Pith Number

pith:P4AFMYCX

pith:2012:P4AFMYCXIFXTXDXMJQFR3P3IFI

not attested not anchored not stored refs pending

A vector-valued almost sure invariance principle for Sinai billiards with random scatterers

Mikko Stenlund

arxiv:1210.0902 v3 · 2012-10-02 · math.DS · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4AFMYCXIFXTXDXMJQFR3P3IFI}

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	2026-05-18T03:21:10.546943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f00566057416f3b8eec4c0b1dbf682a37ebdad55443f39ed9635962da8e4e12

Aliases

arxiv: 1210.0902 · arxiv_version: 1210.0902v3 · doi: 10.48550/arxiv.1210.0902 · pith_short_12: P4AFMYCXIFXT · pith_short_16: P4AFMYCXIFXTXDXM · pith_short_8: P4AFMYCX

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/P4AFMYCXIFXTXDXMJQFR3P3IFI \
  | 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: 7f00566057416f3b8eec4c0b1dbf682a37ebdad55443f39ed9635962da8e4e12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05bd4b230dd020185f4e1bced42bc9b624b15cb74bbb21a342779dbf6f4ac8f0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-02T20:00:01Z",
    "title_canon_sha256": "444d946901353e65d1837eec8795a3c7db4d013cf29f33350d6e49b5782cfc56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0902",
    "kind": "arxiv",
    "version": 3
  }
}