Pith Number

pith:5UIM4B4Q

pith:2002:5UIM4B4QONFAEKDF4PQ2SEHNQ3

not attested not anchored not stored refs pending

The Antipode Construction for Sphere Packings

J.H. Conway, N.J.A. Sloane

arxiv:math/0207182 v1 · 2002-07-21 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UIM4B4QONFAEKDF4PQ2SEHNQ3}

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	2026-05-18T01:38:29.490862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed10ce0790734a022865e3e1a910ed86fb531254bb9c561c3b3be9aab8b32062

Aliases

arxiv: math/0207182 · arxiv_version: math/0207182v1 · doi: 10.48550/arxiv.math/0207182 · pith_short_12: 5UIM4B4QONFA · pith_short_16: 5UIM4B4QONFAEKDF · pith_short_8: 5UIM4B4Q

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/5UIM4B4QONFAEKDF4PQ2SEHNQ3 \
  | 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: ed10ce0790734a022865e3e1a910ed86fb531254bb9c561c3b3be9aab8b32062

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56b5966aadd702a6d274f228101a8534b11a905f9b7c0ae07bfc9a01e60ee631",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2002-07-21T02:50:52Z",
    "title_canon_sha256": "87442dbeb997df10642ed0dfa0b11eaccede56fc68880f3c1a4a8a4153ddd2c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0207182",
    "kind": "arxiv",
    "version": 1
  }
}