Pith Number

pith:XJPAXKUJ

pith:2020:XJPAXKUJW6GZKAW4X5UEU6BID2

not attested not anchored not stored refs pending

Direction Matters: On the Implicit Bias of Stochastic Gradient Descent with Moderate Learning Rate

Difan Zou, Jingfeng Wu, Quanquan Gu, Vladimir Braverman

arxiv:2011.02538 v2 · 2020-11-04 · cs.LG · 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{XJPAXKUJW6GZKAW4X5UEU6BID2}

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	2026-07-05T02:26:51.422023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba5e0baa89b78d9502dcbf684a78281eae35e0eb8f2a143ac019755f4b44f341

Aliases

arxiv: 2011.02538 · arxiv_version: 2011.02538v2 · doi: 10.48550/arxiv.2011.02538 · pith_short_12: XJPAXKUJW6GZ · pith_short_16: XJPAXKUJW6GZKAW4 · pith_short_8: XJPAXKUJ

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/XJPAXKUJW6GZKAW4X5UEU6BID2 \
  | 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: ba5e0baa89b78d9502dcbf684a78281eae35e0eb8f2a143ac019755f4b44f341

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19f30146ef21e31acf0b0b1a8c79eb2832a50a306dd590eaa1a504889368812e",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2020-11-04T21:07:52Z",
    "title_canon_sha256": "ff3941d2be95109b2b8f86d2301239c0b02bec50358e24f4ac0587b7ed9414db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.02538",
    "kind": "arxiv",
    "version": 2
  }
}