Pith Number

pith:BUG7MGQJ

pith:2022:BUG7MGQJLYKV5CLIWW43ADMOED

not attested not anchored not stored refs pending

Upper bound on the number of collisions of pinned billiard balls

Krzysztof Burdzy, Mauricio Duarte

arxiv:2203.09013 v1 · 2022-03-17 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BUG7MGQJLYKV5CLIWW43ADMOED}

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	2026-07-05T04:06:05.931869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d0df61a095e155e8968b5b9b00d8e20cc21d64254c32adc8aa8a8f7fbd396f6

Aliases

arxiv: 2203.09013 · arxiv_version: 2203.09013v1 · doi: 10.48550/arxiv.2203.09013 · pith_short_12: BUG7MGQJLYKV · pith_short_16: BUG7MGQJLYKV5CLI · pith_short_8: BUG7MGQJ

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/BUG7MGQJLYKV5CLIWW43ADMOED \
  | 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: 0d0df61a095e155e8968b5b9b00d8e20cc21d64254c32adc8aa8a8f7fbd396f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "065f0e8c21b6371fd4a4dc757d7139f665da2deb7bce74cbf3b7248525b781a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2022-03-17T01:25:36Z",
    "title_canon_sha256": "444be037d683fa02c9be7085eafedf64365ad41b858cad0008a5a4b7a1ad8e7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.09013",
    "kind": "arxiv",
    "version": 1
  }
}