Pith Number

pith:ODKPM2G4

pith:2009:ODKPM2G4DGPFZ2KGVJ3X6ODL2D

not attested not anchored not stored refs pending

Conditionally monotone independence I: Independence, additive convolutions and related convolutions

Takahiro Hasebe

arxiv:0907.5473 v4 · 2009-07-31 · 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{ODKPM2G4DGPFZ2KGVJ3X6ODL2D}

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	2026-05-18T03:05:45.269631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70d4f668dc199e5ce946aa777f386bd0dd44def312402dbf53cb55ec453cffeb

Aliases

arxiv: 0907.5473 · arxiv_version: 0907.5473v4 · doi: 10.48550/arxiv.0907.5473 · pith_short_12: ODKPM2G4DGPF · pith_short_16: ODKPM2G4DGPFZ2KG · pith_short_8: ODKPM2G4

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/ODKPM2G4DGPFZ2KGVJ3X6ODL2D \
  | 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: 70d4f668dc199e5ce946aa777f386bd0dd44def312402dbf53cb55ec453cffeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36203937e12a4a40032f10ca140e8173f4bc885ca646647bc4e447b99fa3ac00",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2009-07-31T06:03:15Z",
    "title_canon_sha256": "182e65f0fc77ff27691912f7accb38d7898701002451cd5e8d8cc5620ba8b6f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5473",
    "kind": "arxiv",
    "version": 4
  }
}