Pith Number

pith:EVLECKW4

pith:2011:EVLECKW4UAKCW6QKXO4N44FPH2

not attested not anchored not stored refs pending

Non-ergodic Z-periodic billiards and infinite translation surfaces

Corinna Ulcigrai, Krzysztof Fr\k{a}czek

arxiv:1109.4584 v1 · 2011-09-21 · 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{EVLECKW4UAKCW6QKXO4N44FPH2}

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	2026-05-18T04:12:34.414761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2556412adca0142b7a0abbb8de70af3eb145b66cf31858531cf28142909a10d8

Aliases

arxiv: 1109.4584 · arxiv_version: 1109.4584v1 · doi: 10.48550/arxiv.1109.4584 · pith_short_12: EVLECKW4UAKC · pith_short_16: EVLECKW4UAKCW6QK · pith_short_8: EVLECKW4

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/EVLECKW4UAKCW6QKXO4N44FPH2 \
  | 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: 2556412adca0142b7a0abbb8de70af3eb145b66cf31858531cf28142909a10d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d59fb3fbcd53ff74942cbaa3236ecc48112615c1c780cdd98d4800487584bc66",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-09-21T16:48:06Z",
    "title_canon_sha256": "8d5cac36230c9f45aaffdbe72cb2f9a498d59d14738f13f657c1b955582048d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4584",
    "kind": "arxiv",
    "version": 1
  }
}