Pith Number

pith:ETOB5R34

pith:2021:ETOB5R347FDMHCIMIQMVQOOOHC

not attested not anchored not stored refs pending

Chain decompositions of q,t-Catalan numbers: tail extensions and flagpole partitions

Kyungyong Lee, Li Li, Nicholas A. Loehr, Seongjune Han

arxiv:2103.12875 v2 · 2021-03-23 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ETOB5R347FDMHCIMIQMVQOOOHC}

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	2026-07-05T04:29:08.067914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24dc1ec77cf946c3890c44195839ce389f144fdb8bc201b84baa4642f14962cb

Aliases

arxiv: 2103.12875 · arxiv_version: 2103.12875v2 · doi: 10.48550/arxiv.2103.12875 · pith_short_12: ETOB5R347FDM · pith_short_16: ETOB5R347FDMHCIM · pith_short_8: ETOB5R34

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/ETOB5R347FDMHCIMIQMVQOOOHC \
  | 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: 24dc1ec77cf946c3890c44195839ce389f144fdb8bc201b84baa4642f14962cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f293fc14f2d9294d3be202ea36ef06b5d7958fd6cb89d8ad28c04e4bfac0006f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-03-23T22:47:52Z",
    "title_canon_sha256": "0a35d26a59a74f4c483d22f4e8f470dc2426aee83d3f055578de21169ddf7d90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.12875",
    "kind": "arxiv",
    "version": 2
  }
}