diff --git a/cspell.json b/cspell.json
index f0e5dff..35b7457 100644
--- a/cspell.json
+++ b/cspell.json
@@ -43,7 +43,9 @@
         "silverwind",
         "idris",
         "todotasks",
-        "connor"
+        "connor",
+        "injective",
+        "injectivity"
     ],
     "ignorePaths": ["dist", "node_modules", "coverage", "*.svg", ".gitignore"]
 }
diff --git a/src/matcher-shared.ts b/src/matcher-shared.ts
index 9c302fc..fead4cc 100644
--- a/src/matcher-shared.ts
+++ b/src/matcher-shared.ts
@@ -1,4 +1,4 @@
-import type { ValueOf } from "type-fest";
+import type { IsLiteral, IsNever, ValueOf } from "type-fest";
 
 // The primitive-union and tagged-union matchers differ in their universe, but the
 // handler/fallback plumbing is identical; these are the shared pieces. The
@@ -16,11 +16,11 @@ export type Matchable = string | number | boolean | null | undefined;
 
 // `boolean`, `null` and `undefined` cannot be property keys, so a mapped type
 // over a universe that includes one keys each such member by its
-// stringification. `PatternParam` inverts that projection, so a handler callback
-// still receives the *real* member (`true`, not `"true"`). Both matchers use the
-// projection: the primitive-union matcher over its universe, the tagged-union
-// matcher over a discriminant property's values. See README § Caveats for the
-// limits.
+// stringification. `Member` inverts that projection against the universe, so a
+// handler callback still receives the *real* member (`true`, not `"true"`).
+// Both matchers use the projection: the primitive-union matcher over its
+// universe, the tagged-union matcher over a discriminant property's values. See
+// README § Caveats for the limits.
 export type PatternKey<T> = T extends boolean
     ? T extends true
         ? "true"
@@ -30,15 +30,56 @@ export type PatternKey<T> = T extends boolean
       : T extends undefined
         ? "undefined"
         : T;
-export type PatternParam<K> = K extends "true"
-    ? true
-    : K extends "false"
-      ? false
-      : K extends "null"
-        ? null
-        : K extends "undefined"
-          ? undefined
-          : K;
+
+// The member(s) of `T` whose `PatternKey` is `K`: the universe-keyed inverse of
+// `PatternKey`. The key alone cannot recover the member (`"true"` and `true`
+// share it), so the handler parameter is derived from `T` instead. For a
+// supported (injective) universe the result is a single member.
+export type Member<
+    T extends Matchable,
+    K extends PropertyKey,
+> = T extends Matchable ? (PatternKey<T> extends K ? T : never) : never;
+
+// The property key a `Matchable` member takes at runtime: booleans, `null` and
+// `undefined` stringify, and a numeric literal becomes its decimal string.
+export type Stringified<T> = T extends boolean
+    ? T extends true
+        ? "true"
+        : "false"
+    : T extends null
+      ? "null"
+      : T extends undefined
+        ? "undefined"
+        : T extends number
+          ? `${T}`
+          : never;
+
+// The members of `T` that are also the stringification of another member, so
+// `PatternKey` cannot invert them. `never` means the universe is injective.
+export type Collisions<T> = Extract<T, Stringified<T>>;
+
+// Why `T` is not a supported universe, or `never` when it is. A supported
+// universe is a finite union of literals with no value/stringification
+// collision: only then can `PatternKey` be inverted unambiguously.
+export type UnsupportedReason<T extends Matchable> =
+    IsLiteral<PatternKey<T>> extends false
+        ? "broad types like string, number and template literals are not supported"
+        : [Collisions<T>] extends [never]
+          ? never
+          : `a value and its stringification collide. Value is "${Collisions<T> & string}"`;
+
+// The diagnostic for an unsupported universe. Extends `HandlerMap` so the
+// implementation's `handlers: HandlerMap` stays assignable when the gate is
+// intersected into a parameter; the property name is the message.
+export type UnsupportedUniverse<Reason extends string> = HandlerMap &
+    Readonly<Record<`unsupported universe: ${Reason}`, never>>;
+
+// `unknown` for a supported universe (an intersection no-op), the diagnostic
+// otherwise. Intersecting rather than branching keeps `R` inference intact.
+export type UniverseGate<T extends Matchable> =
+    IsNever<UnsupportedReason<T>> extends true
+        ? unknown
+        : UnsupportedUniverse<UnsupportedReason<T>>;
 
 // `Extract` drops optional handlers (`undefined`) so `PatternReturns` also works
 // when `P`'s constraint has optional keys.
diff --git a/src/primitive-union.test.ts b/src/primitive-union.test.ts
index f2235a7..17c2ac0 100644
--- a/src/primitive-union.test.ts
+++ b/src/primitive-union.test.ts
@@ -495,26 +495,392 @@ test("getPrimitiveUnionMatcher factory rejects non-exhaustive boolean and nullis
     );
 });
 
-test("getPrimitiveUnionMatcher: an open universe keeps the fallback's remainder open", () => {
+test("getPrimitiveUnionMatcher: a standalone stringified literal is typed by the member, not its key", () => {
+    // `"true"` is a string member whose `PatternKey` is `"true"`; inverting the
+    // key must recover the string, not the boolean that also stringifies to it.
     // Arrange
-    const factory = getPrimitiveUnionMatcher<string>();
+    const factory = getPrimitiveUnionMatcher<"true" | "1">();
 
