Pith Number

pith:NF6EFPUB

pith:2011:NF6EFPUB5Q5VNPPLGYLWPRZVPA

not attested not anchored not stored refs pending

A Simple Bijective Proof of the Shape-Wilf-Equivalence of the Patterns 231 and 312

Dan Saracino, Jonathan Bloom

arxiv:1110.2564 v2 · 2011-10-12 · 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{NF6EFPUB5Q5VNPPLGYLWPRZVPA}

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	2026-05-18T03:47:01.346066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

697c42be81ec3b56bdeb361767c7357808d7bdceb4275bdf07a518c67bde5910

Aliases

arxiv: 1110.2564 · arxiv_version: 1110.2564v2 · doi: 10.48550/arxiv.1110.2564 · pith_short_12: NF6EFPUB5Q5V · pith_short_16: NF6EFPUB5Q5VNPPL · pith_short_8: NF6EFPUB

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/NF6EFPUB5Q5VNPPLGYLWPRZVPA \
  | 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: 697c42be81ec3b56bdeb361767c7357808d7bdceb4275bdf07a518c67bde5910

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be5e917cb7dbaad1f68fff23f8c87824b521bbd09ce57c74361675412ed1ac0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-12T03:56:42Z",
    "title_canon_sha256": "77e45aa93bca1a752f2032b4fdd6222fff63f021d08c6902a9612f3754439fc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2564",
    "kind": "arxiv",
    "version": 2
  }
}