Pith Number

pith:722DU7KT

pith:2025:722DU7KTJOGTS7CXET4EJU2IRY

not attested not anchored not stored refs pending

The range of the des statistic for conjugacy classes in $S_n$

Yisca Kares

arxiv:2505.22828 v1 · 2025-05-28 · 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{722DU7KTJOGTS7CXET4EJU2IRY}

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	2026-07-05T11:11:50.492106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632

Aliases

arxiv: 2505.22828 · arxiv_version: 2505.22828v1 · doi: 10.48550/arxiv.2505.22828 · pith_short_12: 722DU7KTJOGT · pith_short_16: 722DU7KTJOGTS7CX · pith_short_8: 722DU7KT

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/722DU7KTJOGTS7CXET4EJU2IRY \
  | 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: feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "252229d076b7d4d788bdfcb0a84e2f4fffb59d8e4a36f2adfaca8e62018fb3d9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-28T20:11:03Z",
    "title_canon_sha256": "0d0743bf9944590ff9a4e2cdb24b6634f7b612276506ce417eb7d181bfd22a58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.22828",
    "kind": "arxiv",
    "version": 1
  }
}