Pith Number

pith:W4JVQ3RA

pith:2026:W4JVQ3RAM7EHHMIBEVN64VKDLL

not attested not anchored not stored refs pending

The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks

Eitan Gronich, Gal Vardi

arxiv:2602.16340 v3 · 2026-02-18 · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4JVQ3RAM7EHHMIBEVN64VKDLL}

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

2 papers in Pith

Convergence of Spectral Descent for Non-smooth Optimization

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

Receipt and verification

First computed	2026-05-26T01:03:25.555034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b713586e2067c873b101255bee55435afbbb2c674d0a13a4043588cbfa1ce179

Aliases

arxiv: 2602.16340 · arxiv_version: 2602.16340v3 · doi: 10.48550/arxiv.2602.16340 · pith_short_12: W4JVQ3RAM7EH · pith_short_16: W4JVQ3RAM7EHHMIB · pith_short_8: W4JVQ3RA

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/W4JVQ3RAM7EHHMIBEVN64VKDLL \
  | 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: b713586e2067c873b101255bee55435afbbb2c674d0a13a4043588cbfa1ce179

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aff8fd30733152405ac5eea2f574b759fba6d2e1abf24aca4dff4f8fb395f03d",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-02-18T10:25:07Z",
    "title_canon_sha256": "77999e7dca449a26457d7817214516f3d8a2b366e518e26fc4eace031f243a20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.16340",
    "kind": "arxiv",
    "version": 3
  }
}