Pith Number

pith:K7PPXIPG

pith:2024:K7PPXIPGS4N5IRL5LMQNTETT3E

not attested not anchored not stored refs pending

Decoupled Functional Central Limit Theorems for Two-Time-Scale Stochastic Approximation

Jiadong Liang, Xiang Li, Yuze Han, Zhihua Zhang

arxiv:2412.17070 v5 · 2024-12-22 · math.PR · math.OC · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7PPXIPGS4N5IRL5LMQNTETT3E}

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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

Central Limit Theorems for Asynchronous Averaged Q-Learning

Receipt and verification

First computed	2026-06-30T02:16:49.565542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57defba1e6971bd4457d5b20d99273d92b0c67e72c47498e3a234b940bb833f9

Aliases

arxiv: 2412.17070 · arxiv_version: 2412.17070v5 · doi: 10.48550/arxiv.2412.17070 · pith_short_12: K7PPXIPGS4N5 · pith_short_16: K7PPXIPGS4N5IRL5 · pith_short_8: K7PPXIPG

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/K7PPXIPGS4N5IRL5LMQNTETT3E \
  | 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: 57defba1e6971bd4457d5b20d99273d92b0c67e72c47498e3a234b940bb833f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c1ba84e6e9a52a81d7ea8c1f66e95d0d7767c2b9b2958bab3fa2451737876c7",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-12-22T15:43:01Z",
    "title_canon_sha256": "0d44cc48508e5d858c32b92478ffef1ceff85de03a5bdbfc1da90118772bc183"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.17070",
    "kind": "arxiv",
    "version": 5
  }
}