Pith Number

pith:24WJS6F4

pith:2026:24WJS6F4ZP4AOGOAPJ3U7I2ZP7

not attested not anchored not stored refs pending

A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning

Sunyoung An, Xiaoming Huo

arxiv:2606.17364 v1 · 2026-06-15 · math.ST · math.OC · 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{24WJS6F4ZP4AOGOAPJ3U7I2ZP7}

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	2026-06-19T16:10:10.270291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d72c9978bccbf80719c07a774fa3597feadb7c19417da92ec00ad2969fde970d

Aliases

arxiv: 2606.17364 · arxiv_version: 2606.17364v1 · doi: 10.48550/arxiv.2606.17364 · pith_short_12: 24WJS6F4ZP4A · pith_short_16: 24WJS6F4ZP4AOGOA · pith_short_8: 24WJS6F4

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/24WJS6F4ZP4AOGOAPJ3U7I2ZP7 \
  | 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: d72c9978bccbf80719c07a774fa3597feadb7c19417da92ec00ad2969fde970d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1824216b8b4f892de5f6ee223ebbe02c50b633d8dd0bb01754bd6ec3f56820ef",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-06-15T23:43:49Z",
    "title_canon_sha256": "86b945916f6add069d8d9ab877168332055bcc1efff062bdfe4b1a1a17792315"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17364",
    "kind": "arxiv",
    "version": 1
  }
}