Pith Number

pith:UCNWQB44

pith:2009:UCNWQB44WC53EDRADPRIKZTE6S

not attested not anchored not stored refs pending

Recurrence formulas for Macdonald polynomials of type A

Michael J. Schlosser, Michel Lassalle

arxiv:0902.2099 v2 · 2009-02-12 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UCNWQB44WC53EDRADPRIKZTE6S}

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	2026-05-18T04:40:32.920843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a09b68079cb0bbb20e201be2856664f4bcacc2578e436b4150fcfff4f55fa7d1

Aliases

arxiv: 0902.2099 · arxiv_version: 0902.2099v2 · doi: 10.48550/arxiv.0902.2099 · pith_short_12: UCNWQB44WC53 · pith_short_16: UCNWQB44WC53EDRA · pith_short_8: UCNWQB44

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/UCNWQB44WC53EDRADPRIKZTE6S \
  | 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: a09b68079cb0bbb20e201be2856664f4bcacc2578e436b4150fcfff4f55fa7d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "745b1f608e75beb8ddfa456b40b50d32fe1621528886956c6ed79d7c2b145514",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-02-12T12:53:15Z",
    "title_canon_sha256": "1bc07cd9ef7b9565ae49b29075bc9fbead509b25949f548972691f593b115e9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.2099",
    "kind": "arxiv",
    "version": 2
  }
}