Pith Number

pith:RPKG7LHT

pith:2015:RPKG7LHTQGBDBR7OPCMEVBC3VN

not attested not anchored not stored refs pending

An invariance principle for stochastic series I. Gaussian limits

Lucia Caramellino, Vlad Bally

arxiv:1510.03616 v1 · 2015-10-13 · 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{RPKG7LHTQGBDBR7OPCMEVBC3VN}

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	2026-05-18T01:30:16.675132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8bd46facf3818230c7ee78984a845bab6abb2fd9c963172de3389d2c3f21d3e8

Aliases

arxiv: 1510.03616 · arxiv_version: 1510.03616v1 · doi: 10.48550/arxiv.1510.03616 · pith_short_12: RPKG7LHTQGBD · pith_short_16: RPKG7LHTQGBDBR7O · pith_short_8: RPKG7LHT

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/RPKG7LHTQGBDBR7OPCMEVBC3VN \
  | 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: 8bd46facf3818230c7ee78984a845bab6abb2fd9c963172de3389d2c3f21d3e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6853a6f3647bf91daa07eeb520ab1f895bb4dc79fb476f411ac86c28c48047a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-13T10:33:12Z",
    "title_canon_sha256": "dbd4eeca3e1c908bd322672922c945fe91e25e48dae2a42a9c6124dcdc04cf3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03616",
    "kind": "arxiv",
    "version": 1
  }
}