     // Act
-    const matcher = factory({ a: () => 1 }, (s) => {
-        // The map's literal keys do not close an open universe, so the
-        // remainder stays `string` and the fallback is not redundant.
-        expectTypeOf(s).toEqualTypeOf<string>();
-        // A strict pattern fixes one `R` for every handler, so this fallback
-        // cannot return its shape; `typeof` is the strongest claim the value
-        // makes on its own — any string passes, including `""`.
-        assert.equal(typeof s, "string");
-        return 2 as const;
+    const matcher = factory({
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"true">();
+            assert.equal(s, "true");
+            return 1;
+        },
+        "1": (s) => {
+            expectTypeOf(s).toEqualTypeOf<"1">();
+            assert.equal(s, "1");
+            return 2;
+        },
     });
 
     // Assert
-    expectTypeOf(matcher).toEqualTypeOf<(shape: string) => number>();
-    assert.equal(matcher("a"), 1);
-    assert.equal(matcher("b"), 2);
+    assert.equal(matcher("true"), 1);
+    assert.equal(matcher("1"), 2);
+});
+
+test("getPrimitiveUnionMatcher: a broad universe is rejected", () => {
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error `string` is not a finite union of literals
+    getPrimitiveUnionMatcher<string>()({ a: () => 1 });
+    // @ts-expect-error `number` is not a finite union of literals
+    getPrimitiveUnionMatcher<number>()({ 1: () => 1 });
+    // @ts-expect-error a template literal is open
+    getPrimitiveUnionMatcher<`a${string}`>()({ a: () => 1 });
+    // @ts-expect-error `string | boolean` is open because of `string`
+    getPrimitiveUnionMatcher<string | boolean>()({ true: () => 1 });
+    // @ts-expect-error the widening factory rejects broad universes too
+    getPrimitiveUnionMatcherW<string>()({ a: () => 1 });
+});
+
+test("getPrimitiveUnionMatcher: a value/stringification collision is rejected", () => {
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error `true` collides with the string `"true"`
+    getPrimitiveUnionMatcher<"true" | true>()({ true: () => 1 });
+    // @ts-expect-error `false` collides with the string `"false"`
+    getPrimitiveUnionMatcher<"false" | false>()({ false: () => 1 });
+    // @ts-expect-error `null` collides with the string `"null"`
+    getPrimitiveUnionMatcher<"null" | null>()({ null: () => 1 });
+    // @ts-expect-error `undefined` collides with the string `"undefined"`
+    getPrimitiveUnionMatcher<"undefined" | undefined>()({
+        undefined: () => 1,
+    });
+    // @ts-expect-error the number `1` collides with the string `"1"`
+    getPrimitiveUnionMatcher<1 | "1">()({ 1: () => 1 });
+});
+
+test("getPrimitiveUnionMatcher: a collision is rejected beside legal members", () => {
+    // Act / Assert — the calls below must not compile; the legal members do not
+    // mask the collision. Each map is otherwise complete, so only the collision
+    // can make it invalid.
+    // @ts-expect-error `true` collides with `"true"` beside legal members
+    getPrimitiveUnionMatcher<"true" | true | "a" | 2>()({
+        true: () => 1,
+        a: () => 2,
+        2: () => 3,
+    });
+    // @ts-expect-error `false` collides with `"false"` beside legal members
+    getPrimitiveUnionMatcher<"false" | false | "a" | 2>()({
+        false: () => 1,
+        a: () => 2,
+        2: () => 3,
+    });
+    // @ts-expect-error `null` collides with `"null"` beside legal members
+    getPrimitiveUnionMatcher<"null" | null | "a" | 2>()({
+        null: () => 1,
+        a: () => 2,
+        2: () => 3,
+    });
+    // @ts-expect-error `undefined` collides with `"undefined"` beside legal members
+    getPrimitiveUnionMatcher<"undefined" | undefined | "a" | 2>()({
+        undefined: () => 1,
+        a: () => 2,
+        2: () => 3,
+    });
+    // @ts-expect-error `1` collides with `"1"` beside legal members
+    getPrimitiveUnionMatcher<1 | "1" | "a" | true>()({
+        1: () => 1,
+        a: () => 2,
+        true: () => 3,
+    });
+});
+
+test('getPrimitiveUnionMatcher: `"true"` and a bare `false` are legal together', () => {
+    // Arrange — `false` stringifies to `"false"`, so it does not collide with
+    // the string member `"true"`.
+    const factory = getPrimitiveUnionMatcher<"true" | false | "a" | 2>();
+
+    // Act
+    const matcher = factory({
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"true">();
+            assert.equal(s, "true");
+            return 1;
+        },
+        false: (s) => {
+            expectTypeOf(s).toEqualTypeOf<false>();
+            assert.equal(s, false);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"a">();
+            assert.equal(s, "a");
+            return 3;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<2>();
+            assert.equal(s, 2);
+            return 4;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher("true"), 1);
+    assert.equal(matcher(false), 2);
+    assert.equal(matcher("a"), 3);
+    assert.equal(matcher(2), 4);
+});
+
+test('getPrimitiveUnionMatcher: `"false"` and a bare `true` are legal together', () => {
+    // Arrange — `true` stringifies to `"true"`, not `"false"`.
+    const factory = getPrimitiveUnionMatcher<"false" | true | "a" | 2>();
+
+    // Act
+    const matcher = factory({
+        false: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"false">();
+            assert.equal(s, "false");
+            return 1;
+        },
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<true>();
+            assert.equal(s, true);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"a">();
+            assert.equal(s, "a");
+            return 3;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<2>();
+            assert.equal(s, 2);
+            return 4;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher("false"), 1);
+    assert.equal(matcher(true), 2);
+    assert.equal(matcher("a"), 3);
+    assert.equal(matcher(2), 4);
+});
+
+test('getPrimitiveUnionMatcher: `"null"` and a bare `undefined` are legal together', () => {
+    // Arrange — `undefined` stringifies to `"undefined"`, not `"null"`.
+    const factory = getPrimitiveUnionMatcher<"null" | undefined | "a" | 2>();
+
+    // Act
+    const matcher = factory({
