📝 Document the finite-only universe decision

Record why open universes and value/stringification collisions are
rejected, the `Member<T, K>` inversion, and the findings from the
rejected open-universe attempt so they are not re-run.

README.md

@@ -25,10 +25,15 @@ Yet to be implemented
 
 ## Caveats
 
-- **A value and its stringification collide.** Object keys stringify, so a
-  universe that mixes a member with the string it stringifies to — `1 | "1"`,
-  `true | "true"`, `null | "null"` — collapses to a single handler key and both
-  members are routed to it. Use one form or the other.
+- **Only finite universes are supported.** The factory must be given a finite
+  union of literals; `string`, `number` and template literals are rejected. This
+  is what lets the exhaustive overload be proven, so the runtime `dispatch`
+  throw stays unreachable through the typed API.
+- **A value and its stringification must not both be present.** Object keys
+  stringify, so a universe containing both a member and the string it
+  stringifies to — `1 | "1"`, `true | "true"`, `null | "null"` — is rejected at
+  the factory. Either form alone is fine, and one value's string form may
+  coexist with a _different_ value's bare form (`"true" | false`).
 - **`symbol` and `bigint` are not supported.** A `symbol` brand is a
   compile-time phantom with nothing to match at runtime, and a `bigint` is not a
   valid property key; neither satisfies the matcher's universe constraint.

development/library.md

@@ -97,9 +97,11 @@ Each factory is two overloads whose order is load-bearing:
 
 #### Decision (2026-09)
 
-`src/matcher-shared.ts` holds the seven universe-agnostic pieces both matchers
-use: `UnaryFn`, `PatternReturns`, `RedundantFallback`, `HandlerMap`, the shared
-`Matchable` universe, and the `PatternKey` / `PatternParam` key projection.
+`src/matcher-shared.ts` holds the universe-agnostic pieces both matchers use:
+`UnaryFn`, `PatternReturns`, `RedundantFallback`, `HandlerMap`, the shared
+`Matchable` universe, the `PatternKey` key projection and its `Member` inverse,
+and the `Stringified` / `Collisions` / `UnsupportedReason` / `UnsupportedUniverse`
+/ `UniverseGate` universe gate.
 
 #### Why
 
@@ -118,8 +120,65 @@ use: `UnaryFn`, `PatternReturns`, `RedundantFallback`, `HandlerMap`, the shared
   `Fallback` and `MustBePartial`.** Each is built from its own universe
   (`Tags`/`MapTaggedUnion` vs the primitive values); abstracting over the
   F-bounded `Handled` constraint that makes the remainder work risks the
-  contextual typing it exists to preserve. `Matchable` and the `PatternKey` /
-  `PatternParam` projection are the pieces both universes genuinely share.
+  contextual typing it exists to preserve. `Matchable`, the `PatternKey` /
+  `Member` projection and the `UniverseGate` are the pieces both universes
+  genuinely share.
+
+## Supported universes
+
+#### Decision (2026-09)
+
+A universe must be a **finite union of literals** with **no
+value/stringification collision**. Broad types (`string`, `number`, a template
+literal) and `"true" | true` / `1 | "1"` are rejected; the factory intersects
+`UniverseGate<T>` (the `UnsupportedUniverse<Reason>` diagnostic) into the
+handler and fallback parameters. `Member<T, K>` replaces the `PatternParam<K>`
+inversion: the handler parameter is the member(s) of `T` whose `PatternKey` is
+`K`, so a standalone `"true"` is `"true"`, not `true`.
+
+#### Why
+
+- **`PatternKey` is not injective.** `"true"` and `true` (and `1` / `"1"`)
+  share a runtime key, so `PatternParam<K>` cannot recover the member.
+  `Member<T, K>` inverts against `T`, which is exact.
+- **Broad types cannot be proven exhaustive.** An index-like map lets a partial
+  object satisfy the exhaustive overload and reaches the `dispatch` throw.
+  Rejecting at the boundary avoids threading an open/closed branch through
+  `Handlers`, `Fallback` and `MustBePartial`.
+- **Collisions are rejected, not merged.** `Member<T, K>` would be sound (the
+  handler gets the union), but the API is one handler per member; rejecting
+  keeps `Member` a singleton and the remainder exact.
+- **The collision predicate is type-checkable.** `Collisions<T> =
+Extract<T, Stringified<T>>` catches numeric collisions too.
+- **The gate is an intersection, not a branch,** so `R` inference and the popup
+  survive; a conditional parameter type would not.
+
+#### Rejected
+
+- **Open universes with a required fallback** (`fix/open-universe-*`): sound,
+  but left the collision hole and added an `IsLiteral` /
+  `OpenUniverseNeedsFallback` branch through every handler type. Findings, kept
+  so they are not re-run: `{}` satisfies an index signature (and `Exact` misses
+  it); an index signature dominates contextual typing; `R` infers only from a
+  non-self-referential parameter type (`{ [K in keyof H]: … R … }` gives
+  `unknown`); an F-bounded guard referencing `keyof Handled` in `Handled`'s own
+  constraint sees the constraint, not the map; all handlers share one `R` (only
+  the fallback widens it); `IsLiteral` is the finite-literal predicate.
+- **`Member<T, K>` without the gate:** sound, but a colliding handler gets a
+  union and `1 | "1"` stays one runtime key.
+- **A round-trip injectivity gate** (`IsEqual<T, PatternParam<PatternKey<T>>>`):
+  over-rejects standalone `"true"` / `"false"` / `"null"` / `"undefined"`.
+- **A case-list / ts-pattern builder:** removes the collision class but drops
+  the object map (footprint, popup) and reimplements an existing library.
+- **Normalize numeric keys to strings:** makes `PatternKey` injective but
+  changes "numeric keys stay numbers" and defeats the numeric dispatch fast
+  path.
+
+#### Known issue
+
+- A multi-collision universe lists every collision in the diagnostic.
+- The `dispatch` throw is unreachable through the typed API; the throw tests
+  widen the factory to `Function` to reach it.
 
