Literal alphabet sizes grow via tetration (iterated exponentiation). Starting from n₀ = 2:

Level 4 alone would require ≈ 2¹³⁶ bits just to index a single symbol — far beyond any practical storage or computation.

This module sidesteps that explosion by giving every value a fixed-size 256-bit identifier, regardless of how deeply nested or large the underlying data is. Two identifiers are merged into a single new identifier; the result can itself be used as an input to the next merge. This enables:

• Content-addressed storage: the identifier of a value is determined solely by its content.
• Unbounded recursion: any pair of 256-bit identifiers can be combined into a new 256-bit identifier.
• Compact references: large or frequently-repeated sub-trees are referenced by identifier rather than inlined.

Every value is a 256-bit unsigned integer. The top bits form a discriminator prefix:

A Level 3 literal symbol fits entirely below 2²⁵⁴, so no prefix bits need to be added — the identity function is the encoding. There are f(f(f(2))) = 2¹³⁶ + 1 possible Level 3 symbols, all well within this range.

A raw vector encodes an arbitrary bit sequence of at most 253 bits inline. The layout within the 256-bit value is:

The sentinel 1 bit at position equal to the payload length encodes the length implicitly. Maximum payload length is 253 bits.

A hash identifier has bit 255 always set to 1, leaving 255 bits of hash data. It is produced by the SHA2-based merge:

hashId(a, b) = (2^255) | SHA2_compress(IV, a ∥ b)

where a ∥ b is the 512-bit concatenation of two 256-bit values.

The merge is applied whenever inline storage would exceed 253 bits or when either input is already a hash.

325d5666_573eb118_f32191de_20d17f64_33392ba3_291ae46c_1474a5ed_a5383f25

This is the x-coordinate of a point on secp256r1 (NIST P-256), used as the IV for the SHA2-32 word compress function.

1. Seed string — a 32-byte (256-bit) ASCII/UTF-8 string:

   "Synthetic Universal Language 001"
   

   Chosen to be exactly 32 bytes so it fills one 256-bit block with no padding.

2. Scalar — interpret the UTF-8 bytes as a big-endian 256-bit integer:

   scalar = uint(utf8("Synthetic Universal Language 001"))
   

3. Elliptic curve point — multiply the secp256r1 base point G by the scalar:

   P = scalar × G   (on secp256r1)
   

4. IV — take the x-coordinate of P:

   IV = P.x = 0x325d5666_573eb118_f32191de_20d17f64_33392ba3_291ae46c_1474a5ed_a5383f25
   

Using an elliptic curve operation over a public, standardised curve ensures the IV is a nothing-up-my-sleeve number: anyone can reproduce it from the seed string and verify no trapdoor was introduced. The seed string encodes the purpose of this IV, making it domain-separated from any other use of secp256r1 or SHA2.