Pith Number

pith:7LCWMJZM

pith:2025:7LCWMJZM4FULSVXH2WZMP7IQF4

not attested not anchored not stored refs pending

Number of orbits of $k$-subsets of permutations

Ludovick Bouthat, Raghavendra Tripathi

arxiv:2508.07463 v1 · 2025-08-10 · math.CO · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7LCWMJZM4FULSVXH2WZMP7IQF4}

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	2026-06-23T02:13:16.298938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fac566272ce168b956e7d5b2c7fd102f18054f83c419814b9ac96681dfa2336c

Aliases

arxiv: 2508.07463 · arxiv_version: 2508.07463v1 · doi: 10.48550/arxiv.2508.07463 · pith_short_12: 7LCWMJZM4FUL · pith_short_16: 7LCWMJZM4FULSVXH · pith_short_8: 7LCWMJZM

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/7LCWMJZM4FULSVXH2WZMP7IQF4 \
  | 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: fac566272ce168b956e7d5b2c7fd102f18054f83c419814b9ac96681dfa2336c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a96cd98ba68c0db9ef6b1ac0a2a390e3ccfc6814eb8ba4983b9b376762232a5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-10T19:23:24Z",
    "title_canon_sha256": "6ab585aab4d3a24bdfbe3e51b9c04a097155a674ee048132ccaaed8e829862e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.07463",
    "kind": "arxiv",
    "version": 1
  }
}