E8 receipt-geometry design note

Runtime and project implementation unavailable

No pinned SZL encoder, decoder, route response, receipt, or deployment is established by this recipe. The material below separates cited E8 mathematics from a proposed digest mapping. It is not receipt verification and adds no cryptographic security.

The E8 lattice attains the optimal sphere-packing density in eight dimensions. That mathematical result is cited prior art. A system may choose to map data into eight coordinates and compare them with a lattice, but such a mapping is a separate engineering artifact with its own correctness and security obligations.

Minimum-distance geometry can detect some perturbations relative to a fixed encoding. It does not authenticate an issuer, provide collision resistance, prove a receipt chain, or establish Byzantine-fault tolerance.

Executable local partition fixture

This standard-library example performs only the historical recipe's 256-bit-to-eight-word partition. It does not claim that the resulting point is in E8 and does not run a closest-point decoder.

def digest_words(digest_hex: str) -> list[int]:
    raw = bytes.fromhex(digest_hex)
    if len(raw) != 32:
        raise ValueError("expected one 256-bit digest")
    return [int.from_bytes(raw[offset : offset + 4], "big") for offset in range(0, 32, 4)]


fixture_digest = "d0361e9f2c8d8ac96a1cdab46a6f45de3ed697a9e767d7ccccce2d69b60ae73c"
words = digest_words(fixture_digest)
assert len(words) == 8
assert all(0 <= word < 2**32 for word in words)
print(words)

The output is a deterministic local representation of the fixture digest only. A canonical E8 scheme would still need to define coordinate scaling, coset selection, encoding and decoding, round-trip behavior, error thresholds, and versioned test vectors.

Promotion contract

Before an SZL E8 receipt claim can be called implemented, it needs:

1. a pinned encoder/decoder source revision and exact algorithm specification;
2. executable positive, negative, boundary, and round-trip vectors;
3. a binding from exact receipt bytes to the digest and from the digest to the lattice codeword;
4. a clear error model and an explicit statement of what the scheme cannot detect;
5. cryptographic receipt authentication evaluated separately; and
6. exact runtime request/response evidence if an endpoint is claimed.

Evidence state

Claim	Current status
E8 sphere-packing result	CITED_PRIOR_ART
Eight-word digest partition above	MODELED_LOCAL_FIXTURE
SZL E8 encoder or closest-point decoder	SOURCE_ARTIFACT_UNAVAILABLE
SZL E8 route and deployed response	UNAVAILABLE
Receipt authentication or adversarial security	NOT_ESTABLISHED

References: M. Viazovska, "The sphere packing problem in dimension 8," Annals of Mathematics 185 (2017), 991-1015; J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd edition, Springer (1999).

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Cited lattice geometry is not evidence of an SZL runtime, implementation, or security proof.