Pith Number

pith:V3I4UKLK

pith:2011:V3I4UKLKVSASEKEW5HF73367MR

not attested not anchored not stored refs pending

Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space

Matthew F. Brown, Viacheslav P. Belavkin

arxiv:1112.0159 v1 · 2011-12-01 · math-ph · math.MP · math.QA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V3I4UKLKVSASEKEW5HF73367MR}

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	2026-05-18T04:07:16.755203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aed1ca296aac81222896e9cbfdefdf6462cfb1d9496ca0d6114b26291c3dc580

Aliases

arxiv: 1112.0159 · arxiv_version: 1112.0159v1 · doi: 10.48550/arxiv.1112.0159 · pith_short_12: V3I4UKLKVSAS · pith_short_16: V3I4UKLKVSASEKEW · pith_short_8: V3I4UKLK

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/V3I4UKLKVSASEKEW5HF73367MR \
  | 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: aed1ca296aac81222896e9cbfdefdf6462cfb1d9496ca0d6114b26291c3dc580

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d1c74182d9e967ba253b4e5e9c03a57bd6f3c1044522c5a21614361d77a9e30",
    "cross_cats_sorted": [
      "math.MP",
      "math.QA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-12-01T12:36:56Z",
    "title_canon_sha256": "5140a82ff3530b94a84e14f82babcc3b8b89b8d78d69f04db2a28cd50f20e50a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0159",
    "kind": "arxiv",
    "version": 1
  }
}