Pith Number

pith:D5ZPEWGM

pith:2019:D5ZPEWGM2QBMBO6HHIVYFGEFRU

not attested not anchored not stored refs pending

Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT

Andreas Anastasiou, Krishnakumar Balasubramanian, Murat A. Erdogdu

arxiv:1904.02130 v1 · 2019-04-03 · math.ST · math.OC · math.PR · stat.ML · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D5ZPEWGM2QBMBO6HHIVYFGEFRU}

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	2026-05-17T23:49:28.399061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f72f258ccd402c0bbc73a2b8298858d33220bee5b245f30d84a4c88d485d22d

Aliases

arxiv: 1904.02130 · arxiv_version: 1904.02130v1 · doi: 10.48550/arxiv.1904.02130 · pith_short_12: D5ZPEWGM2QBM · pith_short_16: D5ZPEWGM2QBMBO6H · pith_short_8: D5ZPEWGM

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/D5ZPEWGM2QBMBO6HHIVYFGEFRU \
  | 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: 1f72f258ccd402c0bbc73a2b8298858d33220bee5b245f30d84a4c88d485d22d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edc5810ea13ed4c19883e355edc7cf08dc78263f6668898ac000f7cf5f4c249f",
    "cross_cats_sorted": [
      "math.OC",
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2019-04-03T17:47:46Z",
    "title_canon_sha256": "af842c80245fb440b26c3094c6136605574a93b87bb398194c78f98275322e67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.02130",
    "kind": "arxiv",
    "version": 1
  }
}