Pith Number

pith:FANGPAH4

pith:2026:FANGPAH4IOKIVB5IJCX6ANB6V6

not attested not anchored not stored refs pending

GRZO: Group-Relative Zeroth-Order Optimization for Large Language Model Fine-Tuning

Liyan Tan, Ruijie Zhang, Xinling Yu, Yequan Zhao, Yifan Yang, Zheng Zhang

arxiv:2606.02857 v1 · 2026-06-01 · cs.LG · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FANGPAH4IOKIVB5IJCX6ANB6V6}

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	2026-06-03T01:05:24.691168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

281a6780fc43948a87a848afe0343eaf9749565f0fad56caed5c75d7ef909171

Aliases

arxiv: 2606.02857 · arxiv_version: 2606.02857v1 · doi: 10.48550/arxiv.2606.02857 · pith_short_12: FANGPAH4IOKI · pith_short_16: FANGPAH4IOKIVB5I · pith_short_8: FANGPAH4

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/FANGPAH4IOKIVB5IJCX6ANB6V6 \
  | 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: 281a6780fc43948a87a848afe0343eaf9749565f0fad56caed5c75d7ef909171

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd0f099efa7ecdde3a87857a3257d533b88d1ab57035d091d9fd880004a91d5a",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-01T20:19:36Z",
    "title_canon_sha256": "b109dcd71c4caffe70044ca6195fef5bb2c91f6b38a08df3918abdbae937048a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02857",
    "kind": "arxiv",
    "version": 1
  }
}