Pith Number

pith:JKOTZTC5

pith:2010:JKOTZTC5NZZS4SNMPOE4IDOX3A

not attested not anchored not stored refs pending

Dense graphs with a large triangle cover have a large triangle packing

Raphael Yuster

arxiv:1009.0353 v1 · 2010-09-02 · 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{JKOTZTC5NZZS4SNMPOE4IDOX3A}

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	2026-05-18T04:41:26.888449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a9d3ccc5d6e732e49ac7b89c40dd7d80c6598ceddefd3464193306dcece0659

Aliases

arxiv: 1009.0353 · arxiv_version: 1009.0353v1 · doi: 10.48550/arxiv.1009.0353 · pith_short_12: JKOTZTC5NZZS · pith_short_16: JKOTZTC5NZZS4SNM · pith_short_8: JKOTZTC5

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/JKOTZTC5NZZS4SNMPOE4IDOX3A \
  | 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: 4a9d3ccc5d6e732e49ac7b89c40dd7d80c6598ceddefd3464193306dcece0659

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "298b8be2d4d743a4ab91142e8a2497b78e3072b362a0fe25a3a805c69e6c926b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-02T08:49:32Z",
    "title_canon_sha256": "bdb36f9eb3ba5ddac463703349fd5798307cc1dcc6e2315fc8faee3c78382ed3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0353",
    "kind": "arxiv",
    "version": 1
  }
}