 ## Tagged-union matcher
 
@@ -160,17 +219,19 @@ The key is a separate call because `K` is inferred from its literal argument and
 - **`MapTaggedUnion` distributes with `Extract`.** A duplicated tag yields a
   union of members instead of dropping one.
 - **A `boolean` / `null` / `undefined` tag goes through the shared
-  `PatternKey` / `PatternParam` projection.** `Discriminated` admits those tags
+  `PatternKey` / `Member` projection.** `Discriminated` admits those tags
   (they are in `Tag`), but they cannot key a mapped type, so the handler map is
-  keyed by the stringified form (`true` → `"true"`) and `PatternParam` inverts
-  it to recover the member. This is the same projection the primitive-union
-  matcher uses over its universe, which is why it lives in `matcher-shared.ts`.
+  keyed by the stringified form (`true` → `"true"`) and `Member` inverts it
+  against the tag set to recover the member. This is the same projection the
+  primitive-union matcher uses over its universe, which is why it lives in
+  `matcher-shared.ts`.
 
 #### Known issue
 
 - A member's tag must be unique across the union; two members with the same tag
-  collapse to a union under one handler. The same holds for a tag colliding with
-  its stringification (`true | "true"`) — see [README § Caveats](../README.md#caveats).
+  collapse to a union under one handler. A tag colliding with its
+  stringification (`true | "true"`) is rejected by the universe gate — see
+  § Supported universes.
 
 ## Primitive universe
 
@@ -180,11 +241,12 @@ The universe (`Matchable`) is `string | number | boolean | null | undefined`,
 with `boolean` admitted as `true | false`.
 
 `boolean`/`null`/`undefined` are not property keys, so handler-map keys are a
-projection (`PatternKey`: each member stringified) and `PatternParam` inverts
-it, so callbacks receive the real member (`true`, not `"true"`). The popup
-offers `true`, `false`, `null`, `undefined` by name (verified over LSP). The
-same projection is shared with the tagged-union matcher; see
-§ Tagged-union matcher.
+projection (`PatternKey`: each member stringified) and `Member` inverts it
+against the universe, so callbacks receive the real member (`true`, not
+`"true"`; the standalone string `"true"` stays `"true"`). The popup offers
+`true`, `false`, `null`, `undefined` by name (verified over LSP). The same
+projection is shared with the tagged-union matcher; see § Tagged-union matcher.
+The supported universes are constrained as described in § Supported universes.
 
 #### Why
 
@@ -194,5 +256,5 @@ same projection is shared with the tagged-union matcher; see
   `String()` defeats V8's numeric-key path: measured ~2× on number-keyed
   dispatch).
 - `symbol`/`bigint`/`NaN`/`-0` are rejected, and a member colliding with its
-  stringification is unguarded: user-facing, stated once in
+  stringification is rejected by the gate: user-facing, stated once in
   [README § Caveats](../README.md#caveats).