Pith Number

pith:UGV3USTV

pith:2011:UGV3USTVLWNZBY2KFGH3FVCYXC

not attested not anchored not stored refs pending

The negative q-binomial

Dennis Stanton, Nathaniel Thiem, Shishuo Fu, Victor Reiner

arxiv:1108.4702 v1 · 2011-08-23 · 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{UGV3USTVLWNZBY2KFGH3FVCYXC}

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	2026-05-18T04:14:46.926969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1abba4a755d9b90e34a298fb2d458b88cdeba24eba704c2dd7c05a68a815593

Aliases

arxiv: 1108.4702 · arxiv_version: 1108.4702v1 · doi: 10.48550/arxiv.1108.4702 · pith_short_12: UGV3USTVLWNZ · pith_short_16: UGV3USTVLWNZBY2K · pith_short_8: UGV3USTV

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/UGV3USTVLWNZBY2KFGH3FVCYXC \
  | 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: a1abba4a755d9b90e34a298fb2d458b88cdeba24eba704c2dd7c05a68a815593

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31e5498425107c9ccbec8656db8b4de14716d60c41d55705e0a514bbae8bc67e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-23T20:47:32Z",
    "title_canon_sha256": "9783a6ad9b80f4c3bf6f80e3fd53e487bb1d9d20cf28d24ca598a46f0f42ce57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4702",
    "kind": "arxiv",
    "version": 1
  }
}