Pith Number

pith:PK2XIKCG

pith:2018:PK2XIKCG7QLUWWJZTQA4RF5G4C

not attested not anchored not stored refs pending

$k$-Schur expansions of Catalan functions

Anna Pun, Daniel Summers, Jennifer Morse, Jonah Blasiak

arxiv:1811.02490 v1 · 2018-11-06 · math.CO · math.AG · 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{PK2XIKCG7QLUWWJZTQA4RF5G4C}

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	2026-05-18T00:01:24.128292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ab5742846fc174b59399c01c897a6e0ad24a38cc74ff1407ac5b63b370b780a

Aliases

arxiv: 1811.02490 · arxiv_version: 1811.02490v1 · doi: 10.48550/arxiv.1811.02490 · pith_short_12: PK2XIKCG7QLU · pith_short_16: PK2XIKCG7QLUWWJZ · pith_short_8: PK2XIKCG

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/PK2XIKCG7QLUWWJZTQA4RF5G4C \
  | 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: 7ab5742846fc174b59399c01c897a6e0ad24a38cc74ff1407ac5b63b370b780a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f66c9ae0a6f26497b5348c285d1de06191336577d1484c467c301c8859f822ef",
    "cross_cats_sorted": [
      "math.AG",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-11-06T17:02:56Z",
    "title_canon_sha256": "a6f8ba91c3d41e9ac88bea571ee05a521980e6369d6631790ca5fd8f47a4f8cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.02490",
    "kind": "arxiv",
    "version": 1
  }
}