Pith Number

pith:5YYECY2Y

pith:2010:5YYECY2Y2DNA6KSBLP7ZJCIUQP

not attested not anchored not stored refs pending

General Doubly Stochastic Maximum Principle and Its Applications to Optimal Control of SPDEs

Liangquan Zhang, Yufeng Shi

arxiv:1009.6061 v4 · 2010-09-30 · 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{5YYECY2Y2DNA6KSBLP7ZJCIUQP}

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	2026-05-18T03:41:56.747528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee30416358d0da0f2a415bff94891483c7bbd62540f09ec8e7ee67cd4f5dce1a

Aliases

arxiv: 1009.6061 · arxiv_version: 1009.6061v4 · doi: 10.48550/arxiv.1009.6061 · pith_short_12: 5YYECY2Y2DNA · pith_short_16: 5YYECY2Y2DNA6KSB · pith_short_8: 5YYECY2Y

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/5YYECY2Y2DNA6KSBLP7ZJCIUQP \
  | 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: ee30416358d0da0f2a415bff94891483c7bbd62540f09ec8e7ee67cd4f5dce1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2af2c72fa7661c51d5fd89c5f1b4a764035d8682c4e548785b95491c854ad693",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-09-30T08:17:42Z",
    "title_canon_sha256": "24894d68d20948c76f6d070e89f6858ba459867ab1955198ff248fa6e9b561b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.6061",
    "kind": "arxiv",
    "version": 4
  }
}