Pith Number

pith:FZKC3V4P

pith:2023:FZKC3V4PNY63LKJS2EBUY5UKFF

not attested not anchored not stored refs pending

A Theory of First Order Mean Field Type Control Problems and their Equations

Alain Bensoussan, Hongwei Yuan, Sheung Chi Phillip Yam, Tak Kwong Wong

arxiv:2305.11848 v2 · 2023-05-19 · math.OC · math.AP · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FZKC3V4PNY63LKJS2EBUY5UKFF}

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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.

Cited by

1 paper in Pith

On Mean Field Monotonicity Conditions from Control Theoretical Perspective

Receipt and verification

First computed	2026-07-05T06:50:55.276132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e542dd78f6e3db5a932d1034c768a29700afc73a8ed0cd0dc6d6299d0726302

Aliases

arxiv: 2305.11848 · arxiv_version: 2305.11848v2 · doi: 10.48550/arxiv.2305.11848 · pith_short_12: FZKC3V4PNY63 · pith_short_16: FZKC3V4PNY63LKJS · pith_short_8: FZKC3V4P

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/FZKC3V4PNY63LKJS2EBUY5UKFF \
  | 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: 2e542dd78f6e3db5a932d1034c768a29700afc73a8ed0cd0dc6d6299d0726302

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5fea9fef493752eb2af460962bb2cedf22beaed891394c98d6b8145738dae5f",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2023-05-19T17:40:40Z",
    "title_canon_sha256": "890b6f0c4108c8e3e967e324c0d53479e8741f416eb79bf00fa390acd5285a2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2305.11848",
    "kind": "arxiv",
    "version": 2
  }
}