Pith Number

pith:Z52LRDPV

pith:2015:Z52LRDPV2S5Z6CISOYX7JUHM53

not attested not anchored not stored refs pending

Birthday Inequalities, Repulsion, and Hard Spheres

Will Perkins

arxiv:1506.02700 v2 · 2015-06-03 · math.PR · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z52LRDPV2S5Z6CISOYX7JUHM53}

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	2026-05-18T01:25:55.239866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf74b88df5d4bb9f0912762ff4d0eceeed7c9a97b865381ed97c0daa75e09675

Aliases

arxiv: 1506.02700 · arxiv_version: 1506.02700v2 · doi: 10.48550/arxiv.1506.02700 · pith_short_12: Z52LRDPV2S5Z · pith_short_16: Z52LRDPV2S5Z6CIS · pith_short_8: Z52LRDPV

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/Z52LRDPV2S5Z6CISOYX7JUHM53 \
  | 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: cf74b88df5d4bb9f0912762ff4d0eceeed7c9a97b865381ed97c0daa75e09675

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd0fe9ce7e7c31c3806eb3d241f1968d42099ee89a4583dd79d39c0869e7e0cc",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-03T18:37:47Z",
    "title_canon_sha256": "2f792528d9325453d21386d158fcc605b87eca1bad2990eee82b1ed916792ee2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.02700",
    "kind": "arxiv",
    "version": 2
  }
}