Pith Number

pith:5O3IQ6JF

pith:2014:5O3IQ6JFR3O6XC74UTISTSGTWH

not attested not anchored not stored refs pending

Amenability criterions and critical probabilities in percolation

Antoine Gournay

arxiv:1403.0909 v2 · 2014-03-04 · math.GR · 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{5O3IQ6JFR3O6XC74UTISTSGTWH}

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	2026-05-17T23:57:19.866876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebb68879258eddeb8bfca4d129c8d3b1e9bb17c42e5fe97364dcb34a6896ee33

Aliases

arxiv: 1403.0909 · arxiv_version: 1403.0909v2 · doi: 10.48550/arxiv.1403.0909 · pith_short_12: 5O3IQ6JFR3O6 · pith_short_16: 5O3IQ6JFR3O6XC74 · pith_short_8: 5O3IQ6JF

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/5O3IQ6JFR3O6XC74UTISTSGTWH \
  | 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: ebb68879258eddeb8bfca4d129c8d3b1e9bb17c42e5fe97364dcb34a6896ee33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24fca0664985ff14334153d27c9e0ad0ab0f4831f39463d691fd56ae1562b595",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-03-04T19:24:40Z",
    "title_canon_sha256": "4b765c8031b86004115f869ce0bb47bd85e57b42540e9a4d186c91bdc52143a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.0909",
    "kind": "arxiv",
    "version": 2
  }
}