Pith Number

pith:45JLQWAB

pith:2011:45JLQWABNNNBVEDUJGAHP63EXG

not attested not anchored not stored refs pending

The Theory of Stochastic Pseudo-differential Operators and Its Applications, I

Xu Liu, Xu Zhang

arxiv:1103.0138 v1 · 2011-03-01 · math.AP · 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{45JLQWABNNNBVEDUJGAHP63EXG}

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	2026-05-18T04:27:37.273708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e752b858016b5a1a9074498077fb64b995fcf6e2991b35bbab8a13c681080a3b

Aliases

arxiv: 1103.0138 · arxiv_version: 1103.0138v1 · doi: 10.48550/arxiv.1103.0138 · pith_short_12: 45JLQWABNNNB · pith_short_16: 45JLQWABNNNBVEDU · pith_short_8: 45JLQWAB

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/45JLQWABNNNBVEDUJGAHP63EXG \
  | 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: e752b858016b5a1a9074498077fb64b995fcf6e2991b35bbab8a13c681080a3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efcc1d011f0c138bc38e344467916bbff6f3c93e27a30f1f6eeca3ebeb859f11",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-03-01T11:20:44Z",
    "title_canon_sha256": "9db1a75a4138e2c1997ebce2089ff46cd40e432547be3a13c8536f12c3e3b04c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0138",
    "kind": "arxiv",
    "version": 1
  }
}