+        null: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"null">();
+            assert.equal(s, "null");
+            return 1;
+        },
+        undefined: (s) => {
+            expectTypeOf(s).toEqualTypeOf<undefined>();
+            assert.equal(s, undefined);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"a">();
+            assert.equal(s, "a");
+            return 3;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<2>();
+            assert.equal(s, 2);
+            return 4;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher("null"), 1);
+    assert.equal(matcher(undefined), 2);
+    assert.equal(matcher("a"), 3);
+    assert.equal(matcher(2), 4);
+});
+
+test('getPrimitiveUnionMatcher: `"undefined"` and a bare `null` are legal together', () => {
+    // Arrange — `null` stringifies to `"null"`, not `"undefined"`.
+    const factory = getPrimitiveUnionMatcher<"undefined" | null | "a" | 2>();
+
+    // Act
+    const matcher = factory({
+        undefined: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"undefined">();
+            assert.equal(s, "undefined");
+            return 1;
+        },
+        null: (s) => {
+            expectTypeOf(s).toEqualTypeOf<null>();
+            assert.equal(s, null);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"a">();
+            assert.equal(s, "a");
+            return 3;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<2>();
+            assert.equal(s, 2);
+            return 4;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher("undefined"), 1);
+    assert.equal(matcher(null), 2);
+    assert.equal(matcher("a"), 3);
+    assert.equal(matcher(2), 4);
+});
+
+test('getPrimitiveUnionMatcher: `"1"` beside other numbers and strings is legal', () => {
+    // Arrange — the task's example: `"1"` is the string member, `2` and `3`
+    // are bare numbers, `"4"` is another string. No stringification lands on
+    // another member.
+    const factory = getPrimitiveUnionMatcher<"1" | 2 | 3 | "4">();
+
+    // Act
+    const matcher = factory({
+        "1": (s) => {
+            expectTypeOf(s).toEqualTypeOf<"1">();
+            assert.equal(s, "1");
+            return 1;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<2>();
+            assert.equal(s, 2);
+            return 2;
+        },
+        3: (s) => {
+            expectTypeOf(s).toEqualTypeOf<3>();
+            assert.equal(s, 3);
+            return 3;
+        },
+        "4": (s) => {
+            expectTypeOf(s).toEqualTypeOf<"4">();
+            assert.equal(s, "4");
+            return 4;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher("1"), 1);
+    assert.equal(matcher(2), 2);
+    assert.equal(matcher(3), 3);
+    assert.equal(matcher("4"), 4);
+});
+
+// The maximum legal universe needs one handler per member; the statement count
+// is inherent to the case.
+// oxlint-disable-next-line max-statements
+test("getPrimitiveUnionMatcher: the maximum legal universe is supported", () => {
+    // Arrange — every Matchable kind, one representation per value, plus extra
+    // literals. No member's stringification is another member.
+    type Legal =
+        | "true"
+        | false
+        | null
+        | undefined
+        | "1"
+        | 2
+        | 3
+        | "a"
+        | "b"
+        | "4";
+    const factory = getPrimitiveUnionMatcher<Legal>();
+
+    // Act
+    const matcher = factory({
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"true">();
+            assert.equal(s, "true");
+            return 1;
+        },
+        false: (s) => {
+            expectTypeOf(s).toEqualTypeOf<false>();
+            assert.equal(s, false);
+            return 2;
+        },
+        null: (s) => {
+            expectTypeOf(s).toEqualTypeOf<null>();
+            assert.equal(s, null);
+            return 3;
+        },
+        undefined: (s) => {
+            expectTypeOf(s).toEqualTypeOf<undefined>();
+            assert.equal(s, undefined);
+            return 4;
+        },
+        "1": (s) => {
+            expectTypeOf(s).toEqualTypeOf<"1">();
+            assert.equal(s, "1");
+            return 5;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<2>();
+            assert.equal(s, 2);
+            return 6;
+        },
+        3: (s) => {
+            expectTypeOf(s).toEqualTypeOf<3>();
+            assert.equal(s, 3);
+            return 7;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"a">();
+            assert.equal(s, "a");
+            return 8;
+        },
+        b: (s) => {
+            expectTypeOf(s).toEqualTypeOf<"b">();
+            assert.equal(s, "b");
+            return 9;
+        },
+        "4": (s) => {
+            expectTypeOf(s).toEqualTypeOf<"4">();
+            assert.equal(s, "4");
+            return 10;
+        },
+    });
+
+    // Assert
+    expectTypeOf(matcher).toEqualTypeOf<(shape: Legal) => number>();
+    assert.equal(matcher("true"), 1);
+    assert.equal(matcher(false), 2);
+    assert.equal(matcher(null), 3);
+    assert.equal(matcher(undefined), 4);
+    assert.equal(matcher("1"), 5);
+    assert.equal(matcher(2), 6);
+    assert.equal(matcher(3), 7);
+    assert.equal(matcher("a"), 8);
+    assert.equal(matcher("b"), 9);
+    assert.equal(matcher("4"), 10);
+});
+
+test("getPrimitiveUnionMatcher: the maximum illegal universe is rejected", () => {
+    // Arrange — every value paired with its stringification.
+    type Illegal =
+        | "true"
+        | true
+        | "false"
+        | false
+        | "null"
+        | null
+        | "undefined"
+        | undefined
+        | "1"
+        | 1;
+
+    // Act / Assert — the call below must not compile
+    // @ts-expect-error every value collides with its stringification
+    getPrimitiveUnionMatcher<Illegal>()({
+        true: () => 1,
+        false: () => 2,
+        null: () => 3,
+        undefined: () => 4,
+        "1": () => 5,
+    });
+});
+
+test("getPrimitiveUnionMatcher: an open universe is rejected with a fallback too", () => {
+    // Act / Assert — the call below must not compile; a broad universe is
+    // unsupported whether or not a fallback is supplied.
+    // @ts-expect-error `string` is not a finite union of literals
+    getPrimitiveUnionMatcher<string>()({ a: () => 1 }, () => 2);
 });
 
