Pith Number

pith:2CYJDTGG

pith:2012:2CYJDTGGHPLQS32SHQLPMRUAPD

not attested not anchored not stored refs pending

Linear Transformations & the Multivariate Generating Function

Michael C. Burkhart

arxiv:1209.3357 v1 · 2012-09-15 · math.CO · math.PR · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2CYJDTGGHPLQS32SHQLPMRUAPD}

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	2026-05-18T03:45:31.117507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0b091ccc63bd7096f523c16f6468078ebc75945a122cf824d9276d684b44717

Aliases

arxiv: 1209.3357 · arxiv_version: 1209.3357v1 · doi: 10.48550/arxiv.1209.3357 · pith_short_12: 2CYJDTGGHPLQ · pith_short_16: 2CYJDTGGHPLQS32S · pith_short_8: 2CYJDTGG

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/2CYJDTGGHPLQS32SHQLPMRUAPD \
  | 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: d0b091ccc63bd7096f523c16f6468078ebc75945a122cf824d9276d684b44717

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de7c5a68b0baacf321fbe0f5d8e3f466bd51a1ef009a5e438f35de8dd8e1407b",
    "cross_cats_sorted": [
      "math.PR",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-15T05:56:19Z",
    "title_canon_sha256": "f67884c422e5de52560fd47935bf0c53958f70928e9c66213616c29f35f7b7ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3357",
    "kind": "arxiv",
    "version": 1
  }
}