Pith Number

pith:GXUGXPN5

pith:2013:GXUGXPN5F3MYTSDQ3LVBD2BG5W

not attested not anchored not stored refs pending

The gaps between the sizes of large clusters in 2D critical percolation

Jacob van den Berg, Rene Conijn

arxiv:1310.2019 v1 · 2013-10-08 · 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{GXUGXPN5F3MYTSDQ3LVBD2BG5W}

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	2026-05-18T03:04:59.070630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35e86bbdbd2ed989c870daea11e826ed9311e0a37cf2212e4c95f461ca492c61

Aliases

arxiv: 1310.2019 · arxiv_version: 1310.2019v1 · doi: 10.48550/arxiv.1310.2019 · pith_short_12: GXUGXPN5F3MY · pith_short_16: GXUGXPN5F3MYTSDQ · pith_short_8: GXUGXPN5

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/GXUGXPN5F3MYTSDQ3LVBD2BG5W \
  | 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: 35e86bbdbd2ed989c870daea11e826ed9311e0a37cf2212e4c95f461ca492c61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0725913f4017cc30cb5d1d97f42c49cb0078ab8571074667b283b2f6fa427f38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-08T07:29:08Z",
    "title_canon_sha256": "7ff1df9da5e0580784e7c62dfb561ac98f74b25f83020172c6c5ce88591c0412"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.2019",
    "kind": "arxiv",
    "version": 1
  }
}