Pith Number

pith:ZW5XEE23

pith:2025:ZW5XEE23LILEQUNTBC3LYIY3ZJ

not attested not anchored not stored refs pending

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods

Aleksandr Beznosikov, Aleksandr Bogdanov, Andrey Veprikov, Arman Bolatov, Martin Tak\'a\v{c}, Samuel Horv\'ath, Slavomir Hanzely

arxiv:2510.10777 v3 · 2025-10-12 · cs.LG · 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{ZW5XEE23LILEQUNTBC3LYIY3ZJ}

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

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

LionMuon: Alternating Spectral and Sign Descent for Efficient Training

Receipt and verification

First computed	2026-05-20T00:02:57.195309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdbb72135b5a164851b308b6bc231bca738ef0c76b8d84526d718d21cb1329fd

Aliases

arxiv: 2510.10777 · arxiv_version: 2510.10777v3 · doi: 10.48550/arxiv.2510.10777 · pith_short_12: ZW5XEE23LILE · pith_short_16: ZW5XEE23LILEQUNT · pith_short_8: ZW5XEE23

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/ZW5XEE23LILEQUNTBC3LYIY3ZJ \
  | 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: cdbb72135b5a164851b308b6bc231bca738ef0c76b8d84526d718d21cb1329fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f5f734ce898b52a1d7a8e1fc8878df44b49110137e60b6bd1acb5f5664f685e",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-10-12T19:39:41Z",
    "title_canon_sha256": "e8a2e9c2b92013e968543a044cbbad37dd2fecec485ff140d5735a893971085f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.10777",
    "kind": "arxiv",
    "version": 3
  }
}