Pith Number

pith:3FCIOLPE

pith:2026:3FCIOLPEE73O7BWUSFESJDT6VR

not attested not anchored not stored refs pending

Leveraging Extragradient for Effective Sharpness-Aware Minimization in Deep Learning

Chunxia Zhang, Haishan Ye, Junmin Liu, Yao Fu, Yihang Jin, Yuanao Yang

arxiv:2607.06151 v1 · 2026-07-07 · cs.LG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3FCIOLPEE73O7BWUSFESJDT6VR}

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	2026-07-08T01:18:58.538799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d944872de427f6ef86d49149248e7eac441339c5824c2198770fb66e149d4bc1

Aliases

arxiv: 2607.06151 · arxiv_version: 2607.06151v1 · doi: 10.48550/arxiv.2607.06151 · pith_short_12: 3FCIOLPEE73O · pith_short_16: 3FCIOLPEE73O7BWU · pith_short_8: 3FCIOLPE

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/3FCIOLPEE73O7BWUSFESJDT6VR \
  | 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: d944872de427f6ef86d49149248e7eac441339c5824c2198770fb66e149d4bc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c52efdae8d8e0a0cf803920e6b8247f1195ae1caa38c4c3663d3d618c9881fa",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-07T11:25:46Z",
    "title_canon_sha256": "b110f3661c01719ed51a4e6cd06b64c6a0ca8d52dd4f0d55323383dd7438a06c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06151",
    "kind": "arxiv",
    "version": 1
  }
}