 test("getPrimitiveUnionMatcherW factory rejects patterns outside its contract", () => {
@@ -539,16 +905,11 @@ test("getPrimitiveUnionMatcherW factory rejects patterns outside its contract",
 // ============================================================================
 
 test("getPrimitiveUnionMatcher: an unhandled shape throws without a fallback", () => {
-    // Arrange — an open universe types its handler map as an index signature,
-    // so the type system cannot prove the runtime map is exhaustive.
-    const handlers: Record<string, (shape: unknown) => number> = {
-        a: (shape) => {
-            // The raw shape reaches the handler, not the property key's text.
-            assert.equal(shape, "a");
-            return 1;
-        },
-    };
-    const matcher = getPrimitiveUnionMatcher<string>()(handlers);
+    // Arrange — a finite universe is exhaustive through the typed API, so the
+    // defensive throw is reachable only by widening the factory and dropping a
+    // handler.
+    const bypass: Function = getPrimitiveUnionMatcher<"a" | "b">();
+    const matcher: (shape: "a" | "b") => number = bypass({ a: () => 1 });
 
     // Act / Assert
     assert.equal(matcher("a"), 1);
@@ -556,17 +917,15 @@ test("getPrimitiveUnionMatcher: an unhandled shape throws without a fallback", (
 });
 
 test("getPrimitiveUnionMatcher: an unhandled boolean shape throws without a fallback", () => {
-    // Arrange — an `string | boolean` universe widens its handler map to an
-    // index signature, so the runtime map's exhaustiveness is not provable.
-    const handlers: Record<string, (shape: unknown) => number> = {
-        true: (shape) => {
-            // `true` indexes the map as the property `"true"`, but the handler
-            // is still called with the boolean.
+    // Arrange — as above; `true` indexes the map as the property `"true"`, but
+    // the handler is still called with the boolean.
+    const bypass: Function = getPrimitiveUnionMatcher<true | false>();
+    const matcher: (shape: boolean) => number = bypass({
+        true: (shape: boolean) => {
             assert.equal(shape, true);
             return 1;
         },
-    };
-    const matcher = getPrimitiveUnionMatcher<string | boolean>()(handlers);
+    });
 
     // Act / Assert
     assert.equal(matcher(true), 1);
diff --git a/src/primitive-union.ts b/src/primitive-union.ts
index 7c6061b..f3b328b 100644
--- a/src/primitive-union.ts
+++ b/src/primitive-union.ts
@@ -3,25 +3,26 @@ import type { Exact } from "type-fest";
 import type {
     HandlerMap,
     Matchable,
+    Member,
     PatternKey,
-    PatternParam,
     PatternReturns,
     RedundantFallback,
     UnaryFn,
+    UniverseGate,
 } from "./matcher-shared.ts";
 
 type Handlers<T extends Matchable, R> = {
-    [K in PatternKey<T>]: UnaryFn<PatternParam<K>, R>;
+    [K in PatternKey<T>]: UnaryFn<Member<T, K>, R>;
 };
 
 // The fallback is a *second argument*, not a property of the handler map,
-// because its parameter is the remainder `Exclude<T, keyof Handled>` and TypeScript
+// because its parameter is the remainder `Exclude<T, Member<T, keyof Handled>>` and TypeScript
 // fixes a property's contextual type before it infers its sibling keys. A later
 // argument, by contrast, is contextually typed from inference on an earlier
 // one, so the split is what makes the remainder expressible at all.
 // See development/library.md.
 type Fallback<T extends Matchable, Handled, R> = UnaryFn<
-    Exclude<T, PatternParam<keyof Handled>>,
+    Exclude<T, Member<T, keyof Handled>>,
     R
 >;
 
@@ -44,14 +45,14 @@ type MustBePartial<T extends Matchable, Handled> =
 //   #1 Handlers (first) -> the exhaustive form and the autocomplete popup
 //   #2 Fallback (last)  -> accepts a partial handler map plus a fallback
 interface PrimitiveUnionMatcherStrict<T extends Matchable> {
-    <R>(handlers: Handlers<T, R>): UnaryFn<T, R>;
+    <R>(handlers: Handlers<T, R> & UniverseGate<T>): UnaryFn<T, R>;
     <
         R,
         Handled extends Exact<Partial<Handlers<T, R>>, Handled> &
             MustBePartial<T, Handled>,
     >(
-        handlers: Handled & Partial<Handlers<T, R>>,
-        fallback: Fallback<T, Handled, R>,
+        handlers: Handled & Partial<Handlers<T, R>> & UniverseGate<T>,
+        fallback: Fallback<T, Handled, R> & UniverseGate<T>,
     ): UnaryFn<T, R>;
 }
 
@@ -60,15 +61,15 @@ interface PrimitiveUnionMatcherStrict<T extends Matchable> {
 // contextual/autocomplete type.
 interface PrimitiveUnionMatcherWidening<T extends Matchable> {
     <P extends Exact<Handlers<T, unknown>, P>>(
-        handlers: P,
+        handlers: P & UniverseGate<T>,
     ): UnaryFn<T, PatternReturns<P>>;
     <
         R,
         Handled extends Exact<Partial<Handlers<T, unknown>>, Handled> &
             MustBePartial<T, Handled>,
     >(
-        handlers: Handled,
-        fallback: Fallback<T, Handled, R>,
+        handlers: Handled & UniverseGate<T>,
+        fallback: Fallback<T, Handled, R> & UniverseGate<T>,
     ): UnaryFn<T, PatternReturns<Handled> | R>;
 }
 
diff --git a/src/tagged-union.test.ts b/src/tagged-union.test.ts
index 7873b81..cadb6ed 100644
--- a/src/tagged-union.test.ts
+++ b/src/tagged-union.test.ts
@@ -273,27 +273,17 @@ test("getTaggedUnionMatcher: a fallback receives the unhandled members", () => {
     assert.equal(area({ kind: "triangle", base: 1, height: 1 }), 2);
 });
 
