Pith Number

pith:BLGXVK7J

pith:2011:BLGXVK7JLKJGDYMFKXG7G2WUE2

not attested not anchored not stored refs pending

Dual Lukacs regressions for non-commutative variables

Jacek Wesolowski, Kamil Szpojankowski

arxiv:1110.3419 v2 · 2011-10-15 · math.OA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BLGXVK7JLKJGDYMFKXG7G2WUE2}

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	2026-05-18T03:05:19.061961Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0acd7aabe95a9261e18555cdf36ad4268493ec32c00f2c18d27b9f0aedc6f514

Aliases

arxiv: 1110.3419 · arxiv_version: 1110.3419v2 · doi: 10.48550/arxiv.1110.3419 · pith_short_12: BLGXVK7JLKJG · pith_short_16: BLGXVK7JLKJGDYMF · pith_short_8: BLGXVK7J

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/BLGXVK7JLKJGDYMFKXG7G2WUE2 \
  | 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: 0acd7aabe95a9261e18555cdf36ad4268493ec32c00f2c18d27b9f0aedc6f514

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a72a29af9d1dc63b64a1f395637fe165d1b72941e389cdc4dfcdd7450307aeab",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-10-15T15:39:06Z",
    "title_canon_sha256": "95049417fabf5736cc9030478a6ea11eb2188fe8727ef3738c5a2c8ce11fb17a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3419",
    "kind": "arxiv",
    "version": 2
  }
}