Pith Number

pith:3PX4HOAB

pith:2012:3PX4HOABE77VWOGR5YTEOXEUGU

not attested not anchored not stored refs pending

Two variants of Wythoff's game preserving its P-positions

Nhan Bao Ho

arxiv:1202.3186 v4 · 2012-02-15 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3PX4HOABE77VWOGR5YTEOXEUGU}

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	2026-05-18T04:00:28.064190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbefc3b80127ff5b38d1ee26475c94353ec91aaa4ea6f2ac1d9dea826a85603a

Aliases

arxiv: 1202.3186 · arxiv_version: 1202.3186v4 · doi: 10.48550/arxiv.1202.3186 · pith_short_12: 3PX4HOABE77V · pith_short_16: 3PX4HOABE77VWOGR · pith_short_8: 3PX4HOAB

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/3PX4HOABE77VWOGR5YTEOXEUGU \
  | 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: dbefc3b80127ff5b38d1ee26475c94353ec91aaa4ea6f2ac1d9dea826a85603a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6aa1f7313d646c11149efc4289b43bc084a106a845742cb0bbbf5d8567fb0d00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-15T01:47:01Z",
    "title_canon_sha256": "e126b0a468cff333daf9e69497b0b72ffec6c1ddbd2e57d417d5a35fb3430daa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3186",
    "kind": "arxiv",
    "version": 4
  }
}