-test("getTaggedUnionMatcher: an open discriminant keeps the fallback open", () => {
+test("getTaggedUnionMatcher: an open discriminant is rejected with a fallback too", () => {
     // Arrange
     interface Message {
         readonly kind: string;
         readonly text: string;
     }
-    const factory = getTaggedUnionMatcher<Message>()("kind");
 
-    // Act
-    const matcher = factory({ info: () => 1 as const }, (s) => {
-        // The map's literal key does not close an open discriminant, so the
-        // remainder stays `Message` and the fallback is not redundant.
-        expectTypeOf(s).toEqualTypeOf<Message>();
-        assert.equal(typeof s.text, "string");
-        return 2 as const;
-    });
-
-    // Assert
-    expectTypeOf(matcher).toEqualTypeOf<(shape: Message) => 1 | 2>();
-    assert.equal(matcher({ kind: "info", text: "" }), 1);
-    assert.equal(matcher({ kind: "warn", text: "" }), 2);
+    // Act / Assert — the call below must not compile; a broad tag is unsupported
+    // whether or not a fallback is supplied.
+    // @ts-expect-error `string` tags are not a finite union of literals
+    getTaggedUnionMatcher<Message>()("kind")({ info: () => 1 }, () => 2);
 });
 
 // ============================================================================
@@ -446,28 +436,489 @@ test("getTaggedUnionMatcherW factory rejects patterns outside its contract", ()
     );
 });
 
