Pith Number

pith:FSF7XQFN

pith:2012:FSF7XQFNBXDLYYC57RYKQUSIO6

not attested not anchored not stored refs pending

On the Maximum Density of Graphs with Good Edge-Labellings

Abbas Mehrabian, Dieter Mitsche, Pawe{\l} Pra{\l}at

arxiv:1211.2641 v1 · 2012-11-12 · 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{FSF7XQFNBXDLYYC57RYKQUSIO6}

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	2026-05-18T02:56:19.313830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c8bfbc0ad0dc6bc605dfc70a85248779e487003ce4d509c86a457d0f6d0e47a

Aliases

arxiv: 1211.2641 · arxiv_version: 1211.2641v1 · doi: 10.48550/arxiv.1211.2641 · pith_short_12: FSF7XQFNBXDL · pith_short_16: FSF7XQFNBXDLYYC5 · pith_short_8: FSF7XQFN

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/FSF7XQFNBXDLYYC57RYKQUSIO6 \
  | 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: 2c8bfbc0ad0dc6bc605dfc70a85248779e487003ce4d509c86a457d0f6d0e47a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6bcbffabea8b04216973ee54714f2255788a3e0e57fb35b55bf86aa35fc34cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-12T14:42:18Z",
    "title_canon_sha256": "d8675b481e12c52c403104dfd3798b97da3ab21e7263eed97d0edbed8b187349"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2641",
    "kind": "arxiv",
    "version": 1
  }
}