Pith Number

pith:JOTBNY6C

pith:2016:JOTBNY6C5GMLHXLVRZPVCSZBFW

not attested not anchored not stored refs pending

A weak approximation with asymptotic expansion and multidimensional Malliavin weights

Akihiko Takahashi, Toshihiro Yamada

arxiv:1605.01243 v1 · 2016-05-04 · 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{JOTBNY6C5GMLHXLVRZPVCSZBFW}

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	2026-05-18T01:15:37.388116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ba616e3c2e998b3dd758e5f514b212daabb8af0beb85137fc15bfa47f59a1da

Aliases

arxiv: 1605.01243 · arxiv_version: 1605.01243v1 · doi: 10.48550/arxiv.1605.01243 · pith_short_12: JOTBNY6C5GML · pith_short_16: JOTBNY6C5GMLHXLV · pith_short_8: JOTBNY6C

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/JOTBNY6C5GMLHXLVRZPVCSZBFW \
  | 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: 4ba616e3c2e998b3dd758e5f514b212daabb8af0beb85137fc15bfa47f59a1da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb07fbe380dbebb0f3ac6a58a4215898fa4d8fa940c7b47e85c434185fb9b009",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-05-04T12:15:49Z",
    "title_canon_sha256": "f8e0c381ae7c13083e9259031c072c8958819a8d60caff848e726ca6f2062458"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.01243",
    "kind": "arxiv",
    "version": 1
  }
}