Pith Number

pith:7KNII4V5

pith:2026:7KNII4V5ACBEBX4X7M6ZSFEKTR

not attested not anchored not stored refs pending

Optimal Asymptotic Rates for (Stochastic) Gradient Descent under the Local PL-Condition: A Geometric Approach

Sebastian Kassing, Thomas Kruse

arxiv:2605.14663 v1 · 2026-05-14 · math.OC · math.PR · 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{7KNII4V5ACBEBX4X7M6ZSFEKTR}

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	2026-05-17T23:39:02.174074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa9a8472bd008240df97fb3d99148a9c7370ddded3558bbc7cab7c9d7ec98ec4

Aliases

arxiv: 2605.14663 · arxiv_version: 2605.14663v1 · doi: 10.48550/arxiv.2605.14663 · pith_short_12: 7KNII4V5ACBE · pith_short_16: 7KNII4V5ACBEBX4X · pith_short_8: 7KNII4V5

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/7KNII4V5ACBEBX4X7M6ZSFEKTR \
  | 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: fa9a8472bd008240df97fb3d99148a9c7370ddded3558bbc7cab7c9d7ec98ec4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0642d9ecec0b3300cb122029dfc7b7b44e9c0baf3e78dff65de27d857713f7de",
    "cross_cats_sorted": [
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-14T10:18:21Z",
    "title_canon_sha256": "0428edea11ba77813a3f820c03704e8aacd135846ec5dbc83fd80cbae0f96d9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14663",
    "kind": "arxiv",
    "version": 1
  }
}