Pith Number

pith:K33AXIQ2

pith:2013:K33AXIQ2FASCLFYGMOD3APFDE3

not attested not anchored not stored refs pending

Overlap Cycles for Permutations: Necessary and Sufficient Conditions

Victoria Horan

arxiv:1309.4741 v1 · 2013-09-18 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K33AXIQ2FASCLFYGMOD3APFDE3}

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	2026-05-18T03:12:58.450938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56f60ba21a28242597066387b03ca326e0e419543b41af4752c6667bd87ebbbc

Aliases

arxiv: 1309.4741 · arxiv_version: 1309.4741v1 · doi: 10.48550/arxiv.1309.4741 · pith_short_12: K33AXIQ2FASC · pith_short_16: K33AXIQ2FASCLFYG · pith_short_8: K33AXIQ2

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/K33AXIQ2FASCLFYGMOD3APFDE3 \
  | 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: 56f60ba21a28242597066387b03ca326e0e419543b41af4752c6667bd87ebbbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a118ffb9785cae472ed47b478d3dcb3862d49ab5cc3b70244ea48397afc7f852",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-18T18:39:30Z",
    "title_canon_sha256": "e1cff34dc930cf46bc1c027fa087aa28d7ce9de6b7f9217e51d79d1a108dff88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4741",
    "kind": "arxiv",
    "version": 1
  }
}