Pith Number

pith:VBADOPDG

pith:1997:VBADOPDGCDDICV3VQ3QLYLNG5G

not attested not anchored not stored refs pending

$q$-Rook polynomials and matrices over finite fields

James Haglund

arxiv:math/9706219 v1 · 1997-06-18 · 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{VBADOPDGCDDICV3VQ3QLYLNG5G}

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	2026-05-18T01:05:35.185987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a840373c6610c681577586e0bc2da6e99efcf2080d5d2fb013ff7452b83cb4e7

Aliases

arxiv: math/9706219 · arxiv_version: math/9706219v1 · doi: 10.48550/arxiv.math/9706219 · pith_short_12: VBADOPDGCDDI · pith_short_16: VBADOPDGCDDICV3V · pith_short_8: VBADOPDG

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/VBADOPDGCDDICV3VQ3QLYLNG5G \
  | 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: a840373c6610c681577586e0bc2da6e99efcf2080d5d2fb013ff7452b83cb4e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4cd63cfb81e44be87836461967bb35658df5821c763c858ae8bbbd1c17fbf41",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1997-06-18T00:00:00Z",
    "title_canon_sha256": "9c32ef7d40a8c27dd66e6c222e72d015eb2ae7ffdee0374bd5d30373b049b1af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9706219",
    "kind": "arxiv",
    "version": 1
  }
}