Pith Number

pith:7COUNJA2

pith:2025:7COUNJA2VF2C4ARW4ERNUR3YBU

not attested not anchored not stored refs pending

A Note on the Convergence of Muon

Jiaxiang Li, Mingyi Hong

arxiv:2502.02900 v2 · 2025-02-05 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7COUNJA2VF2C4ARW4ERNUR3YBU}

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.

Cited by

17 papers in Pith

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers

LionMuon: Alternating Spectral and Sign Descent for Efficient Training

Convergence of Spectral Descent for Non-smooth Optimization

Anytime Training with Schedule-Free Spectral Optimization

Receipt and verification

First computed	2026-07-05T11:13:19.814600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f89d46a41aa9742e0236e122da47780d2ac3905ac77facad8e45cc2445e7d461

Aliases

arxiv: 2502.02900 · arxiv_version: 2502.02900v2 · doi: 10.48550/arxiv.2502.02900 · pith_short_12: 7COUNJA2VF2C · pith_short_16: 7COUNJA2VF2C4ARW · pith_short_8: 7COUNJA2

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/7COUNJA2VF2C4ARW4ERNUR3YBU \
  | 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: f89d46a41aa9742e0236e122da47780d2ac3905ac77facad8e45cc2445e7d461

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "505b473b018c923106d182d0bc8c316231d52585b1a4f393f5b7029f74e9035d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-02-05T05:44:22Z",
    "title_canon_sha256": "aadbdf3859aadeee1f5c5ef3c8aee283e5877cc09b2861838f91cea02d462d21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.02900",
    "kind": "arxiv",
    "version": 2
  }
}