Pith Number

pith:PKP6RABQ

pith:2006:PKP6RABQLFTNCPPN3CVHWWBZJF

not attested not anchored not stored refs pending

Billiards in a general domain with random reflections

Francis Comets, Gunter Sch\"utz, Marina Vachkovskaia, Serguei Popov

arxiv:math/0612799 v4 · 2006-12-27 · math.PR · 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{PKP6RABQLFTNCPPN3CVHWWBZJF}

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	2026-05-18T04:03:32.895000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a9fe880305966d13dedd8aa7b5839496463d75d55a52af410dd928fc88c4402

Aliases

arxiv: math/0612799 · arxiv_version: math/0612799v4 · doi: 10.48550/arxiv.math/0612799 · pith_short_12: PKP6RABQLFTN · pith_short_16: PKP6RABQLFTNCPPN · pith_short_8: PKP6RABQ

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/PKP6RABQLFTNCPPN3CVHWWBZJF \
  | 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: 7a9fe880305966d13dedd8aa7b5839496463d75d55a52af410dd928fc88c4402

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a325e15b0bdfcb125e27cbb3f52a5bd155e083a1b649092a18a161d2144c818",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2006-12-27T21:03:05Z",
    "title_canon_sha256": "475cdb1355003588b021e91d1a194b61c07971190a498c021f0628bb8f54e75f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612799",
    "kind": "arxiv",
    "version": 4
  }
}