Pith Number

pith:TZPH52UE

pith:2014:TZPH52UE3L4IYB7JCK2SSGFJHO

not attested not anchored not stored refs pending

Maximum order of triangle-free graphs with a given rank

A. Mohammadian, B. Tayfeh-Rezaie, E. Ghorbani

arxiv:1404.3553 v1 · 2014-04-14 · 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{TZPH52UE3L4IYB7JCK2SSGFJHO}

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	2026-05-18T02:54:14.991303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e5e7eea84daf88c07e912b52918a93b85f216b0121dda62e9dfc24483c74520

Aliases

arxiv: 1404.3553 · arxiv_version: 1404.3553v1 · doi: 10.48550/arxiv.1404.3553 · pith_short_12: TZPH52UE3L4I · pith_short_16: TZPH52UE3L4IYB7J · pith_short_8: TZPH52UE

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/TZPH52UE3L4IYB7JCK2SSGFJHO \
  | 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: 9e5e7eea84daf88c07e912b52918a93b85f216b0121dda62e9dfc24483c74520

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0954197ea741fadbb5ee9a4f75c9a98e14e290e94015b8e0214d610722b3afc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-04-14T12:24:32Z",
    "title_canon_sha256": "63543628ea33ad218a607c6ffff72f1f47931d7c2d7e92c2de0207ef807e4c4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.3553",
    "kind": "arxiv",
    "version": 1
  }
}