Pith Number

pith:C2OJPRZB

pith:2015:C2OJPRZBNXZICOXVG3RDQLHMMR

not attested not anchored not stored refs pending

A Concentration Bound for Stochastic Approximation via Alekseev's Formula

Gugan Thoppe, Vivek S. Borkar

arxiv:1506.08657 v6 · 2015-06-26 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C2OJPRZBNXZICOXVG3RDQLHMMR}

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

Almost Sure Convergence Rates and Concentration of Stochastic Approximation and Reinforcement Learning with Markovian Noise

Receipt and verification

First computed	2026-05-17T23:49:53.434404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

169c97c7216df2813af536e2382cec6463b941b762831bfff90eac25e6e535bf

Aliases

arxiv: 1506.08657 · arxiv_version: 1506.08657v6 · doi: 10.48550/arxiv.1506.08657 · pith_short_12: C2OJPRZBNXZI · pith_short_16: C2OJPRZBNXZICOXV · pith_short_8: C2OJPRZB

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/C2OJPRZBNXZICOXVG3RDQLHMMR \
  | 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: 169c97c7216df2813af536e2382cec6463b941b762831bfff90eac25e6e535bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c017fa9655d7fe399c14dee684485173a40a8fc04dd5c795c511bd197473fd63",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-06-26T15:34:40Z",
    "title_canon_sha256": "6c68a7eebc71e8218bd76fdce7208c3d84478792ac1f62fe48ca95ad68aee8b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.08657",
    "kind": "arxiv",
    "version": 6
  }
}