Pith Number

pith:OYMHYLF6

pith:1997:OYMHYLF67VEEK3WCZCXYFRVRDY

not attested not anchored not stored refs pending

How often is a permutation an n'th power?

Michael Larsen (University of Missouri)

arxiv:math/9712223 v1 · 1997-12-03 · 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{OYMHYLF67VEEK3WCZCXYFRVRDY}

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.

Cited by

1 paper in Pith

Most Words are Geometrically Almost Uniform

Receipt and verification

First computed	2026-07-04T14:40:23.810567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76187c2cbefd48456ec2c8af82c6b11e22f8c52a90575a22fe2f90d9fbe3ad45

Aliases

arxiv: math/9712223 · arxiv_version: math/9712223v1 · doi: 10.48550/arxiv.math/9712223 · pith_short_12: OYMHYLF67VEE · pith_short_16: OYMHYLF67VEEK3WC · pith_short_8: OYMHYLF6

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/OYMHYLF67VEEK3WCZCXYFRVRDY \
  | 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: 76187c2cbefd48456ec2c8af82c6b11e22f8c52a90575a22fe2f90d9fbe3ad45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8543ee42194e0f52a63fa3f53a3ac7a5908e697f75480ba0c9bec957f5f533c6",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1997-12-03T21:34:46Z",
    "title_canon_sha256": "c8b5dc0c0ac11ddf4673d8eab724f1e77e4a02a6f6af5fc73b960cd8821333b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9712223",
    "kind": "arxiv",
    "version": 1
  }
}