Pith Number

pith:FMPOOMRG

pith:2011:FMPOOMRGCZIYN5F7KRWZE5FUT7

not attested not anchored not stored refs pending

Nonmedian Direct Products of Graphs with Loops

Elliot Krop, Kristi Clark

arxiv:1102.4634 v1 · 2011-02-22 · 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{FMPOOMRGCZIYN5F7KRWZE5FUT7}

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	2026-05-18T04:28:07.771016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b1ee73226165186f4bf546d9274b49fe445a6bdf3e2d6b150083dc3743c2626

Aliases

arxiv: 1102.4634 · arxiv_version: 1102.4634v1 · doi: 10.48550/arxiv.1102.4634 · pith_short_12: FMPOOMRGCZIY · pith_short_16: FMPOOMRGCZIYN5F7 · pith_short_8: FMPOOMRG

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/FMPOOMRGCZIYN5F7KRWZE5FUT7 \
  | 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: 2b1ee73226165186f4bf546d9274b49fe445a6bdf3e2d6b150083dc3743c2626

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0beae0a50435bb1e80007707714d93bffb8a2aa814f0e96749a26c87856ab7b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-22T22:27:38Z",
    "title_canon_sha256": "a99a2fe223bcaa991ba07ff2862e45e920fa8110ed1f80741aad037c2b9856f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4634",
    "kind": "arxiv",
    "version": 1
  }
}