Pith Number

pith:L2HVMFNC

pith:2015:L2HVMFNCLRHRDLVRCNX6ZYNXW5

not attested not anchored not stored refs pending

Crossing probabilities for critical Bernoulli percolation on slabs

Artem Sapozhnikov, Deepan Basu

arxiv:1512.05178 v2 · 2015-12-16 · 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{L2HVMFNCLRHRDLVRCNX6ZYNXW5}

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	2026-05-18T01:18:39.045777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e8f5615a25c4f11aeb1136fece1b7b77d2561af423d9f095a2d498a270e3354

Aliases

arxiv: 1512.05178 · arxiv_version: 1512.05178v2 · doi: 10.48550/arxiv.1512.05178 · pith_short_12: L2HVMFNCLRHR · pith_short_16: L2HVMFNCLRHRDLVR · pith_short_8: L2HVMFNC

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/L2HVMFNCLRHRDLVRCNX6ZYNXW5 \
  | 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: 5e8f5615a25c4f11aeb1136fece1b7b77d2561af423d9f095a2d498a270e3354

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1878ce19f890529fe7a09a5e381271e4b752d91043e449fedd39921390e7286",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-16T14:13:38Z",
    "title_canon_sha256": "bf8a6f1f9814d8d2a53b8be921ee5b8258b9a2f7636f01e44be5c3ea4dead347"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05178",
    "kind": "arxiv",
    "version": 2
  }
}