Pith Number

pith:TQI4VUZ5

pith:2010:TQI4VUZ5HLDOOFZJDA5FZ5CPAL

not attested not anchored not stored refs pending

q,t-Catalan numbers and knot homology

E. Gorsky

arxiv:1003.0916 v3 · 2010-03-03 · math.AG · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQI4VUZ5HLDOOFZJDA5FZ5CPAL}

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.

Cited by

1 paper in Pith

Double twist knots and lattice paths

Receipt and verification

First computed	2026-05-18T03:48:24.529523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c11cad33d3ac6e71729183a5cf44f02c46f76e4e63149424da3975d6fa709fa

Aliases

arxiv: 1003.0916 · arxiv_version: 1003.0916v3 · doi: 10.48550/arxiv.1003.0916 · pith_short_12: TQI4VUZ5HLDO · pith_short_16: TQI4VUZ5HLDOOFZJ · pith_short_8: TQI4VUZ5

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/TQI4VUZ5HLDOOFZJDA5FZ5CPAL \
  | 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: 9c11cad33d3ac6e71729183a5cf44f02c46f76e4e63149424da3975d6fa709fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b5e7cf7b5300bc064272dec7a46aeeba1f62b81a9ef51795be0e628a4c23e78",
    "cross_cats_sorted": [
      "math.CO",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-03-03T21:35:08Z",
    "title_canon_sha256": "113b0ff0ba1037aca144d1a7211cac00a812420c525f068ecbb1e07eff923bd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.0916",
    "kind": "arxiv",
    "version": 3
  }
}