refactor: improve explanation on readme

typescript/README.md

@@ -1,6 +1,18 @@
 # @peoplesgrocers/lseq
 
-TypeScript implementation of the L-SEQ algorithm for fractional indexing and list CRDTs.
+TypeScript implementation of the L-SEQ algorithm for fractional indexing and
+list CRDTs.
+
+
+The library handles edge cases that break other more naive implementations of
+fractional indexing.  With this library you can always insert before the first
+item or after the last item, indefinitely.
+
+This is exactly what you need to build realtime collaborative apps with
+ordering for lists or trees of items. Users can reorder or insert at arbitrary
+positions but in practice people really like moving items to the top or end of
+a list. So don't crash accept random crashes from other libraries when Alice
+moves yet another element to the front of the list.
 
 ## Installation
 
@@ -11,51 +23,71 @@ npm install @peoplesgrocers/lseq
 ## Usage
 
 ```typescript
-import { LSEQ, compareLSEQ } from '@peoplesgrocers/lseq';
+import { LSEQ } from '@peoplesgrocers/lseq';
 
-// Create a new L-SEQ instance
 const lseq = new LSEQ();
 
-// Allocate identifiers
-const id1 = lseq.alloc(null, null);        // First identifier
-const id2 = lseq.alloc(id1, null);         // After id1
-const id3 = lseq.alloc(id1, id2);          // Between id1 and id2
+const first = lseq.alloc(null, null);
+const second = lseq.alloc(first, null);
+const between = lseq.alloc(first, second);
 
-// Sort identifiers
-const ids = [id3, id1, id2];
-ids.sort(compareLSEQ);
-console.log(ids); // [id1, id3, id2] - properly ordered
-
-// Custom random function (useful for deterministic testing)
-const deterministicLSEQ = new LSEQ(() => 0.5);
+// String comparison gives correct order
+[second, first, between].sort();  // [first, between, second]
 ```
 
 ## API
 
-### `LSEQ`
+### `new LSEQ(random?: () => number)`
 
-#### `constructor(random?: () => number)`
+Create an allocator. Accepts an optional random function for deterministic testing.
 
-Creates a new L-SEQ instance.
+### `lseq.alloc(before: string | null, after: string | null): string`
 
-- `random`: Optional custom random function (defaults to `Math.random`)
+Allocate a key between `before` and `after`.
 
-#### `alloc(before: string | null, after: string | null): string`
-
-Allocates a new identifier between two existing identifiers.
-
-- `before`: The identifier that should come before the new one (or `null` for beginning)
-- `after`: The identifier that should come after the new one (or `null` for end)
-- Returns: A new identifier that sorts between `before` and `after`
+- `lseq.alloc(null, null)` — first key in an empty list
+- `lseq.alloc(null, first)` — insert at head
+- `lseq.alloc(last, null)` — insert at tail
+- `lseq.alloc(a, b)` — insert between a and b
 
 ### `compareLSEQ(a: string, b: string): number`
 
-Compares two L-SEQ identifiers for sorting.
+Compare two keys. Returns -1, 0, or 1.
 
-- Returns: `-1` if `a < b`, `1` if `a > b`, `0` if `a === b`
+### `EvenSpacingIterator`
 
-## How it works
+Generate evenly-spaced keys for bulk initialization:
 
-L-SEQ generates identifiers using a base-64 alphabet that maintains lexicographic ordering. Each identifier is a sequence of characters from this alphabet, and new identifiers are generated by finding space between existing ones at different depths.
+```typescript
+import { EvenSpacingIterator } from '@peoplesgrocers/lseq';
 
-The algorithm uses alternating allocation strategies (bias toward min or max) at different depths to avoid degenerative cases and maintain good performance characteristics. 
+const { k, iterator } = EvenSpacingIterator.create(1000);
+const keys = [];
+for (const position of iterator) {
+  keys.push(EvenSpacingIterator.positionToKey(k, position));
+}
+```
+
+## Design
+
+Keys are base-64 encoded strings using the base64 url-safe alphabet
+`-0-9A-Z_a-z`. There is a compact binary representation inside. Reasonablt
+efficient and no serialization issues with JSON, databases, or URLs.
+
+Standard string comparison produces correct ordering. Keys work in SQL `ORDER
+BY`, database indexes, and any language with string sorting.
+
+## Cross-language support
+
+I wrote matching implementations for Rust, Golang, and Python; validated
+against a shared conformance test suite with fuzzing. If your backend isn't
+TypeScript, you can still allocate and work with these keys natively.  This
+makes LSEQ a reasonable building block for your application's data model.
+
+## References
+
+- [LSEQ: an Adaptive Structure for Sequences in Distributed Collaborative Editing](https://hal.science/hal-00921633/document) (Nédelec et al., 2013)
+
+## License
+
+AGPL-3.0