Pith Number

pith:VYYDH6T3

pith:2026:VYYDH6T3KJTEWVQQRWWV5KSL5R

not attested not anchored not stored refs pending

Optimal Rates for Generalization of Gradient Descent Methods with Deep Neural Networks

Ding-Xuan Zhou, Junyu Zhou, Puyu Wang, Yiming Ying, Yunwen Lei

arxiv:2606.06764 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{VYYDH6T3KJTEWVQQRWWV5KSL5R}

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	2026-06-08T01:04:27.200750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae3033fa7b52664b56108dad5eaa4bec436ba5e1caec9e62165b44a0726c962c

Aliases

arxiv: 2606.06764 · arxiv_version: 2606.06764v1 · doi: 10.48550/arxiv.2606.06764 · pith_short_12: VYYDH6T3KJTE · pith_short_16: VYYDH6T3KJTEWVQQ · pith_short_8: VYYDH6T3

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/VYYDH6T3KJTEWVQQRWWV5KSL5R \
  | 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: ae3033fa7b52664b56108dad5eaa4bec436ba5e1caec9e62165b44a0726c962c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ac8740213bba18f79f4ed5c3fb0285d9dca934c19ff401c278e5ea34aa7506a",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-06-04T23:04:49Z",
    "title_canon_sha256": "209cbd35c7ce28c2ad3a598f42fde5bf26094bcfb0da604556fe8d01cd0afbb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06764",
    "kind": "arxiv",
    "version": 1
  }
}