Pith Number

pith:QDMKOFZA

pith:2015:QDMKOFZA3Z6SYIKXC72ZTC2LRJ

not attested not anchored not stored refs pending

Associativity and non-associativity of some hypergraph products

Lydia Ostermeier, Marc Hellmuth, Peter F. Stadler, Richard H. Hammack

arxiv:1511.07162 v1 · 2015-11-23 · 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{QDMKOFZA3Z6SYIKXC72ZTC2LRJ}

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	2026-05-18T01:26:12.070897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80d8a71720de7d2c215717f5998b4b8a59842aabeddfbb2e63980f7146f1898a

Aliases

arxiv: 1511.07162 · arxiv_version: 1511.07162v1 · doi: 10.48550/arxiv.1511.07162 · pith_short_12: QDMKOFZA3Z6S · pith_short_16: QDMKOFZA3Z6SYIKX · pith_short_8: QDMKOFZA

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/QDMKOFZA3Z6SYIKXC72ZTC2LRJ \
  | 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: 80d8a71720de7d2c215717f5998b4b8a59842aabeddfbb2e63980f7146f1898a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd2989453b965d8f4f6049fdd1e65f982c0312195fac27e781c9e8112674a410",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-23T10:16:48Z",
    "title_canon_sha256": "8bf5245c181d8ce90444a447c2e649548b964e59518197c817e6bf475ab5c041"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07162",
    "kind": "arxiv",
    "version": 1
  }
}