Pith Number

pith:3GPD5EZA

pith:2010:3GPD5EZARRNF7AUXNCRKEBPI34

not attested not anchored not stored refs pending

(Very) short proof of Rayleigh's Theorem (and extensions)

Olivier Bernardi (MIT)

arxiv:1007.4870 v3 · 2010-07-28 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3GPD5EZARRNF7AUXNCRKEBPI34}

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	2026-05-18T03:53:52.552876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d99e3e93208c5a5f829768a2a205e8df15d6e1284f62c1d4fe316b88f2257132

Aliases

arxiv: 1007.4870 · arxiv_version: 1007.4870v3 · doi: 10.48550/arxiv.1007.4870 · pith_short_12: 3GPD5EZARRNF · pith_short_16: 3GPD5EZARRNF7AUX · pith_short_8: 3GPD5EZA

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/3GPD5EZARRNF7AUXNCRKEBPI34 \
  | 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: d99e3e93208c5a5f829768a2a205e8df15d6e1284f62c1d4fe316b88f2257132

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04a2eae64fc2db6ade2d39b99af9238f322bfc627982f29536f8253bd38ec5c2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-28T04:29:33Z",
    "title_canon_sha256": "ded27db782ff81d3b495f0f6f47d03a34f9ad9d9aad46257c7f31d08b163a4f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4870",
    "kind": "arxiv",
    "version": 3
  }
}