Pith Number

pith:NSPNUOLM

pith:2024:NSPNUOLMQG3U2M63T66LDGP4YH

not attested not anchored not stored refs pending

Counting up-up-or-down-down permutations

Ira M. Gessel

arxiv:2411.16113 v1 · 2024-11-25 · 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{NSPNUOLMQG3U2M63T66LDGP4YH}

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	2026-07-05T09:40:04.340156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c9eda396c81b74d33db9fbcb199fcc1fb90a9c1d84c3406bcffb4629402eb24

Aliases

arxiv: 2411.16113 · arxiv_version: 2411.16113v1 · doi: 10.48550/arxiv.2411.16113 · pith_short_12: NSPNUOLMQG3U · pith_short_16: NSPNUOLMQG3U2M63 · pith_short_8: NSPNUOLM

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/NSPNUOLMQG3U2M63T66LDGP4YH \
  | 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: 6c9eda396c81b74d33db9fbcb199fcc1fb90a9c1d84c3406bcffb4629402eb24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "371ae35f751ff239189ac794460255ca17227c24cd945349e01e42bdf178365c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-11-25T05:58:21Z",
    "title_canon_sha256": "5ba3bdcaa670e0095102eb85cec0437387eb0b2aeba5a5fcfbe7ce1473ffd305"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.16113",
    "kind": "arxiv",
    "version": 1
  }
}