Pith Number

pith:6C6FH7AE

pith:2002:6C6FH7AEBCNH77K65ATMH6IQDZ

not attested not anchored not stored refs pending

Percolation on finite graphs and isoperimetric inequalities

Alan Stacey, Itai Benjamini, Noga Alon

arxiv:math/0207112 v2 · 2002-07-12 · 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{6C6FH7AEBCNH77K65ATMH6IQDZ}

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	2026-07-04T14:36:19.297213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0bc53fc04089a7ffd5ee826c3f9101e497b30047e7359080eb691a0a548a19b

Aliases

arxiv: math/0207112 · arxiv_version: math/0207112v2 · doi: 10.48550/arxiv.math/0207112 · pith_short_12: 6C6FH7AEBCNH · pith_short_16: 6C6FH7AEBCNH77K6 · pith_short_8: 6C6FH7AE

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/6C6FH7AEBCNH77K65ATMH6IQDZ \
  | 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: f0bc53fc04089a7ffd5ee826c3f9101e497b30047e7359080eb691a0a548a19b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a3d10717c0b0878625ed23a8cf2ef67af4be4b9896d961c908ef0ad6f4b6515",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2002-07-12T17:19:03Z",
    "title_canon_sha256": "b0da04ea585599e9f1b544a54c320b045a614f3aca1d366be07e90410e88dfa5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0207112",
    "kind": "arxiv",
    "version": 2
  }
}