Pith Number

pith:USA46GLX

pith:1996:USA46GLXE4X3HXKATP4X2NIXV3

not attested not anchored not stored refs pending

(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula

Andrei Okounkov

arxiv:q-alg/9605013 v2 · 1996-05-09 · q-alg · 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{USA46GLXE4X3HXKATP4X2NIXV3}

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	2026-05-18T01:05:07.511590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a481cf1977272fb3dd409bf97d3517aeed79f9d94e7eaa7fa98c7c4ce032684b

Aliases

arxiv: q-alg/9605013 · arxiv_version: q-alg/9605013v2 · doi: 10.48550/arxiv.q-alg/9605013 · pith_short_12: USA46GLXE4X3 · pith_short_16: USA46GLXE4X3HXKA · pith_short_8: USA46GLX

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/USA46GLXE4X3HXKATP4X2NIXV3 \
  | 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: a481cf1977272fb3dd409bf97d3517aeed79f9d94e7eaa7fa98c7c4ce032684b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b9a907edb810be2a9b7087084e2f5f4aa66d1b9b734b965df783ea09963a7b9",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "q-alg",
    "submitted_at": "1996-05-09T15:45:01Z",
    "title_canon_sha256": "5b6d468e6a449992e3335bedfa9a286ecc3f43ae52b802c4c32484e7596cd46e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "q-alg/9605013",
    "kind": "arxiv",
    "version": 2
  }
}