Pith Number

pith:7OVOS26E

pith:2026:7OVOS26ECPV6T4NJC5NB6OPAQA

not attested not anchored not stored refs pending

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case

Peter Richt\'arik, Xun Qian

arxiv:2606.21581 v1 · 2026-06-19 · 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{7OVOS26ECPV6T4NJC5NB6OPAQA}

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	2026-06-23T01:13:15.307845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbaae96bc413ebe9f1a9175a1f39e08011f70671f0b427dc873a2b1ca16676e6

Aliases

arxiv: 2606.21581 · arxiv_version: 2606.21581v1 · doi: 10.48550/arxiv.2606.21581 · pith_short_12: 7OVOS26ECPV6 · pith_short_16: 7OVOS26ECPV6T4NJ · pith_short_8: 7OVOS26E

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/7OVOS26ECPV6T4NJC5NB6OPAQA \
  | 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: fbaae96bc413ebe9f1a9175a1f39e08011f70671f0b427dc873a2b1ca16676e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "519c3ea2acffdface3215ca57c2ea1fca7c15915d8769dbb2660d1fc3a0c08bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-19T16:36:53Z",
    "title_canon_sha256": "319625040babad1127696e6192c27a45f14bfcef04aba6b702d9b4c5135fc166"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21581",
    "kind": "arxiv",
    "version": 1
  }
}