github.com/akshay-xp/distillate/blob/main/packages/distillate/src/bloom/bloom.ts#L234)
 
 Restores a filter from its [BloomFilter.toJSON](#tojson) envelope.
 
diff --git a/packages/distillate/src/bloom/bloom.ts b/packages/distillate/src/bloom/bloom.ts
index c5041f4..41953bb 100644
--- a/packages/distillate/src/bloom/bloom.ts
+++ b/packages/distillate/src/bloom/bloom.ts
@@ -70,10 +70,9 @@ export class BloomFilter {
    */
   static create(n: number, epsilon: number): BloomFilter {
     assertPositiveInt(n, "n");
+    assertUint32(n, "n");
     assertProbability(epsilon, "epsilon");
-    const f = new BloomFilter(optimal(n, epsilon));
-    f.#n = n;
-    return f;
+    return BloomFilter.#withN(optimal(n, epsilon), n);
   }
 
   /**
@@ -117,8 +116,7 @@ export class BloomFilter {
     const seed = dv.getUint32(6, true);
     const n = dv.getUint32(10, true);
     assertBodyLength(body.length, 14 + Math.ceil(m / 8), "bloom");
-    const f = new BloomFilter({ m, k, seed });
-    f.#n = n;
+    const f = BloomFilter.#withN({ m, k, seed }, n);
     f.#bits.bytes.set(body.subarray(14));
     return f;
   }
@@ -141,6 +139,15 @@ export class BloomFilter {
     this.#n = Math.round((m * Math.LN2) / k);
   }
 
+  // Reconstruct with an explicit expected-key count, overriding the #n the
+  // constructor derives from m/k. The single place #n is carried across
+  // reconstruction, so a caller cannot silently drop it.
+  static #withN(params: BloomParams, n: number): BloomFilter {
+    const f = new BloomFilter(params);
+    f.#n = n;
+    return f;
+  }
+
   /** Number of bits in the filter. */
   get m(): number {
     return this.#m;
@@ -249,7 +256,10 @@ export class BloomFilter {
     const b = other.#bits.bytes;
     const merged = new Uint8Array(a.length);
     for (let i = 0; i < a.length; i++) merged[i] = (a[i] ?? 0) | (b[i] ?? 0);
-    const r = new BloomFilter({ m: this.#m, k: this.#k, seed: this.#seed });
+    const r = BloomFilter.#withN(
+      { m: this.#m, k: this.#k, seed: this.#seed },
+      this.#n,
+    );
     r.#bits.bytes.set(merged);
     return r;
   }
diff --git a/packages/distillate/tests/bloom/bloom.test.ts b/packages/distillate/tests/bloom/bloom.test.ts
index 15e37c1..165f776 100644
--- a/packages/distillate/tests/bloom/bloom.test.ts
+++ b/packages/distillate/tests/bloom/bloom.test.ts
@@ -56,6 +56,9 @@ test("create rejects invalid n and epsilon", () => {
   for (const epsilon of [1, 0, -0.1, NaN]) {
     expect(() => BloomFilter.create(100, epsilon)).toThrow(ParamError);
   }
+  expect(() => BloomFilter.create(2 ** 32, 0.999)).toThrow(ParamError);
+  expect(() => BloomFilter.create(2 ** 32 - 1, 0.999)).not.toThrow();
+
   const f = BloomFilter.create(100000, 0.01);
   f.add("alice");
   expect(f.has("alice")).toBe(true);
@@ -198,6 +201,16 @@ test("union merges two filters without mutating inputs", () => {
   expect(b.toBytes()).toEqual(snapB);
 });
 
+test("union preserves the operand bitsPerKey and equals the receiver", () => {
+  const a = BloomFilter.create(1000, 0.01);
+  a.add("x");
+  const b = BloomFilter.create(1000, 0.01);
+
+  const u = a.union(b);
+  expect(u.bitsPerKey).toBe(a.bitsPerKey);
+  expect(a.equals(u)).toBe(true);
+});
+
 test("union has every key from either input (property)", () => {
   fc.assert(
     fc.property(