Pith Number

pith:IOT4FTW2

pith:2023:IOT4FTW23Y3LUWO5Z73ZTAG3TX

not attested not anchored not stored refs pending

The maximum number of cycles in a triangular-grid billiards system with a given perimeter

Honglin Zhu

arxiv:2309.00100 v3 · 2023-08-31 · 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{IOT4FTW23Y3LUWO5Z73ZTAG3TX}

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

Homology in Combinatorial Refraction Billiards

Receipt and verification

First computed	2026-07-05T08:10:17.377716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43a7c2cedade36ba59ddcff79980db9dd0eafb7dbe67b7ced9ab5b229a53dbb7

Aliases

arxiv: 2309.00100 · arxiv_version: 2309.00100v3 · doi: 10.48550/arxiv.2309.00100 · pith_short_12: IOT4FTW23Y3L · pith_short_16: IOT4FTW23Y3LUWO5 · pith_short_8: IOT4FTW2

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/IOT4FTW23Y3LUWO5Z73ZTAG3TX \
  | 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: 43a7c2cedade36ba59ddcff79980db9dd0eafb7dbe67b7ced9ab5b229a53dbb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9ec7d808bc10c5afb22b5ba8e70cf42741184f1fb712b9e99cdc8b8bf70d732",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-08-31T19:39:06Z",
    "title_canon_sha256": "5e92d7cde23e982fcc6add005187fd2501e0543f67232093ade7bd34f34fcddc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.00100",
    "kind": "arxiv",
    "version": 3
  }
}