Pith Number

pith:ECSEJ7RG

pith:2014:ECSEJ7RG2WDMGOEXGB5MYPCDJZ

not attested not anchored not stored refs pending

The threshold for combs in random graphs

Eyal Lubetzky, Jeff Kahn, Nicholas Wormald

arxiv:1401.2710 v1 · 2014-01-13 · 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{ECSEJ7RG2WDMGOEXGB5MYPCDJZ}

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	2026-05-18T03:02:32.472492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20a444fe26d586c33897307acc3c434e4d361cd723e1d04fe85d24e6d34382a1

Aliases

arxiv: 1401.2710 · arxiv_version: 1401.2710v1 · doi: 10.48550/arxiv.1401.2710 · pith_short_12: ECSEJ7RG2WDM · pith_short_16: ECSEJ7RG2WDMGOEX · pith_short_8: ECSEJ7RG

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/ECSEJ7RG2WDMGOEXGB5MYPCDJZ \
  | 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: 20a444fe26d586c33897307acc3c434e4d361cd723e1d04fe85d24e6d34382a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "542b67f3828486d8bf0ab663f11cf26c0153e33f46e0d997ffc0364fa6c4fb02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-01-13T04:43:00Z",
    "title_canon_sha256": "9464e785c5c3f3c905b9b3fe458eb80ac9932c085a4e822c942592a49b10a48d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.2710",
    "kind": "arxiv",
    "version": 1
  }
}