Pith Number

pith:CFVE2IWK

pith:2005:CFVE2IWKFLCJNS46VFBR2RTKFY

not attested not anchored not stored refs pending

Position play in carom billiards as a Markov process

Mathieu Bouville

arxiv:math/0508089 v5 · 2005-08-04 · math.PR · math.ST · stat.AP · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CFVE2IWKFLCJNS46VFBR2RTKFY}

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	2026-05-18T04:08:35.627213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

116a4d22ca2ac496cb9ea9431d466a2e1774ccf0f34bb9b6942e3afc90723082

Aliases

arxiv: math/0508089 · arxiv_version: math/0508089v5 · doi: 10.48550/arxiv.math/0508089 · pith_short_12: CFVE2IWKFLCJ · pith_short_16: CFVE2IWKFLCJNS46 · pith_short_8: CFVE2IWK

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/CFVE2IWKFLCJNS46VFBR2RTKFY \
  | 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: 116a4d22ca2ac496cb9ea9431d466a2e1774ccf0f34bb9b6942e3afc90723082

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e87d8353ed2be2ba29480edb1065a1c153f73d641ede27fcafbe53a2047a2824",
    "cross_cats_sorted": [
      "math.ST",
      "stat.AP",
      "stat.TH"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-08-04T14:33:52Z",
    "title_canon_sha256": "e557a099725d222ffff0eac5b7a202f8b0c4c2904f41070ff0e6aa0dc267cf28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508089",
    "kind": "arxiv",
    "version": 5
  }
}