Pith Number

pith:TDRBGDVS

pith:2009:TDRBGDVSVDFETT4VKCGL7OG3Y6

not attested not anchored not stored refs pending

Conditionally monotone independence II: Multiplicative convolutions and infinite divisibility

Takahiro Hasebe

arxiv:0910.1319 v3 · 2009-10-07 · 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{TDRBGDVSVDFETT4VKCGL7OG3Y6}

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	2026-05-18T03:05:45.256114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98e2130eb2a8ca49cf95508cbfb8dbc7ae38a1c088e601dd493427f74f85998b

Aliases

arxiv: 0910.1319 · arxiv_version: 0910.1319v3 · doi: 10.48550/arxiv.0910.1319 · pith_short_12: TDRBGDVSVDFE · pith_short_16: TDRBGDVSVDFETT4V · pith_short_8: TDRBGDVS

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/TDRBGDVSVDFETT4VKCGL7OG3Y6 \
  | 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: 98e2130eb2a8ca49cf95508cbfb8dbc7ae38a1c088e601dd493427f74f85998b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "293fef4bf4be5d8b71e6d10cbe37696cb3a21e8d095a0c91d7ee37d643df440f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-10-07T17:10:37Z",
    "title_canon_sha256": "1c01f52311f7cd7c0fee7ea08f3b67d6f9f5237bdff9e175fb4724d5ce7bcf4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.1319",
    "kind": "arxiv",
    "version": 3
  }
}