Pith Number

pith:7BIL6ZFN

pith:2019:7BIL6ZFN4AAGVRZZ434EMZ3E4C

not attested not anchored not stored refs pending

On the Sprague-Grundy function of compound games

Endre Boros, Kazuhisa Makino, Levi Kitrossky, Vladimir Gurvich

arxiv:1903.08138 v1 · 2019-03-19 · 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{7BIL6ZFN4AAGVRZZ434EMZ3E4C}

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	2026-05-17T23:50:52.839486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f850bf64ade0006ac739e6f8466764e09afea28975d666a50e0771e4866f2e99

Aliases

arxiv: 1903.08138 · arxiv_version: 1903.08138v1 · doi: 10.48550/arxiv.1903.08138 · pith_short_12: 7BIL6ZFN4AAG · pith_short_16: 7BIL6ZFN4AAGVRZZ · pith_short_8: 7BIL6ZFN

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/7BIL6ZFN4AAGVRZZ434EMZ3E4C \
  | 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: f850bf64ade0006ac739e6f8466764e09afea28975d666a50e0771e4866f2e99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db37c55bfbe496af0f44a156b855fde770bc2613e9d63973a8d851c00bbd3e00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-03-19T17:48:39Z",
    "title_canon_sha256": "3194b2106293a7768666c6da45e1bed5f50f31fc158641a8daa1dfdc47a5e4fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.08138",
    "kind": "arxiv",
    "version": 1
  }
}