Pith Number

pith:UQMKRGHK

pith:2026:UQMKRGHKTCAIIJJXUB2B2AK6C2

not attested not anchored not stored refs pending

Spectral Scaling Laws of Muon

Asuman Ozdaglar, Gagik Magakyan, Pablo Parrilo

arxiv:2606.04058 v1 · 2026-06-02 · 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{UQMKRGHKTCAIIJJXUB2B2AK6C2}

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	2026-06-04T00:06:45.427329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a418a898ea9880842537a0741d015e168163697b2fe2bb002c24bff8b5635402

Aliases

arxiv: 2606.04058 · arxiv_version: 2606.04058v1 · doi: 10.48550/arxiv.2606.04058 · pith_short_12: UQMKRGHKTCAI · pith_short_16: UQMKRGHKTCAIIJJX · pith_short_8: UQMKRGHK

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/UQMKRGHKTCAIIJJXUB2B2AK6C2 \
  | 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: a418a898ea9880842537a0741d015e168163697b2fe2bb002c24bff8b5635402

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3935044129e1ecced379abdbed057afc6c83ad7235bb655d0d7a5dc23073950a",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-02T11:31:21Z",
    "title_canon_sha256": "a9dabddca531c694290d49f91c6da2c78a0f34bf5f02e8a3b13818a901e88298"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04058",
    "kind": "arxiv",
    "version": 1
  }
}