Pith Number

pith:HZ5VAFFO

pith:2009:HZ5VAFFOOAPYCNSIM3PSTMSCDM

not attested not anchored not stored refs pending

Generalized descent patterns in permutations and associated Hopf algebras

C. Reutenauer, J.-C. Novelli, J.-Y. Thibon

arxiv:0911.5615 v1 · 2009-11-30 · 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{HZ5VAFFOOAPYCNSIM3PSTMSCDM}

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	2026-05-18T03:34:03.789747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e7b5014ae701f81364866df29b2421b3a24653b5622f6fb63fc1a8837ddb248

Aliases

arxiv: 0911.5615 · arxiv_version: 0911.5615v1 · doi: 10.48550/arxiv.0911.5615 · pith_short_12: HZ5VAFFOOAPY · pith_short_16: HZ5VAFFOOAPYCNSI · pith_short_8: HZ5VAFFO

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/HZ5VAFFOOAPYCNSIM3PSTMSCDM \
  | 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: 3e7b5014ae701f81364866df29b2421b3a24653b5622f6fb63fc1a8837ddb248

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fa84d13a6f829b8a7c958ac62870bb36965677ae06f707909741566385c2ec9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-11-30T11:21:41Z",
    "title_canon_sha256": "e842c8eb1800bc470ee29e3a1412b3e715300f643f6be3fc0f509c5011a27d16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.5615",
    "kind": "arxiv",
    "version": 1
  }
}