Pith Number

pith:ZE3RAXVL

pith:2011:ZE3RAXVL3VVQTUUY2L7JXBCFKZ

not attested not anchored not stored refs pending

Winning strategies for aperiodic subtraction games

Alan Guo

arxiv:1108.1239 v2 · 2011-08-05 · 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{ZE3RAXVL3VVQTUUY2L7JXBCFKZ}

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	2026-05-18T04:15:59.155919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c937105eabdd6b09d298d2fe9b8445566d2cc5acb18a855372bd6e27cf4491d9

Aliases

arxiv: 1108.1239 · arxiv_version: 1108.1239v2 · doi: 10.48550/arxiv.1108.1239 · pith_short_12: ZE3RAXVL3VVQ · pith_short_16: ZE3RAXVL3VVQTUUY · pith_short_8: ZE3RAXVL

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/ZE3RAXVL3VVQTUUY2L7JXBCFKZ \
  | 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: c937105eabdd6b09d298d2fe9b8445566d2cc5acb18a855372bd6e27cf4491d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83b96f8b87a3143470b9ec07c8ac3e029584561d0bfc8c297b53f2d49b9c7a5c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-05T02:18:30Z",
    "title_canon_sha256": "e3116ea34941205e1156ff9913ecf2c21d4ca86ffcc2d2e6c21004ca907a490f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1239",
    "kind": "arxiv",
    "version": 2
  }
}