Pith Number

pith:SBV655U5

pith:2026:SBV655U5G6KECBSAOJLJIEXJBZ

not attested not anchored not stored refs pending

Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective

Jianhao Ma, Jiaye Teng, Jinji Yang, Runze Shi, Tianqi Shen, Ziye Ma

arxiv:2606.21514 v1 · 2026-06-19 · 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{SBV655U5G6KECBSAOJLJIEXJBZ}

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	2026-06-23T01:13:13.153783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

906beef69d379441064072569412e90e70cc97bc9e0665f927f5a3b883216881

Aliases

arxiv: 2606.21514 · arxiv_version: 2606.21514v1 · doi: 10.48550/arxiv.2606.21514 · pith_short_12: SBV655U5G6KE · pith_short_16: SBV655U5G6KECBSA · pith_short_8: SBV655U5

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/SBV655U5G6KECBSAOJLJIEXJBZ \
  | 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: 906beef69d379441064072569412e90e70cc97bc9e0665f927f5a3b883216881

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8cc8f14bd72dec7512a18d6ff67572067cee2c84405e90eb30c48f14d0d8959",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-19T15:10:20Z",
    "title_canon_sha256": "17201ac3c37d506a6e587b21a0ea8c2f8d6ba9cdc75216eea27e81e6c252b65c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21514",
    "kind": "arxiv",
    "version": 1
  }
}