Pith Number

pith:MDDGZUX6

pith:2018:MDDGZUX65Z7HXAC22DKB34QZMA

not attested not anchored not stored refs pending

Macdonald Polynomials of Type $C_n$ with One-Column Diagrams and Deformed Catalan Numbers

Ayumu Hoshino, Jun'ichi Shiraishi

arxiv:1801.09939 v2 · 2018-01-30 · math.QA · math.CO · 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{MDDGZUX65Z7HXAC22DKB34QZMA}

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	2026-05-18T00:05:19.506841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60c66cd2feee7e7b805ad0d41df2196014199d9996ef16a9d1e302b593835f5a

Aliases

arxiv: 1801.09939 · arxiv_version: 1801.09939v2 · doi: 10.48550/arxiv.1801.09939 · pith_short_12: MDDGZUX65Z7H · pith_short_16: MDDGZUX65Z7HXAC2 · pith_short_8: MDDGZUX6

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/MDDGZUX65Z7HXAC22DKB34QZMA \
  | 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: 60c66cd2feee7e7b805ad0d41df2196014199d9996ef16a9d1e302b593835f5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b0e22ec8914f495c4f40f2630a4ac3c360fbdfe06b1dba617a88c97a9593f50",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2018-01-30T11:38:40Z",
    "title_canon_sha256": "c4626d056eaae5fad96dd9d53dec7defbce4d74e1f58c3e164e9f6bb94b7dc05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.09939",
    "kind": "arxiv",
    "version": 2
  }
}