Pith Number

pith:7PEISJO3

pith:2024:7PEISJO37LJRB3F4HJWO55RKCK

not attested not anchored not stored refs pending

Linear-Quadratic Stackelberg Mean Field Games and Teams with Arbitrary Population Sizes

Bingchang Wang, Jingtao Shi, Wenyu Cong

arxiv:2412.16203 v1 · 2024-12-17 · 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{7PEISJO37LJRB3F4HJWO55RKCK}

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	2026-07-05T09:52:43.005646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbc88925dbfad310ecbc3a6ceef62a129ddfc34b7080d833bf301f176f0c0c31

Aliases

arxiv: 2412.16203 · arxiv_version: 2412.16203v1 · doi: 10.48550/arxiv.2412.16203 · pith_short_12: 7PEISJO37LJR · pith_short_16: 7PEISJO37LJRB3F4 · pith_short_8: 7PEISJO3

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/7PEISJO37LJRB3F4HJWO55RKCK \
  | 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: fbc88925dbfad310ecbc3a6ceef62a129ddfc34b7080d833bf301f176f0c0c31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80aa107c799e5e164b79417be9291f790194a00fda8b197acef365a8213e6a5f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-12-17T06:50:29Z",
    "title_canon_sha256": "be55f73b19c3e7fc65bf36741ac27633c84726c722230247ab6a65751fe0b2fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.16203",
    "kind": "arxiv",
    "version": 1
  }
}