Pith Number

pith:DBFWZROY

pith:2025:DBFWZROY5MWZG6COPMWL4W7U6V

not attested not anchored not stored refs pending

Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization

Alexander Vinogradov, Alexey Kravatskiy, Daniil Merkulov, Ivan Kozyrev, Ivan Oseledets, Nikolai Kozlov

arxiv:2512.09678 v2 · 2025-12-10 · math.OC · cs.AI · 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{DBFWZROY5MWZG6COPMWL4W7U6V}

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

Anytime Training with Schedule-Free Spectral Optimization

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

Receipt and verification

First computed	2026-06-23T03:13:52.307746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

184b6cc5d8eb2d93784e7b2cbe5bf4f55576a6db0eb44e4c5a9b1c2966ae175c

Aliases

arxiv: 2512.09678 · arxiv_version: 2512.09678v2 · doi: 10.48550/arxiv.2512.09678 · pith_short_12: DBFWZROY5MWZ · pith_short_16: DBFWZROY5MWZG6CO · pith_short_8: DBFWZROY

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/DBFWZROY5MWZG6COPMWL4W7U6V \
  | 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: 184b6cc5d8eb2d93784e7b2cbe5bf4f55576a6db0eb44e4c5a9b1c2966ae175c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ca3a3398946a01c8cad33f9060da04f5621794b8f33b5c5aa5a847968406bec",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-12-10T14:25:45Z",
    "title_canon_sha256": "68a57a3086f1574151bcb9b3b608bb2b74ec4e984ef9f03ec061c86e99c818f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.09678",
    "kind": "arxiv",
    "version": 2
  }
}