Pith Number

pith:SALIBCB3

pith:2012:SALIBCB3IWUF27WEPDASHLKUPZ

not attested not anchored not stored refs pending

On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length

Miklos Bona

arxiv:1209.2404 v1 · 2012-09-11 · 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{SALIBCB3IWUF27WEPDASHLKUPZ}

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	2026-05-18T03:45:52.017779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

901680883b45a85d7ec478c123ad547e5952a3cd6b2d7c9c1ede0861952ad100

Aliases

arxiv: 1209.2404 · arxiv_version: 1209.2404v1 · doi: 10.48550/arxiv.1209.2404 · pith_short_12: SALIBCB3IWUF · pith_short_16: SALIBCB3IWUF27WE · pith_short_8: SALIBCB3

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/SALIBCB3IWUF27WEPDASHLKUPZ \
  | 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: 901680883b45a85d7ec478c123ad547e5952a3cd6b2d7c9c1ede0861952ad100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43045d30b9d00a6094d6740ebd74d74f8f9a333c4e5d3852298a6f5a2e451ede",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-11T19:32:47Z",
    "title_canon_sha256": "0fd36a9a73fcb2af774dd295fe5945b58bffdd82182730ef727f609d3887d7d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2404",
    "kind": "arxiv",
    "version": 1
  }
}