Pith Number

pith:UPYF5XYK

pith:2003:UPYF5XYKDT3DXUN4JUWD4GJKY3

not attested not anchored not stored refs pending

The kissing number in four dimensions

Oleg R. Musin

arxiv:math/0309430 v3 · 2003-09-26 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UPYF5XYKDT3DXUN4JUWD4GJKY3}

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.

Cited by

1 paper in Pith

Variations on five-dimensional sphere packings

Receipt and verification

First computed	2026-07-04T15:13:23.708768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3f05edf0a1cf63bd1bc4d2c3e192ac6d9a4d24fb4967fd61185b068021d759f

Aliases

arxiv: math/0309430 · arxiv_version: math/0309430v3 · doi: 10.48550/arxiv.math/0309430 · pith_short_12: UPYF5XYKDT3D · pith_short_16: UPYF5XYKDT3DXUN4 · pith_short_8: UPYF5XYK

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/UPYF5XYKDT3DXUN4JUWD4GJKY3 \
  | 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: a3f05edf0a1cf63bd1bc4d2c3e192ac6d9a4d24fb4967fd61185b068021d759f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06ea63780c6ce27f27153fb678a7b67f76e91fb51f287778f59c6b725ad9db2f",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2003-09-26T10:02:18Z",
    "title_canon_sha256": "3022edfdb93690f61d89c37debb7afc1d19cb6db0f11c9c7cd540530a2c4fab5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309430",
    "kind": "arxiv",
    "version": 3
  }
}