Pith Number

pith:K42PB6WR

pith:2013:K42PB6WRN2CIHDZJY6ORQP5BNW

not attested not anchored not stored refs pending

Contagious Sets in Expanders

Amin Coja-Oghlan, Daniel Reichman, Michael Krivelevich, Uriel Feige

arxiv:1306.2465 v2 · 2013-06-11 · cs.DM · 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{K42PB6WRN2CIHDZJY6ORQP5BNW}

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	2026-05-18T02:59:44.497544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5734f0fad16e84838f29c79d183fa16da14ed183ca4292be8770942d69773075

Aliases

arxiv: 1306.2465 · arxiv_version: 1306.2465v2 · doi: 10.48550/arxiv.1306.2465 · pith_short_12: K42PB6WRN2CI · pith_short_16: K42PB6WRN2CIHDZJ · pith_short_8: K42PB6WR

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/K42PB6WRN2CIHDZJY6ORQP5BNW \
  | 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: 5734f0fad16e84838f29c79d183fa16da14ed183ca4292be8770942d69773075

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6c38c2d0943d4ec7bcf37ab945d2b9e540a65bd850fc3ab74a16a3be4f07053",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2013-06-11T09:48:52Z",
    "title_canon_sha256": "fde005cf2e072ad4d75df4a0ef346b8416b2ca78097c1055afb6d92cf19e270f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2465",
    "kind": "arxiv",
    "version": 2
  }
}