Pith Number

pith:WIGEI2EI

pith:2013:WIGEI2EI6PUBHM37FCP5JBVQ3G

not attested not anchored not stored refs pending

Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

Shuguang Zhang, Xiuchun Bi, Zhonghao Zheng

arxiv:1306.0176 v2 · 2013-06-02 · 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{WIGEI2EI6PUBHM37FCP5JBVQ3G}

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	2026-05-18T03:15:44.990460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b20c446888f3e813b37f289fd486b0d99fe0a7e3a1cb0e3303110b4904d16212

Aliases

arxiv: 1306.0176 · arxiv_version: 1306.0176v2 · doi: 10.48550/arxiv.1306.0176 · pith_short_12: WIGEI2EI6PUB · pith_short_16: WIGEI2EI6PUBHM37 · pith_short_8: WIGEI2EI

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/WIGEI2EI6PUBHM37FCP5JBVQ3G \
  | 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: b20c446888f3e813b37f289fd486b0d99fe0a7e3a1cb0e3303110b4904d16212

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c370dafff37f31feb2b5cda444d31100842189d52fe50f3ed791f218e8ad8270",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-06-02T06:35:02Z",
    "title_canon_sha256": "40a971fe1e59f99aa3e975c43d30e211aa7febb886dbf84b4fbc780a94e75b28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0176",
    "kind": "arxiv",
    "version": 2
  }
}