Pith Number

pith:IBQUSMZN

pith:2023:IBQUSMZNIJLHFTAZGZBKEIS3ES

not attested not anchored not stored refs pending

Type-II Saddles and Probabilistic Stability of Stochastic Gradient Descent

Botao Li, Liu Ziyin, Masahito Ueda, Tomer Galanti

arxiv:2303.13093 v4 · 2023-03-23 · cs.LG · math.OC · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IBQUSMZNIJLHFTAZGZBKEIS3ES}

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

1 paper in Pith

Zeroth-Order Optimization at the Edge of Stability

Receipt and verification

First computed	2026-07-05T08:38:51.466384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

406149332d425672cc193642a2225b24bc1ec4f67a4645efc77ddc6be6e4db95

Aliases

arxiv: 2303.13093 · arxiv_version: 2303.13093v4 · doi: 10.48550/arxiv.2303.13093 · pith_short_12: IBQUSMZNIJLH · pith_short_16: IBQUSMZNIJLHFTAZ · pith_short_8: IBQUSMZN

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/IBQUSMZNIJLHFTAZGZBKEIS3ES \
  | 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: 406149332d425672cc193642a2225b24bc1ec4f67a4645efc77ddc6be6e4db95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7942b6b2b0ac2a64d058611b9a218a83d443cea5d742d49794464cdfad60d337",
    "cross_cats_sorted": [
      "math.OC",
      "physics.data-an"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-03-23T08:17:10Z",
    "title_canon_sha256": "9723070454e588154ad6d4aafc5217e916d1c82896a2160d9e1bc90116da83c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.13093",
    "kind": "arxiv",
    "version": 4
  }
}