Pith Number

pith:RA73AK3W

pith:2012:RA73AK3WFLKKG73G4MNJUVGHO2

not attested not anchored not stored refs pending

Surprising symmetries in 132-avoiding permutations

Miklos Bona

arxiv:1202.2023 v1 · 2012-02-09 · 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{RA73AK3WFLKKG73G4MNJUVGHO2}

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	2026-05-18T04:02:38.487497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

883fb02b762ad4a37f66e31a9a54c776a12ba5c77f7c52968bf64351f24bd9f3

Aliases

arxiv: 1202.2023 · arxiv_version: 1202.2023v1 · doi: 10.48550/arxiv.1202.2023 · pith_short_12: RA73AK3WFLKK · pith_short_16: RA73AK3WFLKKG73G · pith_short_8: RA73AK3W

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/RA73AK3WFLKKG73G4MNJUVGHO2 \
  | 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: 883fb02b762ad4a37f66e31a9a54c776a12ba5c77f7c52968bf64351f24bd9f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5256be90d9f7303712264822c134bbd3705b462d83e94692357aed51734ec835",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-09T15:41:48Z",
    "title_canon_sha256": "1d90ba6d1fe16f3f478821b996f96763b932a053631a361c9abe281e4fc938b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2023",
    "kind": "arxiv",
    "version": 1
  }
}