Pith Number

pith:B5E63NMU

pith:2026:B5E63NMUJXXY7UWJAUOXEIB7EE

not attested not anchored not stored refs pending

Generalization in Deep Neural Networks: Minimax Rates for Gradient Methods

Junyu Zhou, Marius Kloft, Puyu Wang, Yiming Ying, Yunwen Lei

arxiv:2606.06772 v1 · 2026-06-04 · stat.ML · cs.AI · 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{B5E63NMUJXXY7UWJAUOXEIB7EE}

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	2026-06-08T01:04:27.544149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f49edb5944def8fd2c9051d72203f210b3fe515dbc48a50abc08f4607ca6b18

Aliases

arxiv: 2606.06772 · arxiv_version: 2606.06772v1 · doi: 10.48550/arxiv.2606.06772 · pith_short_12: B5E63NMUJXXY · pith_short_16: B5E63NMUJXXY7UWJ · pith_short_8: B5E63NMU

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/B5E63NMUJXXY7UWJAUOXEIB7EE \
  | 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: 0f49edb5944def8fd2c9051d72203f210b3fe515dbc48a50abc08f4607ca6b18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6a992db1bab891c498fc593856479a4b3baf0a9a3f3a41638441e635d08d5e1",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-06-04T23:31:52Z",
    "title_canon_sha256": "e7bb9a83c2a9f7497fcdf9509871b11645cc5b4ab906e74a0025da53f257e625"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06772",
    "kind": "arxiv",
    "version": 1
  }
}