Pith Number

pith:G55AMEKK

pith:2026:G55AMEKKT5A64BW5RJJOGBLQFM

not attested not anchored not stored refs pending

Central limit theorem for the averaged Adam optimizer

Arnulf Jentzen, Steffen Dereich

arxiv:2606.21433 v1 · 2026-06-19 · math.PR · cs.LG · math.ST · 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{G55AMEKKT5A64BW5RJJOGBLQFM}

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	2026-06-23T01:13:10.020719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

377a06114a9f41ee06dd8a52e305702b20cdd5cd8372d344815f7ae923f55f4e

Aliases

arxiv: 2606.21433 · arxiv_version: 2606.21433v1 · doi: 10.48550/arxiv.2606.21433 · pith_short_12: G55AMEKKT5A6 · pith_short_16: G55AMEKKT5A64BW5 · pith_short_8: G55AMEKK

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/G55AMEKKT5A64BW5RJJOGBLQFM \
  | 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: 377a06114a9f41ee06dd8a52e305702b20cdd5cd8372d344815f7ae923f55f4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2ec36b03b2254286f7ecdc531feec8d7c5c787e6e95a1654da7cecaa7bcfe7c",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-19T13:49:42Z",
    "title_canon_sha256": "0f0cbc1f131a74e3a70c65447867ca458fd7e34f08fc5d84b77e762ea4a8a22f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21433",
    "kind": "arxiv",
    "version": 1
  }
}