Pith Number

pith:T2ZCC5XY

pith:2014:T2ZCC5XYPUIH52EG46CFH3EUCA

not attested not anchored not stored refs pending

The number of the maximal triangle-free graphs

J\'ozsef Balogh, \v{S}\'arka Pet\v{r}\'i\v{c}kov\'a

arxiv:1409.8123 v1 · 2014-09-29 · 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{T2ZCC5XYPUIH52EG46CFH3EUCA}

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	2026-05-18T02:41:33.666544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9eb22176f87d107ee886e78453ec94101f716db339103816ea3f6b709b2e79d2

Aliases

arxiv: 1409.8123 · arxiv_version: 1409.8123v1 · doi: 10.48550/arxiv.1409.8123 · pith_short_12: T2ZCC5XYPUIH · pith_short_16: T2ZCC5XYPUIH52EG · pith_short_8: T2ZCC5XY

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/T2ZCC5XYPUIH52EG46CFH3EUCA \
  | 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: 9eb22176f87d107ee886e78453ec94101f716db339103816ea3f6b709b2e79d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2607053e5ee4a18a9cd8085f95e829c97a2f10e9177bbe8dc39e15223cd95f9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-29T13:48:52Z",
    "title_canon_sha256": "2b59467452496ed91e55309532f71bb8b0e135acecec74c0adeeace7e769e162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.8123",
    "kind": "arxiv",
    "version": 1
  }
}