Pith Number

pith:NPOTXXU3

pith:2003:NPOTXXU3A3DIW4HB5X2H7JWI2T

not attested not anchored not stored refs pending

An analytic formula for Macdonald polynomials

Michael Schlosser, Michel Lassalle

arxiv:math/0307315 v1 · 2003-07-23 · 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{NPOTXXU3A3DIW4HB5X2H7JWI2T}

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	2026-05-17T23:53:03.274634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1

Aliases

arxiv: math/0307315 · arxiv_version: math/0307315v1 · doi: 10.48550/arxiv.math/0307315 · pith_short_12: NPOTXXU3A3DI · pith_short_16: NPOTXXU3A3DIW4HB · pith_short_8: NPOTXXU3

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/NPOTXXU3A3DIW4HB5X2H7JWI2T \
  | 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: 6bdd3bde9b06c68b70e1edf47fa6c8d4e17119d30f05f26627f7a6b6936ed6b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14c5fc621bba3af7c3d209d260c09c607b83b813a70e8ddb6b96effd0e5fb596",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-07-23T14:24:17Z",
    "title_canon_sha256": "9b7d348a51849070619e1de8e311356ca4e395111903cbaf29c568af5267c5d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307315",
    "kind": "arxiv",
    "version": 1
  }
}