Pith Number

pith:56C3GLR5

pith:2014:56C3GLR5AQJNJQH2MKA2AEMTY7

not attested not anchored not stored refs pending

Cycles in triangle-free graphs of large chromatic number

Alexandr Kostochka, Benny Sudakov, Jacques Verstraete

arxiv:1404.4544 v1 · 2014-04-17 · 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{56C3GLR5AQJNJQH2MKA2AEMTY7}

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	2026-05-18T02:54:04.040752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef85b32e3d0412d4c0fa6281a01193c7e4a4e2b3907e095dcba1bfafcbdea8ad

Aliases

arxiv: 1404.4544 · arxiv_version: 1404.4544v1 · doi: 10.48550/arxiv.1404.4544 · pith_short_12: 56C3GLR5AQJN · pith_short_16: 56C3GLR5AQJNJQH2 · pith_short_8: 56C3GLR5

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/56C3GLR5AQJNJQH2MKA2AEMTY7 \
  | 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: ef85b32e3d0412d4c0fa6281a01193c7e4a4e2b3907e095dcba1bfafcbdea8ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f44d54aab67fe4b058eebf6c70a4a7f4dc2567ebc163276398fd4db17b436944",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-04-17T14:42:44Z",
    "title_canon_sha256": "5bfdac43abee560603313c922796632b4b5201b78461cb7795af89ce68a1e926"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.4544",
    "kind": "arxiv",
    "version": 1
  }
}