Pith Number

pith:WP6YA3OP

pith:2012:WP6YA3OP3Q5LXMA2NABTDIYVZE

not attested not anchored not stored refs pending

Edge distribution in generalized graph products

Dan Vilenchik, Michael Langberg

arxiv:1211.1467 v4 · 2012-11-07 · cs.DM · cs.IT · math.CO · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WP6YA3OP3Q5LXMA2NABTDIYVZE}

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	2026-05-18T03:14:17.471926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3fd806dcfdc3abbb01a680331a315c915d8113ef59825346961ec80f20a3451

Aliases

arxiv: 1211.1467 · arxiv_version: 1211.1467v4 · doi: 10.48550/arxiv.1211.1467 · pith_short_12: WP6YA3OP3Q5L · pith_short_16: WP6YA3OP3Q5LXMA2 · pith_short_8: WP6YA3OP

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/WP6YA3OP3Q5LXMA2NABTDIYVZE \
  | 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: b3fd806dcfdc3abbb01a680331a315c915d8113ef59825346961ec80f20a3451

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d038163a62d26d010c310f4ca0f903eecd062877858e27f7abe98024f2b9036",
    "cross_cats_sorted": [
      "cs.IT",
      "math.CO",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-11-07T06:54:27Z",
    "title_canon_sha256": "0c0d9683af00b18996d2ca3fd27412e95d52fd8e39d39e03cdaa27c872c97127"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1467",
    "kind": "arxiv",
    "version": 4
  }
}