Pith Number

pith:UWG3GOJ6

pith:2026:UWG3GOJ64CT46UDUDJ3EM3WQN7

not attested not anchored not stored refs pending

Linear-Quadratic Mean Field Games with Hybrid Local-Global Interactions on Manifolds

Tao Zhang

arxiv:2607.06742 v1 · 2026-07-07 · 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{UWG3GOJ64CT46UDUDJ3EM3WQN7}

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	2026-07-09T00:19:24.947512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a58db3393ee0a7cf50741a76466ed06fe71f958fbfa45c77f0f3e200efb73e2d

Aliases

arxiv: 2607.06742 · arxiv_version: 2607.06742v1 · doi: 10.48550/arxiv.2607.06742 · pith_short_12: UWG3GOJ64CT4 · pith_short_16: UWG3GOJ64CT46UDU · pith_short_8: UWG3GOJ6

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/UWG3GOJ64CT46UDUDJ3EM3WQN7 \
  | 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: a58db3393ee0a7cf50741a76466ed06fe71f958fbfa45c77f0f3e200efb73e2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aafe9904683c942f12dc8e42789a995f494b7e0ae32aa9b4c7ff42feff0c9b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-07T19:12:21Z",
    "title_canon_sha256": "d7d58f20b5532668f57a826f7bc07da5b8d4c4f9b8249c5b2c2ca69354ff9b56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06742",
    "kind": "arxiv",
    "version": 1
  }
}