Pith Number

pith:5UUMSU3A

pith:2017:5UUMSU3AYPNBVLVURWL7MJSBEM

not attested not anchored not stored refs pending

On ergodicity of foliations on $\mathbb{Z}^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses

Krzysztof Fr\k{a}czek, Martin Schmoll

arxiv:1708.05550 v1 · 2017-08-18 · math.DS · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UUMSU3AYPNBVLVURWL7MJSBEM}

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	2026-05-18T00:09:20.017959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed28c95360c3da1aaeb48d97f626412315cb01537c0e4ff88c1c0c01372f79f9

Aliases

arxiv: 1708.05550 · arxiv_version: 1708.05550v1 · doi: 10.48550/arxiv.1708.05550 · pith_short_12: 5UUMSU3AYPNB · pith_short_16: 5UUMSU3AYPNBVLVU · pith_short_8: 5UUMSU3A

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/5UUMSU3AYPNBVLVURWL7MJSBEM \
  | 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: ed28c95360c3da1aaeb48d97f626412315cb01537c0e4ff88c1c0c01372f79f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f26af02b8255e5cde7959faad25be2f4997017aefa8af8f8091ed33d9a2dc95",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-08-18T10:00:57Z",
    "title_canon_sha256": "2fe855a869d861cee4cad8500045d6247f1d1ac18b6d34fab6f236c95972329d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.05550",
    "kind": "arxiv",
    "version": 1
  }
}