Pith Number

pith:GN2H3V7Z

pith:2019:GN2H3V7ZNCZDYBDMVNMNYFMEL4

not attested not anchored not stored refs pending

The maximum length of $K_r$-Bootstrap Percolation

Alexey Pokrovskiy, Gal Kronenberg, J\'ozsef Balogh, Tibor Szab\'o

arxiv:1907.04559 v1 · 2019-07-10 · 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{GN2H3V7ZNCZDYBDMVNMNYFMEL4}

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.

Cited by

2 papers in Pith

Upper bounds on the running time of bootstrap percolation

Bootstrap percolation of extension hypergraphs

Receipt and verification

First computed	2026-05-17T23:40:59.885826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33747dd7f968b23c046cab58dc15845f35e5793807527b29dec35bc547ef082b

Aliases

arxiv: 1907.04559 · arxiv_version: 1907.04559v1 · doi: 10.48550/arxiv.1907.04559 · pith_short_12: GN2H3V7ZNCZD · pith_short_16: GN2H3V7ZNCZDYBDM · pith_short_8: GN2H3V7Z

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/GN2H3V7ZNCZDYBDMVNMNYFMEL4 \
  | 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: 33747dd7f968b23c046cab58dc15845f35e5793807527b29dec35bc547ef082b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2bd8a040908df7426bec6b26c1b24f15e10a3293906738a24d3a22d19f1d3ec5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-07-10T08:05:49Z",
    "title_canon_sha256": "09428d17f5b2ad0c7e22de0af7fb72a4fa9caec493c3b1584ed270b8b5aacf17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.04559",
    "kind": "arxiv",
    "version": 1
  }
}