Pith Number

pith:EGYLBQD6

pith:2016:EGYLBQD6I653Z64X5WDT2D4VLQ

not attested not anchored not stored refs pending

A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers

Kyungyong Lee, Li Li, Nicholas A. Loehr

arxiv:1602.01126 v1 · 2016-02-02 · 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{EGYLBQD6I653Z64X5WDT2D4VLQ}

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	2026-07-05T00:16:01.279036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21b0b0c07e47bbbcfb97ed873d0f955c1b8c49ba41580fa03521e1425ef62dcb

Aliases

arxiv: 1602.01126 · arxiv_version: 1602.01126v1 · doi: 10.48550/arxiv.1602.01126 · pith_short_12: EGYLBQD6I653 · pith_short_16: EGYLBQD6I653Z64X · pith_short_8: EGYLBQD6

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/EGYLBQD6I653Z64X5WDT2D4VLQ \
  | 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: 21b0b0c07e47bbbcfb97ed873d0f955c1b8c49ba41580fa03521e1425ef62dcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a40af635b2a89af9d92374ce4a83247aec0f8ab28560d65fe8c3b5c4a67756e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-02T21:45:15Z",
    "title_canon_sha256": "2b827888a97608ee53977265f88e6b8d507a0f67ad526e97fd93ed0624741c59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01126",
    "kind": "arxiv",
    "version": 1
  }
}