Pith Number

pith:QNRAJRJT

pith:2012:QNRAJRJTABTTPDXVNN7SB6CJM2

not attested not anchored not stored refs pending

Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q,t-Narayana polynomial

Mark Dukes, Yvan Le Borgne

arxiv:1208.0024 v2 · 2012-07-31 · 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{QNRAJRJTABTTPDXVNN7SB6CJM2}

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	2026-05-18T03:36:04.389262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

836204c5330067378ef56b7f20f84966a66459aeee61088fb98a5a92cd32dab7

Aliases

arxiv: 1208.0024 · arxiv_version: 1208.0024v2 · doi: 10.48550/arxiv.1208.0024 · pith_short_12: QNRAJRJTABTT · pith_short_16: QNRAJRJTABTTPDXV · pith_short_8: QNRAJRJT

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/QNRAJRJTABTTPDXVNN7SB6CJM2 \
  | 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: 836204c5330067378ef56b7f20f84966a66459aeee61088fb98a5a92cd32dab7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4468faa7a3438c4cdb9f8e5535a72c9b0b2ea3ef328ad6b989c8d9097cd430b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-31T20:11:02Z",
    "title_canon_sha256": "30fe9b3c28ad7f91913f091f6d342097c5678fa0f95df16608f71850aea178ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0024",
    "kind": "arxiv",
    "version": 2
  }
}