Pith Number

pith:Y2FYORXU

pith:2020:Y2FYORXUZX6OTMML6VZ2PZ52RZ

not attested not anchored not stored refs pending

Weak KAM approach to first-order Mean Field Games with state constraints

Cristian Mendico, Kaizhi Wang, Piermarco Cannarsa, Wei Cheng

arxiv:2004.06505 v1 · 2020-04-14 · math.AP · 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{Y2FYORXUZX6OTMML6VZ2PZ52RZ}

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	2026-07-05T05:57:08.579288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c68b8746f4cdfce9b18bf573a7e7ba8e64cbab0a8f7310143d53ae12a725eca4

Aliases

arxiv: 2004.06505 · arxiv_version: 2004.06505v1 · doi: 10.48550/arxiv.2004.06505 · pith_short_12: Y2FYORXUZX6O · pith_short_16: Y2FYORXUZX6OTMML · pith_short_8: Y2FYORXU

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/Y2FYORXUZX6OTMML6VZ2PZ52RZ \
  | 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: c68b8746f4cdfce9b18bf573a7e7ba8e64cbab0a8f7310143d53ae12a725eca4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "984dce7cb0131921b091690c1a2c0a553aab2e4f2966a062b93f9808dcb74e3a",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-04-14T13:48:10Z",
    "title_canon_sha256": "194afdcd617ec874d96e4eeae6f42e4f9a85773d221488a3b92c0589a2ba5b4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.06505",
    "kind": "arxiv",
    "version": 1
  }
}