Pith Number

pith:B3E3XSEJ

pith:2012:B3E3XSEJGQ3V3A7NJIRXNHKL5M

not attested not anchored not stored refs pending

Ergodic directions for billiards in a strip with periodically located obstacles

Corinna Ulcigrai, Krzysztof Fraczek

arxiv:1208.5212 v1 · 2012-08-26 · 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{B3E3XSEJGQ3V3A7NJIRXNHKL5M}

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	2026-05-18T01:54:58.107967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ec9bbc88934375d83ed4a23769d4beb06ca8ed3b243878ffa7d9e6512ce35e1

Aliases

arxiv: 1208.5212 · arxiv_version: 1208.5212v1 · doi: 10.48550/arxiv.1208.5212 · pith_short_12: B3E3XSEJGQ3V · pith_short_16: B3E3XSEJGQ3V3A7N · pith_short_8: B3E3XSEJ

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/B3E3XSEJGQ3V3A7NJIRXNHKL5M \
  | 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: 0ec9bbc88934375d83ed4a23769d4beb06ca8ed3b243878ffa7d9e6512ce35e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a61102cf2216cdfa27a5d67a109dc7760b10d2ed64701e86042705e6177313a7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-08-26T10:21:21Z",
    "title_canon_sha256": "ed472089048ec63c0eba439d36ad28d288696a4ca26483d3ea76d7b57435e926"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5212",
    "kind": "arxiv",
    "version": 1
  }
}