Pith Number

pith:GHVEZ36M

pith:2011:GHVEZ36MI4GKILLIUUCCZ6TXE5

not attested not anchored not stored refs pending

Mesh patterns and the expansion of permutation statistics as sums of permutation patterns

Anders Claesson, Petter Br\"and\'en

arxiv:1102.4226 v2 · 2011-02-21 · 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{GHVEZ36MI4GKILLIUUCCZ6TXE5}

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	2026-05-18T04:27:17.490195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31ea4cefcc470ca42d68a5042cfa77274a7346a3132cbbb585dfa2a9a973b807

Aliases

arxiv: 1102.4226 · arxiv_version: 1102.4226v2 · doi: 10.48550/arxiv.1102.4226 · pith_short_12: GHVEZ36MI4GK · pith_short_16: GHVEZ36MI4GKILLI · pith_short_8: GHVEZ36M

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/GHVEZ36MI4GKILLIUUCCZ6TXE5 \
  | 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: 31ea4cefcc470ca42d68a5042cfa77274a7346a3132cbbb585dfa2a9a973b807

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5fa81d97590d35b3f2661d726eba5ac17a81972997fa1fc399f4c6aa25b512d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-21T13:53:15Z",
    "title_canon_sha256": "47ea9ce531d3c1a436d9da2a3382e03191dbe815ea033d0865bd5dddad0077e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4226",
    "kind": "arxiv",
    "version": 2
  }
}