Pith Number

pith:E764KQRN

pith:2011:E764KQRNBLRBVXUHOOF4HQ477I

not attested not anchored not stored refs pending

The enumeration of permutations avoiding 2143 and 4231

M. D. Atkinson, Michael Albert, Robert Brignall

arxiv:1108.0989 v1 · 2011-08-04 · 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{E764KQRNBLRBVXUHOOF4HQ477I}

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	2026-05-18T04:16:13.254972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27fdc5422d0ae21ade87738bc3c39ffa0dbfcd6ac6ef69ad836669f0d1b9e5dd

Aliases

arxiv: 1108.0989 · arxiv_version: 1108.0989v1 · doi: 10.48550/arxiv.1108.0989 · pith_short_12: E764KQRNBLRB · pith_short_16: E764KQRNBLRBVXUH · pith_short_8: E764KQRN

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/E764KQRNBLRBVXUHOOF4HQ477I \
  | 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: 27fdc5422d0ae21ade87738bc3c39ffa0dbfcd6ac6ef69ad836669f0d1b9e5dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63d5c0bb0ee167323fb1ccaa0aa90244834b359398043145a48e9b3f35ffa794",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-04T03:35:47Z",
    "title_canon_sha256": "36582bbd58827500fadcb6113f0a77aa3240e506da533073a35541b61383b210"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0989",
    "kind": "arxiv",
    "version": 1
  }
}