Pith Number

pith:7OV5SJGE

pith:2012:7OV5SJGEOUTZYM4HDMBRQINBXO

not attested not anchored not stored refs pending

Weak convergence of self-normalized partial sums processes

Mikl\'os Cs\"org\H{o}, Zhishui Hu

arxiv:1204.2074 v2 · 2012-04-10 · 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{7OV5SJGEOUTZYM4HDMBRQINBXO}

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	2026-05-18T03:20:32.914954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbabd924c475279c33871b031821a1bbb97a550d5dd5dddbb7c682142b4181a5

Aliases

arxiv: 1204.2074 · arxiv_version: 1204.2074v2 · doi: 10.48550/arxiv.1204.2074 · pith_short_12: 7OV5SJGEOUTZ · pith_short_16: 7OV5SJGEOUTZYM4H · pith_short_8: 7OV5SJGE

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/7OV5SJGEOUTZYM4HDMBRQINBXO \
  | 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: fbabd924c475279c33871b031821a1bbb97a550d5dd5dddbb7c682142b4181a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8850b6a2f1aca6a0bfe2497ce43cc49aa62d6b48492ead943d6b1129584abeb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-10T08:09:56Z",
    "title_canon_sha256": "173915e627a6ad5091aef12f9750aafce7a36db288662207030b76be2f25b937"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2074",
    "kind": "arxiv",
    "version": 2
  }
}