Pith Number

pith:D7OSIYT3

pith:2016:D7OSIYT3TXHBFIKGEMIHRZPC7P

not attested not anchored not stored refs pending

On the critical probability in percolation

Lutz Warnke, Svante Janson

arxiv:1611.08549 v1 · 2016-11-25 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D7OSIYT3TXHBFIKGEMIHRZPC7P}

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	2026-05-17T23:59:44.016592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fdd24627b9dce12a146231078e5e2fbf2aa4a4ab184567fa6688188d9230313

Aliases

arxiv: 1611.08549 · arxiv_version: 1611.08549v1 · doi: 10.48550/arxiv.1611.08549 · pith_short_12: D7OSIYT3TXHB · pith_short_16: D7OSIYT3TXHBFIKG · pith_short_8: D7OSIYT3

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/D7OSIYT3TXHBFIKGEMIHRZPC7P \
  | 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: 1fdd24627b9dce12a146231078e5e2fbf2aa4a4ab184567fa6688188d9230313

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b3ea77446da645812f001db0bb683abee20c88d9486b3834720b99e28358cf8",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-25T18:50:54Z",
    "title_canon_sha256": "85f168bae5505de2cd951fd1351ebc01aa88f3e142e97c9a449f7671fa5189a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08549",
    "kind": "arxiv",
    "version": 1
  }
}