Pith Number

pith:LILE3O36

pith:2017:LILE3O36547WXJIJRITLBNA55I

not attested not anchored not stored refs pending

Counting Periodic Trajectories of Finsler Billiards

G\"unter M. Ziegler, Michael Harrison, Pavle V.M. Blagojevi\'c, Serge Tabachnikov

arxiv:1712.07930 v2 · 2017-12-21 · math.DS · math.DG · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LILE3O36547WXJIJRITLBNA55I}

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	2026-07-05T00:52:25.441686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a164dbb7eef3f6ba5098a26b0b41dea3a112be1934c943cdc9c6b089b3608fd

Aliases

arxiv: 1712.07930 · arxiv_version: 1712.07930v2 · doi: 10.48550/arxiv.1712.07930 · pith_short_12: LILE3O36547W · pith_short_16: LILE3O36547WXJIJ · pith_short_8: LILE3O36

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/LILE3O36547WXJIJRITLBNA55I \
  | 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: 5a164dbb7eef3f6ba5098a26b0b41dea3a112be1934c943cdc9c6b089b3608fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a77fa8210c0e39eeb7f9a1cd9eb8a7282682613ae0e6f369c983248f10bc344",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-12-21T13:36:21Z",
    "title_canon_sha256": "1c8e716750610886ab23b6a347149d1956cc60b9ff263e361c1ea18c10a70022"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07930",
    "kind": "arxiv",
    "version": 2
  }
}