Pith Number

pith:ZB4UPOKS

pith:2009:ZB4UPOKSJECTPWFLZJPTMGZXXB

not attested not anchored not stored refs pending

The contact polytope of the Leech lattice (complete version)

Achill Schuermann, Frank Vallentin, Mathieu Dutour Sikiric

arxiv:0906.1427 v2 · 2009-06-08 · math.MG · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZB4UPOKSJECTPWFLZJPTMGZXXB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T04:39:39.214746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c87947b952490537d8abca5f361b37b87fe5ed8dd24eb7622d6cdde85b9e5afa

Aliases

arxiv: 0906.1427 · arxiv_version: 0906.1427v2 · doi: 10.48550/arxiv.0906.1427 · pith_short_12: ZB4UPOKSJECT · pith_short_16: ZB4UPOKSJECTPWFL · pith_short_8: ZB4UPOKS

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/ZB4UPOKSJECTPWFLZJPTMGZXXB \
  | 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: c87947b952490537d8abca5f361b37b87fe5ed8dd24eb7622d6cdde85b9e5afa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bb66db88a1060109fe149745af98053e406ffc6b7c9b34ffd2691b47a4cce40",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2009-06-08T15:09:03Z",
    "title_canon_sha256": "83eef37cd1ef20aca0cb52c3dc9e550618ca0fef79c1fcb862aedde659028d2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1427",
    "kind": "arxiv",
    "version": 2
  }
}