+test("getTaggedUnionMatcher: a standalone stringified tag is typed by the member, not its key", () => {
+    // `kind: "true"` is a string tag whose `PatternKey` is `"true"`; inverting
+    // the key must recover the member, not the boolean tag.
+    // Arrange
+    interface StringTag {
+        readonly kind: "true";
+        readonly a: number;
+    }
+    const factory = getTaggedUnionMatcher<StringTag>()("kind");
+
+    // Act
+    const matcher = factory({
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<StringTag>();
+            assert.equal(s.kind, "true");
+            return 1;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher({ kind: "true", a: 1 }), 1);
+});
+
+test("getTaggedUnionMatcher: a broad tag is rejected", () => {
+    // Arrange
+    interface Message {
+        readonly kind: string;
+    }
+    interface Count {
+        readonly kind: number;
+    }
+
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error `string` tags are not a finite union of literals
+    getTaggedUnionMatcher<Message>()("kind")({ a: () => 1 });
+    // @ts-expect-error `number` tags are not a finite union of literals
+    getTaggedUnionMatcher<Count>()("kind")({ 1: () => 1 });
+    // @ts-expect-error the widening factory rejects broad tags too
+    getTaggedUnionMatcherW<Message>()("kind")({ a: () => 1 });
+});
+
+test("getTaggedUnionMatcher: a value/stringification tag collision is rejected", () => {
+    // Arrange
+    type Colliding =
+        | { readonly kind: "true"; readonly a: number }
+        | { readonly kind: true; readonly b: number };
+    type NumericColliding =
+        | { readonly kind: "1"; readonly a: number }
+        | { readonly kind: 1; readonly b: number };
+
+    // Act / Assert — the calls below must not compile
+    // @ts-expect-error `true` collides with the string tag `"true"`
+    getTaggedUnionMatcher<Colliding>()("kind")({ true: () => 1 });
+    // @ts-expect-error the number tag `1` collides with the string tag `"1"`
+    getTaggedUnionMatcher<NumericColliding>()("kind")({ "1": () => 1 });
+});
+
+test("getTaggedUnionMatcher: a tag collision is rejected beside legal members", () => {
+    // Act / Assert — the calls below must not compile. Each map is otherwise
+    // complete, so only the collision can make it invalid.
+    type TrueColliding =
+        | { readonly kind: "true"; readonly a: number }
+        | { readonly kind: true; readonly b: number }
+        | { readonly kind: "a"; readonly c: number };
+    // @ts-expect-error `true` collides with the string tag `"true"`
+    getTaggedUnionMatcher<TrueColliding>()("kind")({
+        true: () => 1,
+        a: () => 2,
+    });
+
+    type FalseColliding =
+        | { readonly kind: "false"; readonly a: number }
+        | { readonly kind: false; readonly b: number }
+        | { readonly kind: "a"; readonly c: number };
+    // @ts-expect-error `false` collides with the string tag `"false"`
+    getTaggedUnionMatcher<FalseColliding>()("kind")({
+        false: () => 1,
+        a: () => 2,
+    });
+
+    type NullColliding =
+        | { readonly kind: "null"; readonly a: number }
+        | { readonly kind: null; readonly b: number }
+        | { readonly kind: "a"; readonly c: number };
+    // @ts-expect-error `null` collides with the string tag `"null"`
+    getTaggedUnionMatcher<NullColliding>()("kind")({
+        null: () => 1,
+        a: () => 2,
+    });
+
+    type UndefinedColliding =
+        | { readonly kind: "undefined"; readonly a: number }
+        | { readonly kind: undefined; readonly b: number }
+        | { readonly kind: "a"; readonly c: number };
+    // @ts-expect-error `undefined` collides with the string tag `"undefined"`
+    getTaggedUnionMatcher<UndefinedColliding>()("kind")({
+        undefined: () => 1,
+        a: () => 2,
+    });
+
+    type NumericColliding =
+        | { readonly kind: "1"; readonly a: number }
+        | { readonly kind: 1; readonly b: number }
+        | { readonly kind: "a"; readonly c: number };
+    // @ts-expect-error the number tag `1` collides with the string tag `"1"`
+    getTaggedUnionMatcher<NumericColliding>()("kind")({
+        "1": () => 1,
+        a: () => 2,
+    });
+});
+
+test('getTaggedUnionMatcher: a `"true"` tag and a `false` tag are legal together', () => {
+    // Arrange
+    interface TrueString {
+        readonly kind: "true";
+        readonly a: number;
+    }
+    interface FalseBare {
+        readonly kind: false;
+        readonly b: number;
+    }
+    interface Extra {
+        readonly kind: "a";
+        readonly c: number;
+    }
+    type Legal = TrueString | FalseBare | Extra;
+
+    // Act
+    const matcher = getTaggedUnionMatcher<Legal>()("kind")({
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<TrueString>();
+            assert.equal(s.kind, "true");
+            return 1;
+        },
+        false: (s) => {
+            expectTypeOf(s).toEqualTypeOf<FalseBare>();
+            assert.equal(s.kind, false);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Extra>();
+            assert.equal(s.kind, "a");
+            return 3;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher({ kind: "true", a: 1 }), 1);
+    assert.equal(matcher({ kind: false, b: 2 }), 2);
+    assert.equal(matcher({ kind: "a", c: 3 }), 3);
+});
+
+test('getTaggedUnionMatcher: a `"false"` tag and a `true` tag are legal together', () => {
+    // Arrange
+    interface FalseString {
+        readonly kind: "false";
+        readonly a: number;
+    }
+    interface TrueBare {
+        readonly kind: true;
+        readonly b: number;
+    }
+    interface Extra {
+        readonly kind: "a";
+        readonly c: number;
+    }
+    type Legal = FalseString | TrueBare | Extra;
+
+    // Act
+    const matcher = getTaggedUnionMatcher<Legal>()("kind")({
+        false: (s) => {
+            expectTypeOf(s).toEqualTypeOf<FalseString>();
+            assert.equal(s.kind, "false");
+            return 1;
+        },
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<TrueBare>();
+            assert.equal(s.kind, true);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Extra>();
+            assert.equal(s.kind, "a");
+            return 3;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher({ kind: "false", a: 1 }), 1);
+    assert.equal(matcher({ kind: true, b: 2 }), 2);
+    assert.equal(matcher({ kind: "a", c: 3 }), 3);
+});
+
+test('getTaggedUnionMatcher: a `"null"` tag and an `undefined` tag are legal together', () => {
+    // Arrange
+    interface NullString {
+        readonly kind: "null";
+        readonly a: number;
+    }
+    interface UndefinedBare {
+        readonly kind: undefined;
+        readonly b: number;
+    }
+    interface Extra {
+        readonly kind: "a";
+        readonly c: number;
+    }
+    type Legal = NullString | UndefinedBare | Extra;
+
+    // Act
+    const matcher = getTaggedUnionMatcher<Legal>()("kind")({
+        null: (s) => {
+            expectTypeOf(s).toEqualTypeOf<NullString>();
+            assert.equal(s.kind, "null");
+            return 1;
+        },
+        undefined: (s) => {
+            expectTypeOf(s).toEqualTypeOf<UndefinedBare>();
