Pith Number

pith:2UC5XBY6

pith:2015:2UC5XBY6OAIHDATXW2ZTN7AIQU

not attested not anchored not stored refs pending

Arithmetic and pseudo-arithmetic billiards

Petr Braun

arxiv:1508.02075 v1 · 2015-08-09 · nlin.CD · math.DS · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2UC5XBY6OAIHDATXW2ZTN7AIQU}

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

Semiclassical periodic-orbit theory for quantum spectra

Receipt and verification

First computed	2026-05-18T01:35:34.295761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d505db871e7010718277b6b336fc088507ded114fa9671e68e74e1e6e2091251

Aliases

arxiv: 1508.02075 · arxiv_version: 1508.02075v1 · doi: 10.48550/arxiv.1508.02075 · pith_short_12: 2UC5XBY6OAIH · pith_short_16: 2UC5XBY6OAIHDATX · pith_short_8: 2UC5XBY6

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/2UC5XBY6OAIHDATXW2ZTN7AIQU \
  | 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: d505db871e7010718277b6b336fc088507ded114fa9671e68e74e1e6e2091251

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "558f7c71249fd72fd24ef964c034c0e61fb7ec27924e7c473dfae0e3f65b9950",
    "cross_cats_sorted": [
      "math.DS",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "nlin.CD",
    "submitted_at": "2015-08-09T19:54:34Z",
    "title_canon_sha256": "8a046437509fda7cf7ea6d74da641a2d0b4f31576eeca1e1c7a2c961797e40a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02075",
    "kind": "arxiv",
    "version": 1
  }
}