Pith Number

pith:AT4VBOJY

pith:2026:AT4VBOJYJ7PLOPN7ANRDSPO55J

not attested not anchored not stored refs pending

Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer

Aratrika Mustafi, Bharath K. Sriperumbudur, Soumya Mukherjee

arxiv:2605.23871 v1 · 2026-05-22 · stat.ML · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AT4VBOJYJ7PLOPN7ANRDSPO55J}

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	2026-05-25T02:02:36.974156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04f950b9384fdeb73dbf0362393dddea42f418278470f6cae5695a4f5b8db4b0

Aliases

arxiv: 2605.23871 · arxiv_version: 2605.23871v1 · doi: 10.48550/arxiv.2605.23871 · pith_short_12: AT4VBOJYJ7PL · pith_short_16: AT4VBOJYJ7PLOPN7 · pith_short_8: AT4VBOJY

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/AT4VBOJYJ7PLOPN7ANRDSPO55J \
  | 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: 04f950b9384fdeb73dbf0362393dddea42f418278470f6cae5695a4f5b8db4b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95be6c0e279434cb8b618e8e73241792cb2aec36b1b2f55b718a02c5c175afef",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-22T17:28:53Z",
    "title_canon_sha256": "a2a527bc0ca97ffe94709753e7d0645053d142dbffe98aaee2d4672483d7e869"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.23871",
    "kind": "arxiv",
    "version": 1
  }
}