+            assert.equal(s.kind, undefined);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Extra>();
+            assert.equal(s.kind, "a");
+            return 3;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher({ kind: "null", a: 1 }), 1);
+    assert.equal(matcher({ kind: undefined, b: 2 }), 2);
+    assert.equal(matcher({ kind: "a", c: 3 }), 3);
+});
+
+test('getTaggedUnionMatcher: an `"undefined"` tag and a `null` tag are legal together', () => {
+    // Arrange
+    interface UndefinedString {
+        readonly kind: "undefined";
+        readonly a: number;
+    }
+    interface NullBare {
+        readonly kind: null;
+        readonly b: number;
+    }
+    interface Extra {
+        readonly kind: "a";
+        readonly c: number;
+    }
+    type Legal = UndefinedString | NullBare | Extra;
+
+    // Act
+    const matcher = getTaggedUnionMatcher<Legal>()("kind")({
+        undefined: (s) => {
+            expectTypeOf(s).toEqualTypeOf<UndefinedString>();
+            assert.equal(s.kind, "undefined");
+            return 1;
+        },
+        null: (s) => {
+            expectTypeOf(s).toEqualTypeOf<NullBare>();
+            assert.equal(s.kind, null);
+            return 2;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<Extra>();
+            assert.equal(s.kind, "a");
+            return 3;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher({ kind: "undefined", a: 1 }), 1);
+    assert.equal(matcher({ kind: null, b: 2 }), 2);
+    assert.equal(matcher({ kind: "a", c: 3 }), 3);
+});
+
+test('getTaggedUnionMatcher: a `"1"` tag beside other tags is legal', () => {
+    // Arrange
+    interface OneString {
+        readonly kind: "1";
+        readonly a: number;
+    }
+    interface TwoBare {
+        readonly kind: 2;
+        readonly b: number;
+    }
+    interface ThreeBare {
+        readonly kind: 3;
+        readonly c: number;
+    }
+    interface FourString {
+        readonly kind: "4";
+        readonly d: number;
+    }
+    type Legal = OneString | TwoBare | ThreeBare | FourString;
+
+    // Act
+    const matcher = getTaggedUnionMatcher<Legal>()("kind")({
+        "1": (s) => {
+            expectTypeOf(s).toEqualTypeOf<OneString>();
+            assert.equal(s.kind, "1");
+            return 1;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<TwoBare>();
+            assert.equal(s.kind, 2);
+            return 2;
+        },
+        3: (s) => {
+            expectTypeOf(s).toEqualTypeOf<ThreeBare>();
+            assert.equal(s.kind, 3);
+            return 3;
+        },
+        "4": (s) => {
+            expectTypeOf(s).toEqualTypeOf<FourString>();
+            assert.equal(s.kind, "4");
+            return 4;
+        },
+    });
+
+    // Assert
+    assert.equal(matcher({ kind: "1", a: 1 }), 1);
+    assert.equal(matcher({ kind: 2, b: 2 }), 2);
+    assert.equal(matcher({ kind: 3, c: 3 }), 3);
+    assert.equal(matcher({ kind: "4", d: 4 }), 4);
+});
+
+// The maximum legal tag universe needs one handler per member; the statement
+// count is inherent to the case.
+// oxlint-disable-next-line max-statements
+test("getTaggedUnionMatcher: the maximum legal tag universe is supported", () => {
+    // Arrange — every tag kind, one representation per value, plus extra tags.
+    interface M1 {
+        readonly kind: "true";
+        readonly a: 1;
+    }
+    interface M2 {
+        readonly kind: false;
+        readonly b: 2;
+    }
+    interface M3 {
+        readonly kind: null;
+        readonly c: 3;
+    }
+    interface M4 {
+        readonly kind: undefined;
+        readonly d: 4;
+    }
+    interface M5 {
+        readonly kind: "1";
+        readonly e: 5;
+    }
+    interface M6 {
+        readonly kind: 2;
+        readonly f: 6;
+    }
+    interface M7 {
+        readonly kind: 3;
+        readonly g: 7;
+    }
+    interface M8 {
+        readonly kind: "a";
+        readonly h: 8;
+    }
+    interface M9 {
+        readonly kind: "b";
+        readonly i: 9;
+    }
+    type Legal = M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | M9;
+
+    // Act
+    const matcher = getTaggedUnionMatcher<Legal>()("kind")({
+        true: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M1>();
+            assert.equal(s.kind, "true");
+            return 1;
+        },
+        false: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M2>();
+            assert.equal(s.kind, false);
+            return 2;
+        },
+        null: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M3>();
+            assert.equal(s.kind, null);
+            return 3;
+        },
+        undefined: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M4>();
+            assert.equal(s.kind, undefined);
+            return 4;
+        },
+        "1": (s) => {
+            expectTypeOf(s).toEqualTypeOf<M5>();
+            assert.equal(s.kind, "1");
+            return 5;
+        },
+        2: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M6>();
+            assert.equal(s.kind, 2);
+            return 6;
+        },
+        3: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M7>();
+            assert.equal(s.kind, 3);
+            return 7;
+        },
+        a: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M8>();
+            assert.equal(s.kind, "a");
+            return 8;
+        },
+        b: (s) => {
+            expectTypeOf(s).toEqualTypeOf<M9>();
+            assert.equal(s.kind, "b");
+            return 9;
+        },
+    });
+
+    // Assert
+    expectTypeOf(matcher).toEqualTypeOf<(shape: Legal) => number>();
+    assert.equal(matcher({ kind: "true", a: 1 }), 1);
+    assert.equal(matcher({ kind: false, b: 2 }), 2);
+    assert.equal(matcher({ kind: null, c: 3 }), 3);
+    assert.equal(matcher({ kind: undefined, d: 4 }), 4);
+    assert.equal(matcher({ kind: "1", e: 5 }), 5);
+    assert.equal(matcher({ kind: 2, f: 6 }), 6);
+    assert.equal(matcher({ kind: 3, g: 7 }), 7);
+    assert.equal(matcher({ kind: "a", h: 8 }), 8);
+    assert.equal(matcher({ kind: "b", i: 9 }), 9);
+});
+
+test("getTaggedUnionMatcher: the maximum illegal tag universe is rejected", () => {
+    // Arrange — every tag paired with its stringification.
+    type Illegal =
+        | { readonly kind: "true"; readonly a: 1 }
+        | { readonly kind: true; readonly a: 1 }
+        | { readonly kind: "false"; readonly b: 2 }
+        | { readonly kind: false; readonly b: 2 }
+        | { readonly kind: "null"; readonly c: 3 }
+        | { readonly kind: null; readonly c: 3 }
+        | { readonly kind: "undefined"; readonly d: 4 }
+        | { readonly kind: undefined; readonly d: 4 }
+        | { readonly kind: "1"; readonly e: 5 }
+        | { readonly kind: 1; readonly e: 5 };
+
+    // Act / Assert — the call below must not compile
+    // @ts-expect-error every tag collides with its stringification
+    getTaggedUnionMatcher<Illegal>()("kind")({
+        true: () => 1,
+        false: () => 2,
+        null: () => 3,
+        undefined: () => 4,
+        "1": () => 5,
+    });
+});
+
 // ============================================================================
 // Dispatch — runtime behavior
 // ============================================================================
 
