Pith Number

pith:5YUHSNNR

pith:2010:5YUHSNNRBIDMSAAFM5WRBTFTDX

not attested not anchored not stored refs pending

Bootstrap percolation on the random graph $G_{n,p}$

Svante Janson, Tatyana Turova, Thomas Vallier, Tomasz {\L}uczak

arxiv:1012.3535 v2 · 2010-12-16 · 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{5YUHSNNRBIDMSAAFM5WRBTFTDX}

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	2026-05-18T03:42:46.320557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee287935b10a06c90005676d10ccb31df3b95263fc559049ab104ecc48e433ae

Aliases

arxiv: 1012.3535 · arxiv_version: 1012.3535v2 · doi: 10.48550/arxiv.1012.3535 · pith_short_12: 5YUHSNNRBIDM · pith_short_16: 5YUHSNNRBIDMSAAF · pith_short_8: 5YUHSNNR

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/5YUHSNNRBIDMSAAFM5WRBTFTDX \
  | 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: ee287935b10a06c90005676d10ccb31df3b95263fc559049ab104ecc48e433ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e65a292cc558ab54526afec9a634a5447ae9d93a23cbaa62c90adebfd416bfd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-16T09:06:12Z",
    "title_canon_sha256": "4feae6dd1724bdd394ce04b2a320ae35b1e6f916cad849d9c06f25a18c3aa48b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3535",
    "kind": "arxiv",
    "version": 2
  }
}