Pith Number

pith:AZCKUDWI

pith:2011:AZCKUDWIKB4FXAKQO6JGYN3NLN

not attested not anchored not stored refs pending

On a sparse random graph with minimum degree {three}: Likely Posa's sets are large

Alan Frieze, Boris Pittel

arxiv:1107.4944 v1 · 2011-07-25 · 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{AZCKUDWIKB4FXAKQO6JGYN3NLN}

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	2026-05-18T04:16:54.198666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0644aa0ec850785b815077926c376d5b5e7f495602b96e52315cec359cf01c82

Aliases

arxiv: 1107.4944 · arxiv_version: 1107.4944v1 · doi: 10.48550/arxiv.1107.4944 · pith_short_12: AZCKUDWIKB4F · pith_short_16: AZCKUDWIKB4FXAKQ · pith_short_8: AZCKUDWI

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/AZCKUDWIKB4FXAKQO6JGYN3NLN \
  | 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: 0644aa0ec850785b815077926c376d5b5e7f495602b96e52315cec359cf01c82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "449ac40dec5233f604d5f10244e5da045ed29d1300829c44f0d83888c5d50809",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-07-25T13:25:02Z",
    "title_canon_sha256": "b966e1062fad6f80507c0c652e44523fd8c17c138a2d00f941f36202c2ed4fdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4944",
    "kind": "arxiv",
    "version": 1
  }
}