Pith Number

pith:GFFRAKQ7

pith:2013:GFFRAKQ7RT7BDLDEG7KSNA7ONA

not attested not anchored not stored refs pending

Sparse halves in dense triangle-free graphs

Liana Yepremyan, Sergey Norin

arxiv:1311.5818 v2 · 2013-11-22 · 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{GFFRAKQ7RT7BDLDEG7KSNA7ONA}

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	2026-05-18T02:27:29.472028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

314b102a1f8cfe11ac6437d52683ee680ea6616d774d13cd3c7fcbbc60d7e239

Aliases

arxiv: 1311.5818 · arxiv_version: 1311.5818v2 · doi: 10.48550/arxiv.1311.5818 · pith_short_12: GFFRAKQ7RT7B · pith_short_16: GFFRAKQ7RT7BDLDE · pith_short_8: GFFRAKQ7

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/GFFRAKQ7RT7BDLDEG7KSNA7ONA \
  | 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: 314b102a1f8cfe11ac6437d52683ee680ea6616d774d13cd3c7fcbbc60d7e239

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1513a7072c70125f6bf6ce25e2b4b8aa97c5363f82ba43fb82d1718713bfaa57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-22T17:13:00Z",
    "title_canon_sha256": "dea3783549b5669c1e7fe397728c4008d056f7ab52b7be4ab4efc9ea32cab2c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5818",
    "kind": "arxiv",
    "version": 2
  }
}