Pith Number

pith:MSN5M7KN

pith:2016:MSN5M7KN5BXSQ4IC5UMCCXS23E

not attested not anchored not stored refs pending

Optimal control and zero-sum stochastic differential game problems of mean-field type

Boualem Djehiche, Said Hamad\`ene

arxiv:1603.06071 v3 · 2016-03-19 · math.PR · 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{MSN5M7KN5BXSQ4IC5UMCCXS23E}

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	2026-05-18T00:39:47.880378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6

Aliases

arxiv: 1603.06071 · arxiv_version: 1603.06071v3 · doi: 10.48550/arxiv.1603.06071 · pith_short_12: MSN5M7KN5BXS · pith_short_16: MSN5M7KN5BXSQ4IC · pith_short_8: MSN5M7KN

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/MSN5M7KN5BXSQ4IC5UMCCXS23E \
  | 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: 649bd67d4de86f287102ed18215e5ad92549303fb62872174247370779a0cce6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a39ad9acdcc4c5ffc53e4c3da8c21e4cb1a37d93ffd8323a6f4118ffa38e0cd",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-19T09:52:43Z",
    "title_canon_sha256": "bcee541fff9a3ff670b1f009087a515af1ddd0c135f1fe30792ddcd7db6c5f6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06071",
    "kind": "arxiv",
    "version": 3
  }
}