Pith Number

pith:DCXPIFM3

pith:2026:DCXPIFM3OKID4CKGMFPLYCCOKS

not attested not anchored not stored refs pending

Why Muon Outperforms Adam: A Curvature Perspective

Dirk Bergemann, Fengzhuo Zhang, Jiaxiang Li, Shuche Wang, Zhuoran Yang

arxiv:2606.04662 v1 · 2026-06-03 · 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{DCXPIFM3OKID4CKGMFPLYCCOKS}

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	2026-06-04T01:09:23.806967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18aef4159b72903e0946615ebc084e549562527f25e315fbf763707f1f7c5553

Aliases

arxiv: 2606.04662 · arxiv_version: 2606.04662v1 · doi: 10.48550/arxiv.2606.04662 · pith_short_12: DCXPIFM3OKID · pith_short_16: DCXPIFM3OKID4CKG · pith_short_8: DCXPIFM3

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/DCXPIFM3OKID4CKGMFPLYCCOKS \
  | 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: 18aef4159b72903e0946615ebc084e549562527f25e315fbf763707f1f7c5553

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5e97016fa00c44db0d4831d74ba4ab4ad73a3f384e642c7b7784557280486d4",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-03T09:40:30Z",
    "title_canon_sha256": "3a091e6fe2f2ea838c36eb88a992eec7bdb3816ed9cb3f01097a2c91984dee6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04662",
    "kind": "arxiv",
    "version": 1
  }
}