Pith Number

pith:C5I2RRJD

pith:2010:C5I2RRJDIJXUGEQPKUDBG5D3GL

not attested not anchored not stored refs pending

The sharp threshold for bootstrap percolation in all dimensions

B\'ela Bollob\'as, Hugo Duminil-Copin, J\'ozsef Balogh, Robert Morris

arxiv:1010.3326 v2 · 2010-10-16 · math.PR · math-ph · math.CO · math.DS · 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{C5I2RRJDIJXUGEQPKUDBG5D3GL}

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	2026-05-18T04:27:58.694741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1751a8c523426f43120f550613747b32e9c15a97fc426eb5fb18a528ca5043fc

Aliases

arxiv: 1010.3326 · arxiv_version: 1010.3326v2 · doi: 10.48550/arxiv.1010.3326 · pith_short_12: C5I2RRJDIJXU · pith_short_16: C5I2RRJDIJXUGEQP · pith_short_8: C5I2RRJD

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/C5I2RRJDIJXUGEQPKUDBG5D3GL \
  | 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: 1751a8c523426f43120f550613747b32e9c15a97fc426eb5fb18a528ca5043fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "926780e0f5e275bf61cc3f6eed8fe894e15e1ab59967953dc1358e345ab669b2",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-16T06:22:53Z",
    "title_canon_sha256": "ba790195c12e01be35cdab3c92cdc81e0f311090ac4489d68dc203bc35eb8a56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3326",
    "kind": "arxiv",
    "version": 2
  }
}