Pith Number

pith:EKD6VWRI

pith:2019:EKD6VWRIXOPIECT23XB6FJHIED

not attested not anchored not stored refs pending

Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games

Georgios Piliouras, Yun Kuen Cheung

arxiv:1905.08396 v2 · 2019-05-21 · cs.GT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EKD6VWRIXOPIECT23XB6FJHIED}

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.

Cited by

1 paper in Pith

Higher-Order Uncoupled Learning Dynamics and Nash Equilibrium

Receipt and verification

First computed	2026-05-17T23:44:47.198836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2287eada28bb9e820a7addc3e2a4e820fffe56e64762c89064330812cf66471a

Aliases

arxiv: 1905.08396 · arxiv_version: 1905.08396v2 · doi: 10.48550/arxiv.1905.08396 · pith_short_12: EKD6VWRIXOPI · pith_short_16: EKD6VWRIXOPIECT2 · pith_short_8: EKD6VWRI

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/EKD6VWRIXOPIECT23XB6FJHIED \
  | 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: 2287eada28bb9e820a7addc3e2a4e820fffe56e64762c89064330812cf66471a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "544425bd16d3f9e3f82ded6d5907f72f68f3d47f1fe6238328c0132563365b63",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2019-05-21T01:09:44Z",
    "title_canon_sha256": "070de518bf4ff201ee83992ddf894b791d3c9913e0e58b7b146d1730743d748d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.08396",
    "kind": "arxiv",
    "version": 2
  }
}