Pith Number

pith:SOFVN6HY

pith:2021:SOFVN6HYRLZT7YX2K7MFZ2QRFS

not attested not anchored not stored refs pending

NG+ : A Multi-Step Matrix-Product Natural Gradient Method for Deep Learning

Dong Xu, Minghan Yang, Pengxiang Xu, Qiwen Cui, Zaiwen Wen

arxiv:2106.07454 v1 · 2021-06-14 · math.OC · cs.AI · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SOFVN6HYRLZT7YX2K7MFZ2QRFS}

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	2026-07-05T02:49:05.382774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

938b56f8f88af33fe2fa57d85cea112c9bbaa5427cb040c2d4fe3461b0844e97

Aliases

arxiv: 2106.07454 · arxiv_version: 2106.07454v1 · doi: 10.48550/arxiv.2106.07454 · pith_short_12: SOFVN6HYRLZT · pith_short_16: SOFVN6HYRLZT7YX2 · pith_short_8: SOFVN6HY

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/SOFVN6HYRLZT7YX2K7MFZ2QRFS \
  | 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: 938b56f8f88af33fe2fa57d85cea112c9bbaa5427cb040c2d4fe3461b0844e97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77f2dfb5a4d9d6a514cfa5825f3b2949fdb7cfcdb0adeb57396b9b8f6e05ac85",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-06-14T14:31:31Z",
    "title_canon_sha256": "febd7f6a1ae6088fc0b1a13f527b19628014d1cab4a3a35fd65e8aced747d4a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.07454",
    "kind": "arxiv",
    "version": 1
  }
}