Pith Number

pith:OKFEZZZY

pith:2015:OKFEZZZY4FW4ZO2OYADIIL3XEG

not attested not anchored not stored refs pending

Exceptional rotations of random graphs: a VC theory

Gabor Lugosi, Louigi Addario-Berry, Luc Devroye, Roberto Imbuzeiro Oliveira, S\'ebastien Bubeck, Shankar Bhamidi

arxiv:1506.02811 v1 · 2015-06-09 · math.PR · math.CO · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OKFEZZZY4FW4ZO2OYADIIL3XEG}

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	2026-05-18T01:55:40.849359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

728a4ce738e16dccbb4ec006842f77218ab7dfe9190ca90146f53136e919e854

Aliases

arxiv: 1506.02811 · arxiv_version: 1506.02811v1 · doi: 10.48550/arxiv.1506.02811 · pith_short_12: OKFEZZZY4FW4 · pith_short_16: OKFEZZZY4FW4ZO2O · pith_short_8: OKFEZZZY

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/OKFEZZZY4FW4ZO2OYADIIL3XEG \
  | 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: 728a4ce738e16dccbb4ec006842f77218ab7dfe9190ca90146f53136e919e854

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24c340b5edc4353308727a77e79737663950edb50823dcf3c7a15fa0c4bdf9aa",
    "cross_cats_sorted": [
      "math.CO",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-09T07:50:16Z",
    "title_canon_sha256": "0c6c4f3434c06e933860b59c0bcd03a4fd46bfc431525cb1307a2432af2cd8e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.02811",
    "kind": "arxiv",
    "version": 1
  }
}