Pith Number

pith:2UJPQCZG

pith:2018:2UJPQCZGJ5E4SWNSNQHFWLZJWA

not attested not anchored not stored refs pending

Catalan functions and $k$-Schur positivity

Anna Pun, Daniel Summers, Jennifer Morse, Jonah Blasiak

arxiv:1804.03701 v1 · 2018-04-10 · math.CO · 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{2UJPQCZGJ5E4SWNSNQHFWLZJWA}

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	2026-05-18T00:18:45.276372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d512f80b264f49c959b26c0e5b2f29b0279102093566836f2eeab17d5a0deabb

Aliases

arxiv: 1804.03701 · arxiv_version: 1804.03701v1 · doi: 10.48550/arxiv.1804.03701 · pith_short_12: 2UJPQCZGJ5E4 · pith_short_16: 2UJPQCZGJ5E4SWNS · pith_short_8: 2UJPQCZG

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/2UJPQCZGJ5E4SWNSNQHFWLZJWA \
  | 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: d512f80b264f49c959b26c0e5b2f29b0279102093566836f2eeab17d5a0deabb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e20ef9d68153eeaaee67cc6a25214870629a1241ea733a0c21d001648d91e18",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-10T19:59:34Z",
    "title_canon_sha256": "3335d0654ddf67f0fd97f160474b8f40863e48c5b22dff037673fe164c76fbb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.03701",
    "kind": "arxiv",
    "version": 1
  }
}