Pith Number

pith:7S7MHVD5

pith:2026:7S7MHVD5AFM6552OPONA2I4CG6

not attested not anchored not stored refs pending

From Rules to Nash Equilibria: A Lean 4 Case Study in Game-Theoretic Analysis of a Competitive Trading Card Game

Arthur F. Ramos, Tulio Soria

arxiv:2607.08692 v1 · 2026-07-09 · cs.GT · cs.FL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7S7MHVD5AFM6552OPONA2I4CG6}

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	2026-07-10T01:19:57.711914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcbec3d47d0159eef74e7b9a0d23823785fbb2bf8097b65dce9009fc643d159c

Aliases

arxiv: 2607.08692 · arxiv_version: 2607.08692v1 · doi: 10.48550/arxiv.2607.08692 · pith_short_12: 7S7MHVD5AFM6 · pith_short_16: 7S7MHVD5AFM6552O · pith_short_8: 7S7MHVD5

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/7S7MHVD5AFM6552OPONA2I4CG6 \
  | 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: fcbec3d47d0159eef74e7b9a0d23823785fbb2bf8097b65dce9009fc643d159c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f14638d37e18a63a7799c7d4c220f96edfdda0dfcd99f77f5393b79a2bda872b",
    "cross_cats_sorted": [
      "cs.FL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-07-09T16:52:05Z",
    "title_canon_sha256": "75e48aa913cf80ae31cfb9f53b28b5a5629e073cb12e7c19667a5414edc719e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08692",
    "kind": "arxiv",
    "version": 1
  }
}