Pith Number

pith:EKY5ANCA

pith:2013:EKY5ANCAP6FU5N2MPET5KFTVV4

not attested not anchored not stored refs pending

An extension of the Hajnal-Szemeredi theorem to directed graphs

Andrzej Czygrinow, H.A. Kierstead, Louis DeBiasio, Theodore Molla

arxiv:1307.4803 v1 · 2013-07-17 · 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{EKY5ANCAP6FU5N2MPET5KFTVV4}

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	2026-05-18T03:18:08.633988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22b1d034407f8b4eb74c7927d51675af07fe0a50fca2b7fbb20d843c90be98b4

Aliases

arxiv: 1307.4803 · arxiv_version: 1307.4803v1 · doi: 10.48550/arxiv.1307.4803 · pith_short_12: EKY5ANCAP6FU · pith_short_16: EKY5ANCAP6FU5N2M · pith_short_8: EKY5ANCA

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/EKY5ANCAP6FU5N2MPET5KFTVV4 \
  | 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: 22b1d034407f8b4eb74c7927d51675af07fe0a50fca2b7fbb20d843c90be98b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfea46986b442657862b5b1225f87c3489986dec5a97538ca9750ec1b8a0666d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-17T22:46:10Z",
    "title_canon_sha256": "9ba34b5ceb278eb7fd497beb567aec8b7062a0ccfa88180233bad906e6734f9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4803",
    "kind": "arxiv",
    "version": 1
  }
}