Pith Number

pith:HFZ6GSR6

pith:2001:HFZ6GSR6PQ523M3AP2IT6YIIP5

not attested not anchored not stored refs pending

The cycle enumerator of unimodal permutations

Jean-Yves Thibon

arxiv:math/0102051 v1 · 2001-02-07 · 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{HFZ6GSR6PQ523M3AP2IT6YIIP5}

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	2026-05-18T03:34:00.611878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3973e34a3e7c3badb3607e913f61087f7cde42ebd4b904758e9b52684a9974db

Aliases

arxiv: math/0102051 · arxiv_version: math/0102051v1 · doi: 10.48550/arxiv.math/0102051 · pith_short_12: HFZ6GSR6PQ52 · pith_short_16: HFZ6GSR6PQ523M3A · pith_short_8: HFZ6GSR6

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/HFZ6GSR6PQ523M3AP2IT6YIIP5 \
  | 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: 3973e34a3e7c3badb3607e913f61087f7cde42ebd4b904758e9b52684a9974db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a204be5cf5dba182fe5276f30014e803c12c409ef833aeb98b39355081b15c26",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2001-02-07T09:20:45Z",
    "title_canon_sha256": "4d58136e2c6bc487e3fb65d46d95c32656fa95a5d516c248cb06cb81320cab22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0102051",
    "kind": "arxiv",
    "version": 1
  }
}