Pith Number

pith:6HIW3ZTV

pith:2015:6HIW3ZTVENN2QRMOJDGZXM7DSY

not attested not anchored not stored refs pending

Matrix product formula for Macdonald polynomials

Jan de Gier, Luigi Cantini, Michael Wheeler

arxiv:1505.00287 v2 · 2015-05-01 · math-ph · math.CO · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6HIW3ZTVENN2QRMOJDGZXM7DSY}

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	2026-05-18T01:31:39.363134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1d16de675235ba8458e48cd9bb3e3962027d5637d4ca0b593a1a53e31beed43

Aliases

arxiv: 1505.00287 · arxiv_version: 1505.00287v2 · doi: 10.48550/arxiv.1505.00287 · pith_short_12: 6HIW3ZTVENN2 · pith_short_16: 6HIW3ZTVENN2QRMO · pith_short_8: 6HIW3ZTV

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/6HIW3ZTVENN2QRMOJDGZXM7DSY \
  | 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: f1d16de675235ba8458e48cd9bb3e3962027d5637d4ca0b593a1a53e31beed43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed40317ebe126f3017fc7c1d04f363b4ddc4f1b9f63b7b1813ccf7e3830266ab",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-05-01T21:55:25Z",
    "title_canon_sha256": "4fcfcbca42d3592230357bb01de6015c2ea29395946b32c70b5decf6b8e3cdd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.00287",
    "kind": "arxiv",
    "version": 2
  }
}