Pith Number

pith:ZLITMSUU

pith:2010:ZLITMSUUVWXTLR6YMZLIVBQEF2

not attested not anchored not stored refs pending

Densest local sphere-packing diversity: General concepts and application to two dimensions

A. B. Hopkins, F. H. Stillinger, S. Torquato

arxiv:1002.0604 v1 · 2010-02-02 · cond-mat.stat-mech · cond-mat.soft · 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{ZLITMSUUVWXTLR6YMZLIVBQEF2}

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	2026-05-18T02:09:20.661601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cad1364a94adaf35c7d866568a86042e990cf08e149f6427be6761d0efef0328

Aliases

arxiv: 1002.0604 · arxiv_version: 1002.0604v1 · doi: 10.48550/arxiv.1002.0604 · pith_short_12: ZLITMSUUVWXT · pith_short_16: ZLITMSUUVWXTLR6Y · pith_short_8: ZLITMSUU

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/ZLITMSUUVWXTLR6YMZLIVBQEF2 \
  | 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: cad1364a94adaf35c7d866568a86042e990cf08e149f6427be6761d0efef0328

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc0b2a53decd96581311dc009d89470ba66fe6f6fc2249c54340f0915533a256",
    "cross_cats_sorted": [
      "cond-mat.soft",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-02-02T21:57:55Z",
    "title_canon_sha256": "25b93e15e17d7a01c1d3341a5a6110a60064a53ece9da119591bb3234e094827"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.0604",
    "kind": "arxiv",
    "version": 1
  }
}