Pith Number

pith:IR5EHIZ5

pith:2011:IR5EHIZ5O5MHN7PVUSIPH2TTNX

not attested not anchored not stored refs pending

Three-Period Orbits in Billiards on the Surfaces of Constant Curvature

Joe Nance, Ki Yeun Kim, Vadim Zharnitsky, Victoria Blumen

arxiv:1108.0987 v2 · 2011-08-04 · 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{IR5EHIZ5O5MHN7PVUSIPH2TTNX}

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	2026-05-18T04:09:56.136683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

447a43a33d775876fdf5a490f3ea736de18df7128b76f59e68fabba9e80a96ad

Aliases

arxiv: 1108.0987 · arxiv_version: 1108.0987v2 · doi: 10.48550/arxiv.1108.0987 · pith_short_12: IR5EHIZ5O5MH · pith_short_16: IR5EHIZ5O5MHN7PV · pith_short_8: IR5EHIZ5

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/IR5EHIZ5O5MHN7PVUSIPH2TTNX \
  | 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: 447a43a33d775876fdf5a490f3ea736de18df7128b76f59e68fabba9e80a96ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76f44033391aa84cd424dde614a632b0730a3cdcc60036282c11834a9d40abb2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-04T02:57:45Z",
    "title_canon_sha256": "a017e34834ac87983e6cbaa4a5a4c7e1f91a415a4c942f7bf771464309579611"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0987",
    "kind": "arxiv",
    "version": 2
  }
}