Pith Number

pith:G5Z5OBFQ

pith:2012:G5Z5OBFQOPX4YL6OLOIJTOKCQT

not attested not anchored not stored refs pending

Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes

Khalifa Es-Sebaiy, Peggy C\'enac

arxiv:1209.0137 v1 · 2012-09-01 · 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{G5Z5OBFQOPX4YL6OLOIJTOKCQT}

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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	2026-05-18T03:46:29.809537Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3773d704b073efcc2fce5b9099b94284f9c7701243b6549c093e1f0b1f78ecd7

Aliases

arxiv: 1209.0137 · arxiv_version: 1209.0137v1 · doi: 10.48550/arxiv.1209.0137 · pith_short_12: G5Z5OBFQOPX4 · pith_short_16: G5Z5OBFQOPX4YL6O · pith_short_8: G5Z5OBFQ

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/G5Z5OBFQOPX4YL6OLOIJTOKCQT \
  | 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: 3773d704b073efcc2fce5b9099b94284f9c7701243b6549c093e1f0b1f78ecd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09aa9ef085a0f78e48c19a40f0be4dec048e5fcad806ad47d01cd1a6cf09bb9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-01T22:02:01Z",
    "title_canon_sha256": "ca6c5a5ef231064cff6e48f6ddee9e8ddd931bf4111c828ff111b32e6390c0dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0137",
    "kind": "arxiv",
    "version": 1
  }
}