 test("getTaggedUnionMatcher: an unhandled tag throws without a fallback", () => {
-    // Arrange — an open discriminant widens its handler map to an index
-    // signature, so the type system cannot prove the runtime map is exhaustive.
+    // Arrange — a finite tag set is exhaustive through the typed API, so the
+    // defensive throw is reachable only by widening the factory and dropping a
+    // handler.
     interface Message {
-        readonly kind: string;
+        readonly kind: "info" | "warn";
+        readonly text: string;
     }
-    const handlers: Record<string, (shape: Message) => number> = {
-        info: (shape) => {
+    const bypass: Function = getTaggedUnionMatcher<Message>()("kind");
+    const matcher: (shape: Message) => number = bypass({
+        info: (shape: Message) => {
             // The full member reaches the handler, not its tag.
             assert.equal(shape.kind, "info");
             return 1;
         },
-    };
-    const matcher = getTaggedUnionMatcher<Message>()("kind")(handlers);
+    });
 
     // Act / Assert
-    assert.equal(matcher({ kind: "info" }), 1);
-    assert.throws(() => matcher({ kind: "warn" }), /Unhandled tag: warn/);
+    assert.equal(matcher({ kind: "info", text: "" }), 1);
+    assert.throws(
+        () => matcher({ kind: "warn", text: "" }),
+        /Unhandled tag: warn/,
+    );
 });
 
 // ============================================================================
diff --git a/src/tagged-union.ts b/src/tagged-union.ts
index f501cc3..fabfb07 100644
--- a/src/tagged-union.ts
+++ b/src/tagged-union.ts
@@ -3,11 +3,12 @@ import type { Exact, UnknownRecord } from "type-fest";
 import type {
     HandlerMap,
     Matchable,
+    Member,
     PatternKey,
-    PatternParam,
     PatternReturns,
     RedundantFallback,
     UnaryFn,
+    UniverseGate,
 } from "./matcher-shared.ts";
 
 // A tagged union is discriminated by one property whose values are the tags (a
@@ -17,8 +18,8 @@ import type {
 // to write a handler under, and `bigint` is not a property key.
 
 // The discriminant values of `T` under `K`. `Extract` keeps the finite literal
-// tags and leaves a widened `string`/`number` as itself, so an open universe
-// keeps an open fallback.
+// tags and leaves a widened `string`/`number` as itself; a broad tag is then
+// rejected by the universe gate.
 type Tags<T extends object, K extends keyof T> = Extract<T[K], Matchable>;
 
 // The keys of `T` that can act as a discriminant. `getTaggedUnionMatcher<T>()`
@@ -30,9 +31,10 @@ type Discriminated<T extends object> = {
 // The member(s) of `T` tagged `V`. `Extract` distributes over the union, so a
 // duplicated tag maps to a union of members rather than silently dropping one.
 // Keyed by `PatternKey`, so `boolean`/`null`/`undefined` tags can key a mapped
-// type; `PatternParam` inverts the projection to recover the member.
+// type; `Member` inverts the projection against the tag set to recover the
+// member.
 type MapTaggedUnion<T extends object, K extends keyof T> = {
-    [P in PatternKey<Tags<T, K>>]: Extract<T, Record<K, PatternParam<P>>>;
+    [P in PatternKey<Tags<T, K>>]: Extract<T, Record<K, Member<Tags<T, K>, P>>>;
 };
 
 type Handlers<T extends object, K extends keyof T, R> = {
@@ -43,7 +45,7 @@ type Handlers<T extends object, K extends keyof T, R> = {
 // index within `MapTaggedUnion`'s keys, and the conditional drops a stray key
 // outside `T` so it cannot widen the remainder. The remainder is
 // `Exclude<T, …>`, mirroring the primitive-union matcher's
-// `Exclude<T, PatternParam<keyof Handled>>`.
+// `Exclude<T, Member<T, keyof Handled>>`.
 type HandledMembers<T extends object, K extends keyof T, Handled> = {
     [P in PatternKey<Tags<T, K>>]: P extends keyof Handled
         ? MapTaggedUnion<T, K>[P]
@@ -51,7 +53,7 @@ type HandledMembers<T extends object, K extends keyof T, Handled> = {
 }[PatternKey<Tags<T, K>>];
 
 // The fallback is a *second argument*, not a property of the handler map, so
-// its parameter can be the remainder the map left open. See development/library.md.
+// its parameter can be the remainder the map left uncovered. See development/library.md.
 type Fallback<T extends object, K extends keyof T, Handled, R> = UnaryFn<
     Exclude<T, HandledMembers<T, K, Handled>>,
     R
@@ -71,14 +73,16 @@ type MustBePartial<T extends object, K extends keyof T, Handled> =
 //   #1 Handlers (first) -> the exhaustive form and the autocomplete popup
 //   #2 Fallback (last)  -> accepts a partial handler map plus a fallback
 interface TaggedUnionMatcherStrict<T extends object, K extends keyof T> {
-    <R>(handlers: Handlers<T, K, R>): UnaryFn<T, R>;
+    <R>(handlers: Handlers<T, K, R> & UniverseGate<Tags<T, K>>): UnaryFn<T, R>;
     <
         R,
         Handled extends Exact<Partial<Handlers<T, K, R>>, Handled> &
             MustBePartial<T, K, Handled>,
     >(
-        handlers: Handled & Partial<Handlers<T, K, R>>,
-        fallback: Fallback<T, K, Handled, R>,
+        handlers: Handled &
+            Partial<Handlers<T, K, R>> &
+            UniverseGate<Tags<T, K>>,
+        fallback: Fallback<T, K, Handled, R> & UniverseGate<Tags<T, K>>,
     ): UnaryFn<T, R>;
 }
 
@@ -87,15 +91,15 @@ interface TaggedUnionMatcherStrict<T extends object, K extends keyof T> {
 // contextual/autocomplete type.
 interface TaggedUnionMatcherWidening<T extends object, K extends keyof T> {
     <P extends Exact<Handlers<T, K, unknown>, P>>(
-        handlers: P,
+        handlers: P & UniverseGate<Tags<T, K>>,
     ): UnaryFn<T, PatternReturns<P>>;
     <
         R,
         Handled extends Exact<Partial<Handlers<T, K, unknown>>, Handled> &
             MustBePartial<T, K, Handled>,
     >(
-        handlers: Handled,
-        fallback: Fallback<T, K, Handled, R>,
+        handlers: Handled & UniverseGate<Tags<T, K>>,
+        fallback: Fallback<T, K, Handled, R> & UniverseGate<Tags<T, K>>,
     ): UnaryFn<T, PatternReturns<Handled> | R>;
 }