Pith Number

pith:44DKDZZN

pith:2015:44DKDZZNXER2V6GN3AUIDEMTLS

not attested not anchored not stored refs pending

The threshold for jigsaw percolation on random graphs

B\'ela Bollob\'as, Erik Slivken, Oliver Riordan, Paul Smith

arxiv:1503.05186 v3 · 2015-03-17 · 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{44DKDZZNXER2V6GN3AUIDEMTLS}

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	2026-05-18T00:41:42.279665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e706a1e72db923aaf8cdd8288191935c9dc5519a98b9cb39c2012f093feb6467

Aliases

arxiv: 1503.05186 · arxiv_version: 1503.05186v3 · doi: 10.48550/arxiv.1503.05186 · pith_short_12: 44DKDZZNXER2 · pith_short_16: 44DKDZZNXER2V6GN · pith_short_8: 44DKDZZN

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/44DKDZZNXER2V6GN3AUIDEMTLS \
  | 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: e706a1e72db923aaf8cdd8288191935c9dc5519a98b9cb39c2012f093feb6467

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b654d842ed39d17415b27255eadab04e68fee07ff7a3188c3e747ae0ec53e38a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-17T19:59:04Z",
    "title_canon_sha256": "5e1263f93d7b03d9327f69935985e9291d640b4bee807d43789aac0148773b77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.05186",
    "kind": "arxiv",
    "version": 3
  }
}