Pith Number

pith:GSZ5RTIK

pith:2026:GSZ5RTIKK45NOQQLQGUVUVEAKT

not attested not anchored not stored refs pending

Optimal Play, Nontransitivity, and Nash Equilibria in Dice Bingo

Benjamin W. Ong, David J. Hemmer

arxiv:2606.20744 v1 · 2026-06-17 · math.HO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GSZ5RTIKK45NOQQLQGUVUVEAKT}

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	2026-06-23T00:11:55.324010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34b3d8cd0a573ad7420b81a95a548054c956c87849a9c6aa1e8ce806e7c40b2c

Aliases

arxiv: 2606.20744 · arxiv_version: 2606.20744v1 · doi: 10.48550/arxiv.2606.20744 · pith_short_12: GSZ5RTIKK45N · pith_short_16: GSZ5RTIKK45NOQQL · pith_short_8: GSZ5RTIK

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/GSZ5RTIKK45NOQQLQGUVUVEAKT \
  | 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: 34b3d8cd0a573ad7420b81a95a548054c956c87849a9c6aa1e8ce806e7c40b2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18f85a3af6e3b838277deec2a43a9e5dc71664071d7e7772cfa8826e3700d4f9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2026-06-17T21:44:49Z",
    "title_canon_sha256": "8bf4fa073f0c3a981743c3a4a4453e14ee2fc172fa9befd0efc5419d2f36045a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.20744",
    "kind": "arxiv",
    "version": 1
  }
}