Pith Number

pith:HSMR67UJ

pith:2011:HSMR67UJRBQRVKNNLEINGJOBCD

not attested not anchored not stored refs pending

A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations

Jiongmin Yong

arxiv:1110.1564 v1 · 2011-10-07 · math.OC · 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{HSMR67UJRBQRVKNNLEINGJOBCD}

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	2026-05-18T04:11:29.740763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c991f7e8988611aa9ad5910d325c110dcda31db1ade1ad2f3a0f4370f02a96d

Aliases

arxiv: 1110.1564 · arxiv_version: 1110.1564v1 · doi: 10.48550/arxiv.1110.1564 · pith_short_12: HSMR67UJRBQR · pith_short_16: HSMR67UJRBQRVKNN · pith_short_8: HSMR67UJ

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/HSMR67UJRBQRVKNNLEINGJOBCD \
  | 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: 3c991f7e8988611aa9ad5910d325c110dcda31db1ade1ad2f3a0f4370f02a96d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "141bf47c14e8857c7554cd683c4ba9cdb1cfeeb04dfb8adccf93317466c87bfb",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-10-07T15:16:41Z",
    "title_canon_sha256": "d0aa54b3e9995fcc8532857231466c1c117486ce85e71c9c01d1c777a6b10b60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1564",
    "kind": "arxiv",
    "version": 1
  }
}