SUL is a universal encoding that bijectively maps any finite sequence of symbols to a single root symbol via a balanced tree, from which the original sequence can be uniquely recovered.

• A symbol is an element of a level's finite alphabet [0, n).
• A word is a finite sequence of symbols that encodes into a single symbol of the next level.
• A level defines a finite alphabet [0, n) and the bijection between words over that alphabet and symbols of the next level.

A valid word has the form [s0, s1, ..., sk, t] where:

• s0 > s1 > ... > sk — a strictly decreasing prefix of at least one symbol
• sk <= t — a terminating symbol no less than the last prefix element

The minimum word length is 2: one prefix symbol is required to provide a value to compare against t, ensuring each word collapses to a single symbol at the next level — so the sequence strictly shrinks at every step and converges to a single root symbol in a finite number of levels.

The top-level encoder accepts a stream of bits and produces a single Id:

import { encode } from './module.f.mjs'
import { run } from '../types/list/module.f.js'
import type { Add } from './level/hash/types.ts'

const enc = encode(add)(storage)     // add: Add<S> — called on every merge
const root: Id = run(enc)(bits)      // consume 0n/1n bits, pad, return the root

init is a next step holding the initial state. update(state, bit) returns a new next step; end(state) pads with 1, then 0s, and returns a done step holding the root. No items are emitted before completion. The common driver handles these steps, and a caller can save a step's state and resume it.

A bit's height is how many levels close a word on it, counting up from L1: 0 for none, 2 for L1 and L2, 5 for L1 to H2. updateWithHeight(state, bit) returns it with the next state, and endWithHeights(state) returns it for each padding bit with the root. These additional observations share the lifecycle's encoding and padding operations. The demo draws its stripes from these heights.

The Add<S> callback is invoked once per compress(left, right) merge. isSymbol is true for the terminal merge that produces a hash-level output symbol and false for Patricia trie internal merges.

Bits flow through four stages in sequence:

bits → L1 → L2 → L3 → Hash[0] → Hash[1] → … → Id

The hash stack grows dynamically: each time a hash level emits a symbol, it is pushed into the next level (created on demand).

• level/ — level hierarchy: literal and hash levels
• id/ — 256-bit content-addressed identifier