E8 lattice receipt verification

Encode a 256-bit Khipu receipt digest onto the E8 lattice — the densest sphere packing in ℝ⁸ — and read its minimum-distance integrity geometry. Error-DETECTION only; not security.

Headline number: 1 GET → an on-lattice receipt reports min_squared_distance = 0; E8's minimal separation is exactly 2.

E8 is the unique densest lattice sphere packing in eight dimensions — a result that won Maryna Viazovska the 2022 Fields Medal (proof: Viazovska 2017, Annals of Mathematics 185:991–1015; later formalized in Lean at EPFL). This recipe maps a receipt digest onto E8 and uses the nearest-lattice-point distance as a structural integrity metric.

Honest posture — read this first. E8 gives error-DETECTION geometry only: the minimum distance between distinct lattice codepoints (squared distance 2) is a separation metric. It does NOT give adversarial-substitution resistance, collision resistance, tamper-proofing, or BFT safety — adversarial substitution is Conjecture 2 (Khipu BFT), NOT proven. The Viazovska proof is cited prior art, not produced here. This encoding adds zero to the locked-proven count (stays 8). Λ = Conjecture 1.

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Prerequisites

python3 -m pip install httpx   # plus stdlib hashlib for the offline check

Live base: https://a-11-oy.com.

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Quickstart (live, verified)

import httpx

BASE = "https://a-11-oy.com"

# GET verifies the current ledger head; POST verifies any digest you supply.
digest = "d0361e9f2c8d8ac96a1cdab46a6f45de3ed697a9e767d7ccccce2d69b60ae73c"
r = httpx.post(f"{BASE}/api/a11oy/v1/e8/verify", json={"digest": digest}, timeout=30).json()

print("coords (8 × 32-bit):", r["encoding"]["coords"])
print("on_lattice:", r["on_lattice"])                       # => True
print("min_squared_distance:", r["min_squared_distance"])   # => 0.0 ⇒ exact lattice member
print("E8 minimal separation:", r["e8_min_squared_distance"])  # => 2
print("algorithm:", r["algorithm"])   # Conway & Sloane closest-point (decode D8 and D8+glue)

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Full walkthrough

Step 1 — Encode the digest

A SHA3-256 digest is 64 hex chars. Split it into 8 × 8-hex groups; each becomes a 32-bit unsigned integer coordinate. That gives an 8-vector in ℝ⁸ — the input to the E8 closest-point search.

Step 2 — Find the nearest lattice point

E8 = D8 ∪ (D8 + glue), where D8 is the even-coordinate-sum integer lattice and the glue vector is (½,…,½). The Conway & Sloane algorithm decodes the input in both cosets and picks the nearer point. min_squared_distance is the squared Euclidean distance to that point.

# min_squared_distance == 0  ⇒  the encoded vector lies EXACTLY on E8 (a lattice member)
# min_squared_distance > 0   ⇒  off-lattice by that amount (a perturbation / corruption signal)
assert r["error_detection"]["is_member"] is True
print(r["error_detection"]["interpretation"])

Step 3 — Interpret it as error-detection geometry

The minimal squared distance between two distinct E8 points is 2. So any perturbation that moves a codepoint less than that separation is detectable as "off-lattice by δ." This is exactly sphere-packing error-detection — the same family of idea as a lattice code's minimum distance.

Step 4 — Do NOT overclaim

The endpoint ships a do_not_claim block. Honor it:

import json
print(json.dumps(r["do_not_claim"]["must_not_claim"], indent=2))
# - "E8 gives sphere-packing / minimum-distance error-DETECTION geometry ONLY."
# - "E8 does NOT give adversarial-substitution resistance, tamper-proofing, or BFT safety."
# - "This encoding adds ZERO to the locked-proven count (stays 8)."
# - "Λ = Conjecture 1, never a theorem."

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Honest scope table

Claim	Status
E8 is the densest packing in ℝ⁸	PROVEN — Viazovska 2017 (cited, formalized in Lean at EPFL)
Closest-point decode	REAL — Conway & Sloane deterministic algorithm
min_squared_distance integrity metric	REAL error-DETECTION geometry
Adversarial / collision / BFT resistance	NOT claimed — Conjecture 2, OPEN
Locked-proven count contribution	0 (stays 8 @ c7c0ba17)

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See also

• 01 — Verify a receipt end-to-end — the receipt the digest comes from.
• 08 — Receipt knot algebra — another structural integrity lens.
• 20 — Evidence pack for auditors — bundles ledger heads for offline audit.

Cite this recipe

@misc{szl_cookbook_e8_verify_2026,
  title        = {E8 lattice receipt verification (SZL Cookbook recipe 17)},
  author       = {{SZL Holdings}},
  year         = {2026},
  howpublished = {\url{https://github.com/szl-holdings/szl-cookbook/blob/main/recipes/17-e8-lattice-receipt-verification.md}},
  note         = {E8 error-DETECTION geometry; cites Viazovska 2017; NOT security. Λ = Conjecture 1; locked count stays 8.}
}

References: M. Viazovska, "The sphere packing problem in dimension 8," Annals of Mathematics 185 (2017) 991–1015. J. H. Conway & N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed., Springer 1999 (E8 closest-point algorithm).

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Doctrine v11 LOCKED — 749/14/163 — kernel c7c0ba17 · Λ = Conjecture 1 · SLSA L1 (honest)