Pith Number

pith:F2HWTROU

pith:2012:F2HWTROULNRWKYIN5HUEZBOPH7

not attested not anchored not stored refs pending

Stochastic Maximum Principle for Mean-field Controls and Non-Zero Sum Mean-field Game Problems for Forward-Backward Systems

Liangquan Zhang, Ruimin Xu

arxiv:1207.4326 v1 · 2012-07-18 · 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{F2HWTROULNRWKYIN5HUEZBOPH7}

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	2026-05-18T03:50:47.006157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e8f69c5d45b6365610de9e84c85cf3fda81e80a0f47878ee2306b14316220fa

Aliases

arxiv: 1207.4326 · arxiv_version: 1207.4326v1 · doi: 10.48550/arxiv.1207.4326 · pith_short_12: F2HWTROULNRW · pith_short_16: F2HWTROULNRWKYIN · pith_short_8: F2HWTROU

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/F2HWTROULNRWKYIN5HUEZBOPH7 \
  | 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: 2e8f69c5d45b6365610de9e84c85cf3fda81e80a0f47878ee2306b14316220fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70f65006ba124624c5d22027e54d2febe3dce0a749af04c3678388a171824038",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-07-18T10:17:02Z",
    "title_canon_sha256": "7e2ade9cb6b9197b454c39e0572d15289e4471e81756254456d9dba157f064d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4326",
    "kind": "arxiv",
    "version": 1
  }
}