Pith Number

pith:ZMGFG6CH

pith:2025:ZMGFG6CHNYSY6JP3HKJCGERLE3

not attested not anchored not stored refs pending

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer

Arnulf Jentzen, Philippe von Wurstemberger, Steffen Dereich, Thang Do

arxiv:2511.06675 v2 · 2025-11-10 · math.OC · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZMGFG6CHNYSY6JP3HKJCGERLE3}

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	2026-06-23T03:13:51.142441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb0c5378476e258f25fb3a9223122b26f793eb57cf1855afc876641593227314

Aliases

arxiv: 2511.06675 · arxiv_version: 2511.06675v2 · doi: 10.48550/arxiv.2511.06675 · pith_short_12: ZMGFG6CHNYSY · pith_short_16: ZMGFG6CHNYSY6JP3 · pith_short_8: ZMGFG6CH

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/ZMGFG6CHNYSY6JP3HKJCGERLE3 \
  | 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: cb0c5378476e258f25fb3a9223122b26f793eb57cf1855afc876641593227314

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eda5c38bd9b9347012e32bae4e258617c3c4ad2a6b91abc33937cd5a4fc86e7c",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-11-10T03:45:32Z",
    "title_canon_sha256": "c1cc4d2f2b929e8b9647da03aa410e7ceeb2fc5df3a1390dfec7128193efab24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.06675",
    "kind": "arxiv",
    "version": 2
  }
}