Pith Number

pith:YTTCBNTW

pith:2023:YTTCBNTWFQ7U3SFMDWV3R2SIZS

not attested not anchored not stored refs pending

Boltzmann's Billiard Systems: Computation of the Billiard Mapping and Some Numerical Results

Airi Takeuchi, Lei Zhao, Michael Plum

arxiv:2311.09699 v1 · 2023-11-16 · 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{YTTCBNTWFQ7U3SFMDWV3R2SIZS}

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	2026-07-05T07:13:31.603938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4e620b6762c3f4dc8ac1dabb8ea48ccbc8ebd82f28d7fc4bd6cd401fd918c85

Aliases

arxiv: 2311.09699 · arxiv_version: 2311.09699v1 · doi: 10.48550/arxiv.2311.09699 · pith_short_12: YTTCBNTWFQ7U · pith_short_16: YTTCBNTWFQ7U3SFM · pith_short_8: YTTCBNTW

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/YTTCBNTWFQ7U3SFMDWV3R2SIZS \
  | 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: c4e620b6762c3f4dc8ac1dabb8ea48ccbc8ebd82f28d7fc4bd6cd401fd918c85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1cf00cc11adb54d7618afaee2a80cfb272c4d176c0129654099daa32b46a0a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2023-11-16T09:16:43Z",
    "title_canon_sha256": "a900e67db6226a8279bc9813f6e99a43c9f4a0925e8c5353280bce4b4814bcb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.09699",
    "kind": "arxiv",
    "version": 1
  }
}