Pith Number

pith:Y2C6DFYB

pith:2012:Y2C6DFYBWQAXRHSLBAMNRUB56F

not attested not anchored not stored refs pending

Long paths and cycles in random subgraphs of graphs with large minimum degree

Benny Sudakov, Choongbum Lee, Michael Krivelevich

arxiv:1207.0312 v3 · 2012-07-02 · 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{Y2C6DFYBWQAXRHSLBAMNRUB56F}

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	2026-05-18T03:24:54.246153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c685e19701b401789e4b0818d8d03df1415f0098f9cf7eae298469d894364b91

Aliases

arxiv: 1207.0312 · arxiv_version: 1207.0312v3 · doi: 10.48550/arxiv.1207.0312 · pith_short_12: Y2C6DFYBWQAX · pith_short_16: Y2C6DFYBWQAXRHSL · pith_short_8: Y2C6DFYB

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/Y2C6DFYBWQAXRHSLBAMNRUB56F \
  | 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: c685e19701b401789e4b0818d8d03df1415f0098f9cf7eae298469d894364b91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a9444418efe1900b9aeb83249e822fe5a59af56a6d78aac2715bcf198f7c76b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-02T09:15:38Z",
    "title_canon_sha256": "2e2b37d5f5f340e798c444f4ff8ff810319b68a56dad86d4c6f1a22b67b79469"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0312",
    "kind": "arxiv",
    "version": 3
  }
}