Pith Number

pith:AEOYIWDF

pith:2011:AEOYIWDFD77HQHXBQSVDFDKKJ7

not attested not anchored not stored refs pending

Limit theorems for stochastic approximation algorithms

Henrik Renlund

arxiv:1102.4741 v1 · 2011-02-23 · 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{AEOYIWDFD77HQHXBQSVDFDKKJ7}

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.

Cited by

1 paper in Pith

Moderate Deviation Principle for a Stochastic Approximation Process

Receipt and verification

First computed	2026-05-18T04:28:07.441876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

011d8458651ffe781ee184aa328d4a4fd1b825c21d4e6636692bcbd801187a4d

Aliases

arxiv: 1102.4741 · arxiv_version: 1102.4741v1 · doi: 10.48550/arxiv.1102.4741 · pith_short_12: AEOYIWDFD77H · pith_short_16: AEOYIWDFD77HQHXB · pith_short_8: AEOYIWDF

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/AEOYIWDFD77HQHXBQSVDFDKKJ7 \
  | 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: 011d8458651ffe781ee184aa328d4a4fd1b825c21d4e6636692bcbd801187a4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78e861c91453d1dca07c49bef67568369c1e49a59bdf24f09d3467a6f5861b75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-23T14:02:31Z",
    "title_canon_sha256": "41ae4db8981fac326c020347f3cf035737053a5a477ae6c6012424251cb7a2e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4741",
    "kind": "arxiv",
    "version": 1
  }
}