Pith Number

pith:KUMWQOJI

pith:2026:KUMWQOJIFRLUASJQD4XYXIAMDS

not attested not anchored not stored refs pending

On MUON optimization: From non-convergence to an error analysis with Polar Express and the Newton-Schulz polynomial from implementations

Arnulf Jentzen, Steffen Dereich, Thang Do

arxiv:2608.04607 v1 · 2026-08-05 · math.OC · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KUMWQOJIFRLUASJQD4XYXIAMDS}

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	2026-08-06T01:36:15.534135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55196839282c574049301f2f8ba00c1ca9d70951d8c9186c1081bc8b12af2d70

Aliases

arxiv: 2608.04607 · arxiv_version: 2608.04607v1 · doi: 10.48550/arxiv.2608.04607 · pith_short_12: KUMWQOJIFRLU · pith_short_16: KUMWQOJIFRLUASJQ · pith_short_8: KUMWQOJI

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/KUMWQOJIFRLUASJQD4XYXIAMDS \
  | 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: 55196839282c574049301f2f8ba00c1ca9d70951d8c9186c1081bc8b12af2d70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "713f0af45a1b5587ab837e6b87fabfa56480d6a137d39e79dfb81e7a5553ba47",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-05T09:14:22Z",
    "title_canon_sha256": "a6aa22c5695f6a4cb6339fd8c7c0a3eb3c6194c8d17219e981a1cc05300b496a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04607",
    "kind": "arxiv",
    "version": 1
  }
}