Pith Number

pith:46PGWHUO

pith:2010:46PGWHUOMKQ5DC7CAVQ4W24FRJ

not attested not anchored not stored refs pending

On the multiplicity of non-iterated periodic billiard trajectories

Marco Mazzucchelli

arxiv:1012.5593 v3 · 2010-12-27 · math.DS · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{46PGWHUOMKQ5DC7CAVQ4W24FRJ}

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	2026-05-18T04:10:58.741662Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e79e6b1e8e62a1d18be20561cb6b858a752126e4be7803b049518db67692b2d6

Aliases

arxiv: 1012.5593 · arxiv_version: 1012.5593v3 · doi: 10.48550/arxiv.1012.5593 · pith_short_12: 46PGWHUOMKQ5 · pith_short_16: 46PGWHUOMKQ5DC7C · pith_short_8: 46PGWHUO

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/46PGWHUOMKQ5DC7CAVQ4W24FRJ \
  | 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: e79e6b1e8e62a1d18be20561cb6b858a752126e4be7803b049518db67692b2d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b78f079def4cc7a90aa36ece658dc8f719b16928ecbb91bc8eddc5dbda35b23a",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-12-27T11:14:19Z",
    "title_canon_sha256": "78de20cb45013a5c08200ba410332634f23770abedf15f9ed3824aeb78d45529"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5593",
    "kind": "arxiv",
    "version": 3
  }
}