Pith Number

pith:Q7OFG4IN

pith:2018:Q7OFG4INFVWRHW32ILZ3RBARWA

not attested not anchored not stored refs pending

On the structure of random graphs with constant $r$-balls

David Ellis, Itai Benjamini

arxiv:1802.02002 v7 · 2018-02-06 · math.CO · math.GR · 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{Q7OFG4INFVWRHW32ILZ3RBARWA}

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	2026-07-05T01:53:44.789044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87dc53710d2d6d13db7a42f3b88411b00f1ffed1cd59af3575776327458d539a

Aliases

arxiv: 1802.02002 · arxiv_version: 1802.02002v7 · doi: 10.48550/arxiv.1802.02002 · pith_short_12: Q7OFG4INFVWR · pith_short_16: Q7OFG4INFVWRHW32 · pith_short_8: Q7OFG4IN

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/Q7OFG4INFVWRHW32ILZ3RBARWA \
  | 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: 87dc53710d2d6d13db7a42f3b88411b00f1ffed1cd59af3575776327458d539a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ded36878d8c4d044e69138024d51cd0ba6fe33c6c823810075febe2772aa9857",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-02-06T15:30:39Z",
    "title_canon_sha256": "58ff533b22ab901934884cb963200dc46a6e967bdb23e85f134ff915a3c68b82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.02002",
    "kind": "arxiv",
    "version": 7
  }
}