Pith Number

pith:4TKP7Y2Q

pith:2012:4TKP7Y2QNREP5FLYL3FCDYIIIG

not attested not anchored not stored refs pending

Scaling limit for the random walk on the largest connected component of the critical random graph

David A. Croydon

arxiv:1210.5865 v1 · 2012-10-22 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4TKP7Y2QNREP5FLYL3FCDYIIIG}

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	2026-05-18T03:42:34.872239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4d4ffe3506c48fe95785eca21e10841853e66dc1fac8af9d1ca24c892c790cb

Aliases

arxiv: 1210.5865 · arxiv_version: 1210.5865v1 · doi: 10.48550/arxiv.1210.5865 · pith_short_12: 4TKP7Y2QNREP · pith_short_16: 4TKP7Y2QNREP5FLY · pith_short_8: 4TKP7Y2Q

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/4TKP7Y2QNREP5FLYL3FCDYIIIG \
  | 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: e4d4ffe3506c48fe95785eca21e10841853e66dc1fac8af9d1ca24c892c790cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4d34f69c7845a9df910e538297e976ca5c6d59df409e32c120048840b9637d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-22T10:49:55Z",
    "title_canon_sha256": "d32054d6fa710e8feb9d6f3384d99b04cd1d5ee6e0fa55d82d76f54c07c42ee7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5865",
    "kind": "arxiv",
    "version": 1
  }
}