Pith Number

pith:B3ENOFSL

pith:2018:B3ENOFSLLRP63RYFSS7JTRFDSW

not attested not anchored not stored refs pending

An entropy minimization approach to second-order variational mean-field games

Guillaume Carlier, Jean-David Benamou, Luca Nenna, Simone Di Marino

arxiv:1807.09078 v2 · 2018-07-24 · math.OC · math.AP · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B3ENOFSLLRP63RYFSS7JTRFDSW}

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	2026-05-17T23:49:57.129091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ec8d7164b5c5fedc70594be99c4a395b690223f00e104550862d5427934796d

Aliases

arxiv: 1807.09078 · arxiv_version: 1807.09078v2 · doi: 10.48550/arxiv.1807.09078 · pith_short_12: B3ENOFSLLRP6 · pith_short_16: B3ENOFSLLRP63RYF · pith_short_8: B3ENOFSL

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/B3ENOFSLLRP63RYFSS7JTRFDSW \
  | 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: 0ec8d7164b5c5fedc70594be99c4a395b690223f00e104550862d5427934796d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae0bcb639c2ee2b51ef7041c80626e3788cc33c7a74101d05b8745a85d596a23",
    "cross_cats_sorted": [
      "math.AP",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-07-24T13:04:29Z",
    "title_canon_sha256": "c6e454e7510eab5e639ed3a425f51069cdd271b97366b7e32f1a614f8990c11c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.09078",
    "kind": "arxiv",
    "version": 2
  }
}