Pith Number

pith:YMMLS5P2

pith:2013:YMMLS5P2UPJJL45DOXYXDELPLW

not attested not anchored not stored refs pending

Normal ordering problem and the extensions of the Stirling grammar

Matthias Schork, Shi-Mei Ma, Toufik Mansour

arxiv:1308.0169 v1 · 2013-08-01 · 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{YMMLS5P2UPJJL45DOXYXDELPLW}

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	2026-05-18T01:48:31.733931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c318b975faa3d295f3a375f171916f5da565d2693ffa4a3d929c403961d525a9

Aliases

arxiv: 1308.0169 · arxiv_version: 1308.0169v1 · doi: 10.48550/arxiv.1308.0169 · pith_short_12: YMMLS5P2UPJJ · pith_short_16: YMMLS5P2UPJJL45D · pith_short_8: YMMLS5P2

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/YMMLS5P2UPJJL45DOXYXDELPLW \
  | 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: c318b975faa3d295f3a375f171916f5da565d2693ffa4a3d929c403961d525a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2525a16b98719ac4106cf0c422fd2a3e88ce7a7e9d7d4240a841c41daeb31e04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-08-01T12:21:21Z",
    "title_canon_sha256": "7492947c9dabefb9de56671c3d1659a57c95d6c0c1aaf8ea8733d3b1eac32854"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.0169",
    "kind": "arxiv",
    "version": 1
  }
}