Pith Number

pith:FKGXOGJJ

pith:2011:FKGXOGJJO26FPL365QRY2BZP7P

not attested not anchored not stored refs pending

Optimal strategies for a game on amenable semigroups

Kent Morrison, Valerio Capraro

arxiv:1104.3098 v3 · 2011-04-15 · cs.GT · math.GR · 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{FKGXOGJJO26FPL365QRY2BZP7P}

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	2026-05-18T01:11:22.006839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a8d77192976bc57af7eec238d072ffbd07924aa5ff411d8f5eefbe0646b6f03

Aliases

arxiv: 1104.3098 · arxiv_version: 1104.3098v3 · doi: 10.48550/arxiv.1104.3098 · pith_short_12: FKGXOGJJO26F · pith_short_16: FKGXOGJJO26FPL36 · pith_short_8: FKGXOGJJ

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/FKGXOGJJO26FPL365QRY2BZP7P \
  | 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: 2a8d77192976bc57af7eec238d072ffbd07924aa5ff411d8f5eefbe0646b6f03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4c03f97ee9225bc2d9cb0f8db7c965da143178d4b8edc566b356c7261b28fd6",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2011-04-15T16:03:59Z",
    "title_canon_sha256": "e81e9ca69ee1afe5e75d1e7c611dda853423f35c4a346627f418b2087839ca60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3098",
    "kind": "arxiv",
    "version": 3
  }
}