Pith Number

pith:FRASENSD

pith:2013:FRASENSD2KXMYIBGPGFTYLLTWW

not attested not anchored not stored refs pending

Subcritical $\mathcal{U}$-bootstrap percolation models have non-trivial phase transitions

B\'ela Bollob\'as, Micha{\l} Przykucki, Paul Balister, Paul Smith

arxiv:1311.5883 v2 · 2013-11-22 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FRASENSD2KXMYIBGPGFTYLLTWW}

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	2026-05-18T02:43:16.420282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c41223643d2aecc2026798b3c2d73b586e6584aa00bfb2d3e9666a874dbce98

Aliases

arxiv: 1311.5883 · arxiv_version: 1311.5883v2 · doi: 10.48550/arxiv.1311.5883 · pith_short_12: FRASENSD2KXM · pith_short_16: FRASENSD2KXMYIBG · pith_short_8: FRASENSD

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/FRASENSD2KXMYIBGPGFTYLLTWW \
  | 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: 2c41223643d2aecc2026798b3c2d73b586e6584aa00bfb2d3e9666a874dbce98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4eff2795c717caa72020aad287eff3f7bdbb8da276fd41463c344e3c3c0cafe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-22T20:55:06Z",
    "title_canon_sha256": "421841baf43bd173659faa55229434acba1fda42ff7c32da09bf030f1d5bab61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5883",
    "kind": "arxiv",
    "version": 2
  }
}