Pith Number

pith:ZJVQGRWS

pith:2010:ZJVQGRWSHEK4A3MH6IXDMAYHKT

not attested not anchored not stored refs pending

Representation of It\^o Integrals by Lebesgue/Bochner Integrals

Jiongmin Yong, Qi L\"u, Xu Zhang

arxiv:1007.2969 v1 · 2010-07-18 · math.PR · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZJVQGRWSHEK4A3MH6IXDMAYHKT}

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	2026-05-18T01:09:23.775436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca6b0346d23915c06d87f22e36030754d39ab8324bdc8f4bf081c2df91807e3d

Aliases

arxiv: 1007.2969 · arxiv_version: 1007.2969v1 · doi: 10.48550/arxiv.1007.2969 · pith_short_12: ZJVQGRWSHEK4 · pith_short_16: ZJVQGRWSHEK4A3MH · pith_short_8: ZJVQGRWS

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/ZJVQGRWSHEK4A3MH6IXDMAYHKT \
  | 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: ca6b0346d23915c06d87f22e36030754d39ab8324bdc8f4bf081c2df91807e3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49bf76102dcbc97bd6845428b131babe1562713aaefbb20f90d1b3acf3003d79",
    "cross_cats_sorted": [
      "math.FA",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-07-18T03:19:28Z",
    "title_canon_sha256": "c6448fc05f1df98241434aca66bdeda5f883ecbfead8d7e151ad2e7e2b6629ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2969",
    "kind": "arxiv",
    "version": 1
  }
}