Pith Number

pith:TZFUBO3L

pith:2023:TZFUBO3LGRPDY5IKFGRAHQFQX2

not attested not anchored not stored refs pending

Rhombic staircase tableaux and Koornwinder polynomials

Lauren Williams, Olya Mandelshtam, Sylvie Corteel

arxiv:2312.17469 v4 · 2023-12-29 · math.CO · math-ph · math.MP · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZFUBO3LGRPDY5IKFGRAHQFQX2}

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.

Cited by

1 paper in Pith

Formulas for Koornwinder polynomials

Receipt and verification

First computed	2026-07-05T08:20:26.511297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e4b40bb6b345e3c750a29a203c0b0be8afcd855a5809f546c8492c7b3652399

Aliases

arxiv: 2312.17469 · arxiv_version: 2312.17469v4 · doi: 10.48550/arxiv.2312.17469 · pith_short_12: TZFUBO3LGRPD · pith_short_16: TZFUBO3LGRPDY5IK · pith_short_8: TZFUBO3L

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/TZFUBO3LGRPDY5IKFGRAHQFQX2 \
  | 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: 9e4b40bb6b345e3c750a29a203c0b0be8afcd855a5809f546c8492c7b3652399

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9687063c144027e90bab6fc61b2a249ef2f0b108dda138da489c133e36db9f6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-12-29T04:40:59Z",
    "title_canon_sha256": "79c765ad3b70b832ea2355aeccbc0417f25ba7d9b570639a11844f27ea23c7a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.17469",
    "kind": "arxiv",
    "version": 4
  }
}