Pith Number

pith:X66IX3D7

pith:2010:X66IX3D7SPUU4ENS3SVTVRXXAA

not attested not anchored not stored refs pending

A sharper threshold for bootstrap percolation in two dimensions

Alexander E. Holroyd, Janko Gravner, Robert Morris

arxiv:1002.3881 v2 · 2010-02-20 · 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{X66IX3D7SPUU4ENS3SVTVRXXAA}

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	2026-05-18T04:32:35.278490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfbc8bec7f93e94e11b2dcab3ac6f700000cf8cf26f0992d468fba756b9e66d8

Aliases

arxiv: 1002.3881 · arxiv_version: 1002.3881v2 · doi: 10.48550/arxiv.1002.3881 · pith_short_12: X66IX3D7SPUU · pith_short_16: X66IX3D7SPUU4ENS · pith_short_8: X66IX3D7

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/X66IX3D7SPUU4ENS3SVTVRXXAA \
  | 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: bfbc8bec7f93e94e11b2dcab3ac6f700000cf8cf26f0992d468fba756b9e66d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88411dbbe623360e3ea7143e9f80f2ad9bf9c28dd8419daae1c6cdecf7b973d2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-02-20T13:07:24Z",
    "title_canon_sha256": "8827e0afa9f1698ddd1daeeb16e22343be15baffd48b802cf4da144d98cf5f61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.3881",
    "kind": "arxiv",
    "version": 2
  }
}