Pith Number

pith:V4VMICRG

pith:2026:V4VMICRG5QROBF5YOQ7V45UVHS

not attested not anchored not stored refs pending

Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics

Bingcong Li, Liang Zhang, Niao He, Yudong Wei

arxiv:2606.31390 v1 · 2026-06-30 · 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{V4VMICRG5QROBF5YOQ7V45UVHS}

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	2026-07-01T01:18:01.661188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af2ac40a26ec22e097b8743f5e76953caa97ed943ef70f83b51cc4005caa84ca

Aliases

arxiv: 2606.31390 · arxiv_version: 2606.31390v1 · doi: 10.48550/arxiv.2606.31390 · pith_short_12: V4VMICRG5QRO · pith_short_16: V4VMICRG5QROBF5Y · pith_short_8: V4VMICRG

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/V4VMICRG5QROBF5YOQ7V45UVHS \
  | 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: af2ac40a26ec22e097b8743f5e76953caa97ed943ef70f83b51cc4005caa84ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69cf0bbba6f0ee5a3797b20f00ed2fe29701778cee67e6b930a4a572f689c90c",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-30T09:19:16Z",
    "title_canon_sha256": "12f5a085c98fc9c4fdf7b29ef8a407a5c9f9809ad04a274408f4c2943076d17e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31390",
    "kind": "arxiv",
    "version": 1
  }
}