Pith Number

pith:YZQ4J4G5

pith:2012:YZQ4J4G5F3HHXU6DARSCHPPQ7Z

not attested not anchored not stored refs pending

Two constructions relating to conjectures of Beck on positional games

Fiachra Knox

arxiv:1212.3345 v1 · 2012-12-13 · 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{YZQ4J4G5F3HHXU6DARSCHPPQ7Z}

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.

Cited by

1 paper in Pith

Stotting in positional games

Receipt and verification

First computed	2026-05-18T03:38:32.479098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c661c4f0dd2ece7bd3c3046423bdf0fe4e8c7fbad39ec0272d135d2e25502fef

Aliases

arxiv: 1212.3345 · arxiv_version: 1212.3345v1 · doi: 10.48550/arxiv.1212.3345 · pith_short_12: YZQ4J4G5F3HH · pith_short_16: YZQ4J4G5F3HHXU6D · pith_short_8: YZQ4J4G5

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/YZQ4J4G5F3HHXU6DARSCHPPQ7Z \
  | 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: c661c4f0dd2ece7bd3c3046423bdf0fe4e8c7fbad39ec0272d135d2e25502fef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8be3e6bc175eee1c2dac0e358e6ffdf2027b4716960ce31c33903c30bdb4b94d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-13T21:11:17Z",
    "title_canon_sha256": "91b537bd81f875af49cf88cd79088baad2017dcb341ef9851ad759ccb1c5ac3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3345",
    "kind": "arxiv",
    "version": 1
  }
}