Pith Number

pith:ZQB6A3M6

pith:2025:ZQB6A3M6TWJUYNZVELCXPMHVTK

not attested not anchored not stored refs pending

Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries

James P. Bailey, Taemin Kim

arxiv:2507.11366 v2 · 2025-07-15 · cs.GT · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZQB6A3M6TWJUYNZVELCXPMHVTK}

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	2026-06-19T16:10:30.452039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc03e06d9e9d934c373522c577b0f59a907a73b8620ed75868b1080fa0ac3f18

Aliases

arxiv: 2507.11366 · arxiv_version: 2507.11366v2 · doi: 10.48550/arxiv.2507.11366 · pith_short_12: ZQB6A3M6TWJU · pith_short_16: ZQB6A3M6TWJUYNZV · pith_short_8: ZQB6A3M6

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/ZQB6A3M6TWJUYNZVELCXPMHVTK \
  | 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: cc03e06d9e9d934c373522c577b0f59a907a73b8620ed75868b1080fa0ac3f18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c2614cd582b438bf09f7406cd66c2ed7e930769350a1882bdb675669a769d51",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2025-07-15T14:39:40Z",
    "title_canon_sha256": "a0a823688936410f2e778b87cc01630a5f0e0501747319db1a520db05b6fd8ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.11366",
    "kind": "arxiv",
    "version": 2
  }
}