Pith Number

pith:7QCK7SAR

pith:2026:7QCK7SARDONQ65KJWMLYLUHJMY

not attested not anchored not stored refs pending

On Cycles in Multiset Permutations, Parking Functions, and Related Structures

Calum Buchanan, Fabian Burghart, Mei Yin, Stephan Wagner

arxiv:2606.19500 v1 · 2026-06-17 · 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{7QCK7SARDONQ65KJWMLYLUHJMY}

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	2026-06-19T16:12:27.336264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc04afc8111b9b0f7549b31785d0e9663718ebc07c2dd87d60f861fc91f974f4

Aliases

arxiv: 2606.19500 · arxiv_version: 2606.19500v1 · doi: 10.48550/arxiv.2606.19500 · pith_short_12: 7QCK7SARDONQ · pith_short_16: 7QCK7SARDONQ65KJ · pith_short_8: 7QCK7SAR

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/7QCK7SARDONQ65KJWMLYLUHJMY \
  | 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: fc04afc8111b9b0f7549b31785d0e9663718ebc07c2dd87d60f861fc91f974f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6972d31646a5c054d499c5c6e14483db91f9ac3f328e2d8ef2e1cf0888adf7ff",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-17T18:39:31Z",
    "title_canon_sha256": "56cd382d948e5ddc03a351ee2963bec88fa027087690c106bd5f1e3964916acb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19500",
    "kind": "arxiv",
    "version": 1
  }
}