Pith Number

pith:AQXEXSOR

pith:2012:AQXEXSORN5JZFLEOPNFS6GOKIO

not attested not anchored not stored refs pending

On the densities of cliques and independent sets in graphs

Benny Sudakov, Hao Huang, Humberto Naves, Nati Linial, Yuval Peled

arxiv:1211.4532 v2 · 2012-11-19 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AQXEXSORN5JZFLEOPNFS6GOKIO}

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	2026-05-18T03:05:18.761249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

042e4bc9d16f5392ac8e7b4b2f19ca43897b5dd727a55c8f201d85a5b158928e

Aliases

arxiv: 1211.4532 · arxiv_version: 1211.4532v2 · doi: 10.48550/arxiv.1211.4532 · pith_short_12: AQXEXSORN5JZ · pith_short_16: AQXEXSORN5JZFLEO · pith_short_8: AQXEXSOR

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/AQXEXSORN5JZFLEOPNFS6GOKIO \
  | 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: 042e4bc9d16f5392ac8e7b4b2f19ca43897b5dd727a55c8f201d85a5b158928e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "441acaa83acfc3c4d36e1e88615788dba9c28097f010ff28a9894b3755b88716",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-19T18:44:35Z",
    "title_canon_sha256": "9a387e4433c2de4b37b1fc6c63852c69ed2e01cf1b0ebd4a8d082f6a6bd8b2e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4532",
    "kind": "arxiv",
    "version": 2
  }
}