Pith Number

pith:ROC472EE

pith:2022:ROC472EEIY6M3LNEB6BLQHFXUT

not attested not anchored not stored refs pending

Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability

Adrian Riekert, Arnulf Jentzen, Shokhrukh Ibragimov

arxiv:2212.13111 v2 · 2022-12-26 · 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{ROC472EEIY6M3LNEB6BLQHFXUT}

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	2026-07-05T12:01:17.012676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b85cfe884463ccdada40f82b81cb7a4f1e78159528126b354744a6492f9336e

Aliases

arxiv: 2212.13111 · arxiv_version: 2212.13111v2 · doi: 10.48550/arxiv.2212.13111 · pith_short_12: ROC472EEIY6M · pith_short_16: ROC472EEIY6M3LNE · pith_short_8: ROC472EE

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/ROC472EEIY6M3LNEB6BLQHFXUT \
  | 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: 8b85cfe884463ccdada40f82b81cb7a4f1e78159528126b354744a6492f9336e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "526e363ccdb8f3ec943494178b68b806c18a5b4fe38ea6758a3cb91753d0b4d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2022-12-26T12:29:12Z",
    "title_canon_sha256": "5d045218c247d7eac91ee024e366afd75678ee04c3c2aae840c1f53e596dd1f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.13111",
    "kind": "arxiv",
    "version": 2
  }
}