Pith Number

pith:5ZP5LPSC

pith:2014:5ZP5LPSCTLH6YAVY3X6NK2KMZ4

not attested not anchored not stored refs pending

Product Formula, Independence and Asymptotic Moment-Independence for Complex Multiple Wiener-Ito Integrals

Yong Chen

arxiv:1412.1877 v2 · 2014-12-05 · 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{5ZP5LPSCTLH6YAVY3X6NK2KMZ4}

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	2026-05-18T01:01:29.409329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee5fd5be429acfec02b8ddfcd5694ccf3bb8fd4face8b3ae63e8614b8475ad77

Aliases

arxiv: 1412.1877 · arxiv_version: 1412.1877v2 · doi: 10.48550/arxiv.1412.1877 · pith_short_12: 5ZP5LPSCTLH6 · pith_short_16: 5ZP5LPSCTLH6YAVY · pith_short_8: 5ZP5LPSC

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/5ZP5LPSCTLH6YAVY3X6NK2KMZ4 \
  | 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: ee5fd5be429acfec02b8ddfcd5694ccf3bb8fd4face8b3ae63e8614b8475ad77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f48230096ccf505f01b8dd8185c4f7b61dd59b86b77ea971633fe5c0e2997efb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-12-05T01:54:34Z",
    "title_canon_sha256": "0b7fda40dc69e56d51e7550d0b59387a7b941b416c57dd2aa24604a9fe97faed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.1877",
    "kind": "arxiv",
    "version": 2
  }
}