Pith Number

pith:MVDDDZSA

pith:2026:MVDDDZSA6BVAKTC6DXQ437BSPK

not attested not anchored not stored refs pending

Graphon Mean Field Game of mutual holding

Daorong Cui, Shuoqing Deng, Yang Xiang

arxiv:2606.28254 v1 · 2026-06-26 · 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{MVDDDZSA6BVAKTC6DXQ437BSPK}

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	2026-06-29T01:15:10.474291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

654631e640f06a054c5e1de1cdfc327abfdd9a50e03a2c824f1853ab741aaa54

Aliases

arxiv: 2606.28254 · arxiv_version: 2606.28254v1 · doi: 10.48550/arxiv.2606.28254 · pith_short_12: MVDDDZSA6BVA · pith_short_16: MVDDDZSA6BVAKTC6 · pith_short_8: MVDDDZSA

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/MVDDDZSA6BVAKTC6DXQ437BSPK \
  | 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: 654631e640f06a054c5e1de1cdfc327abfdd9a50e03a2c824f1853ab741aaa54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb3d6cbc67d5d55b8d78fc2cd561dd35e6a8bab97ae0bfe7086834aeceda4eb9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-26T16:40:55Z",
    "title_canon_sha256": "b2427571eeab6978a35175954956e056887e601b86f0ef586a6c7afdcebfc258"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28254",
    "kind": "arxiv",
    "version": 1
  }
}