Pith Number

pith:VV7MSTPB

pith:2009:VV7MSTPBISARHUY3I4NDO6SBLZ

not attested not anchored not stored refs pending

The growth of the infinite long-range percolation cluster

Pieter Trapman

arxiv:0901.0661 v3 · 2009-01-06 · 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{VV7MSTPBISARHUY3I4NDO6SBLZ}

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	2026-05-18T04:32:00.133231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad7ec94de1448113d31b471a377a415e697ca42ca6fa13bcb8ae951da00e3cfd

Aliases

arxiv: 0901.0661 · arxiv_version: 0901.0661v3 · doi: 10.48550/arxiv.0901.0661 · pith_short_12: VV7MSTPBISAR · pith_short_16: VV7MSTPBISARHUY3 · pith_short_8: VV7MSTPB

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/VV7MSTPBISARHUY3I4NDO6SBLZ \
  | 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: ad7ec94de1448113d31b471a377a415e697ca42ca6fa13bcb8ae951da00e3cfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51d0e41b73f8a95e974231595df020c9e6a208f68e22e9483f951092ecd05cc9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-01-06T15:35:59Z",
    "title_canon_sha256": "586d69a94750536374cf5da8cdae3c4cd163c71fb546f513c5786f6f6c866aba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.0661",
    "kind": "arxiv",
    "version": 3
  }
}