Pith Number

pith:VH43TBW2

pith:2010:VH43TBW2D3K4DVO42OVCKZ4QYF

not attested not anchored not stored refs pending

Long cycles in subgraphs of (pseudo)random directed graphs

Benny Sudakov, Ido Ben-Eliezer, Michael Krivelevich

arxiv:1009.3721 v1 · 2010-09-20 · 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{VH43TBW2D3K4DVO42OVCKZ4QYF}

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	2026-05-18T04:40:43.996669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9f9b986da1ed5c1d5dcd3aa256790c17d31c8bb440a40c8fa70544715b749c1

Aliases

arxiv: 1009.3721 · arxiv_version: 1009.3721v1 · doi: 10.48550/arxiv.1009.3721 · pith_short_12: VH43TBW2D3K4 · pith_short_16: VH43TBW2D3K4DVO4 · pith_short_8: VH43TBW2

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/VH43TBW2D3K4DVO42OVCKZ4QYF \
  | 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: a9f9b986da1ed5c1d5dcd3aa256790c17d31c8bb440a40c8fa70544715b749c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8064b2dd27b4118bd338d126755bb3cb517b9cf9bd6df7cd10d5c560c8be4181",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-20T07:47:18Z",
    "title_canon_sha256": "2edf66b4f33af8742c907e28066cd28aa3d2e2efffc8b0f96332f503ce54bee4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3721",
    "kind": "arxiv",
    "version": 1
  }
}