Pith Number

pith:S3RIVBA3

pith:2009:S3RIVBA3YRQAMVADKFBWX25FFV

not attested not anchored not stored refs pending

Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series

Alain Lascoux, S. Ole Warnaar

arxiv:0903.3996 v1 · 2009-03-24 · math.CO · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S3RIVBA3YRQAMVADKFBWX25FFV}

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	2026-05-18T04:06:21.260705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96e28a841bc46006540351436beba52d7e75aeff2e71bd5cdb4269159cff1a81

Aliases

arxiv: 0903.3996 · arxiv_version: 0903.3996v1 · doi: 10.48550/arxiv.0903.3996 · pith_short_12: S3RIVBA3YRQA · pith_short_16: S3RIVBA3YRQAMVAD · pith_short_8: S3RIVBA3

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/S3RIVBA3YRQAMVADKFBWX25FFV \
  | 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: 96e28a841bc46006540351436beba52d7e75aeff2e71bd5cdb4269159cff1a81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bc19d4298d908c85083171a82f2bd2a2784a59beb605185aeab7fe82d90ac43",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-03-24T01:38:45Z",
    "title_canon_sha256": "cb2b013600f7412116038af12bcad15033e0220dd28cfafb7bf99f66747f81ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3996",
    "kind": "arxiv",
    "version": 1
  }
}