Pith Number

pith:TLFOS2FG

pith:2010:TLFOS2FGEOZCLGWR34ZBBJUPK7

not attested not anchored not stored refs pending

A proof of factorization formula for critical percolation

Dmitry Beliaev, Konstantin Izyurov

arxiv:1011.5822 v3 · 2010-11-26 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TLFOS2FGEOZCLGWR34ZBBJUPK7}

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	2026-05-18T04:10:34.487296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e

Aliases

arxiv: 1011.5822 · arxiv_version: 1011.5822v3 · doi: 10.48550/arxiv.1011.5822 · pith_short_12: TLFOS2FGEOZC · pith_short_16: TLFOS2FGEOZCLGWR · pith_short_8: TLFOS2FG

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/TLFOS2FGEOZCLGWR34ZBBJUPK7 \
  | 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: 9acae968a623b2259ad1df3210a68f57c0fa2e53708588041fcac0ab3b4e492e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e71100e45a91259e448d497555dd25a3dfd1675883a9b9a84f73ea3befb13935",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-26T15:27:34Z",
    "title_canon_sha256": "a50b5424f3479381ef1cd3a758459df5321a75fcbec5dc538cc308de78039ddc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5822",
    "kind": "arxiv",
    "version": 3
  }
}