Pith Number

pith:VB3E4C7Q

pith:2009:VB3E4C7QDQIYXHQLLVWM62GREG

not attested not anchored not stored refs pending

Periodic billiard trajectories in smooth convex bodies

R.N. Karasev

arxiv:0905.1761 v1 · 2009-05-12 · math.AT · math.DG · 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{VB3E4C7QDQIYXHQLLVWM62GREG}

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	2026-05-18T04:18:53.422069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8764e0bf01c118b9e0b5d6ccf68d121b75e93ae1fe3b51553ccfe80a04561ce

Aliases

arxiv: 0905.1761 · arxiv_version: 0905.1761v1 · doi: 10.48550/arxiv.0905.1761 · pith_short_12: VB3E4C7QDQIY · pith_short_16: VB3E4C7QDQIYXHQL · pith_short_8: VB3E4C7Q

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/VB3E4C7QDQIYXHQLLVWM62GREG \
  | 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: a8764e0bf01c118b9e0b5d6ccf68d121b75e93ae1fe3b51553ccfe80a04561ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d2dc009d1a2f7029b727e0a2030cd15ccc2091b07c0f118390034c47a29a397",
    "cross_cats_sorted": [
      "math.DG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-05-12T05:55:44Z",
    "title_canon_sha256": "47631dd012816fa422a713fbe114a7ab6b919a12ff5794b8135363f11a4763ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.1761",
    "kind": "arxiv",
    "version": 1
  }
}