Pith Number

pith:W4K5ZXVJ

pith:2026:W4K5ZXVJHC43ODZSNDG4MKV3YY

not attested not anchored not stored refs pending

Progress in Formalizing Sphere Packing in Dimension 8

Auguste Poiroux, Bhavik Mehta, Christopher Birkbeck, Ho Kiu Gareth Ma, Maryna Viazovska, Seewoo Lee, Sidharth Hariharan

The sphere packing problem in eight dimensions has been formally verified in Lean with AI assistance.

arxiv:2604.23468 v3 · 2026-04-25 · math.MG · cs.AI · cs.LO · math.NT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4K5ZXVJHC43ODZSNDG4MKV3YY}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'.

C2weakest assumption

That the combination of human-written Lean code and the Gauss AI model correctly captured every detail of Viazovska's original proof without introducing or overlooking logical gaps.

C3one line summary

The sphere packing problem in dimension 8 has been formally verified in the Lean theorem prover, with the final stages completed by the AI model Gauss.

Cited by

2 papers in Pith

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$L^2$-Stability for STFT phase retrieval

Receipt and verification

First computed	2026-06-01T02:03:41.451169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b715dcdea938b9b70f3268cdc62abbc630925ff44e05cf4a1ff5e697a858b1b8

Aliases

arxiv: 2604.23468 · arxiv_version: 2604.23468v3 · doi: 10.48550/arxiv.2604.23468 · pith_short_12: W4K5ZXVJHC43 · pith_short_16: W4K5ZXVJHC43ODZS · pith_short_8: W4K5ZXVJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W4K5ZXVJHC43ODZSNDG4MKV3YY \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b715dcdea938b9b70f3268cdc62abbc630925ff44e05cf4a1ff5e697a858b1b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22e53e41204d1fc70837f90acde17580449e0bba8f2cb552657e70779c2395d1",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LO",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-04-25T23:27:10Z",
    "title_canon_sha256": "d18d0b16e2164e1e10341059708c33204414571a8fa3f1cc08a51139a012338d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.23468",
    "kind": "arxiv",
    "version": 3
  }
}