Pith Number

pith:ZPKT2ZYA

pith:2023:ZPKT2ZYAAISEBO2JUOJ3KUQSGJ

not attested not anchored not stored refs pending

Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult

Molei Tao, Tuo Zhao, Yuqing Wang, Zhenghao Xu

arxiv:2310.17087 v2 · 2023-10-26 · cs.LG · math.DS · math.OC · 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{ZPKT2ZYAAISEBO2JUOJ3KUQSGJ}

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

Convergence of Gradient Descent for General Neural Network Architectures Beyond the NTK Regime

SGD at the Edge of Stability: The Stochastic Sharpness Gap

Receipt and verification

First computed	2026-07-05T07:23:09.128752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbd53d6700022440bb49a393b55212327ba67221f0bf050005bb47613d7a083a

Aliases

arxiv: 2310.17087 · arxiv_version: 2310.17087v2 · doi: 10.48550/arxiv.2310.17087 · pith_short_12: ZPKT2ZYAAISE · pith_short_16: ZPKT2ZYAAISEBO2J · pith_short_8: ZPKT2ZYA

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/ZPKT2ZYAAISEBO2JUOJ3KUQSGJ \
  | 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: cbd53d6700022440bb49a393b55212327ba67221f0bf050005bb47613d7a083a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c6dbe9148db167553df6d23c4e16084280b2f467b9f31bc91e54c8f22a26faa",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2023-10-26T01:11:17Z",
    "title_canon_sha256": "2df60af4059079e2275083c1ce70dd52fa207375d82c9e37f6d6fdfa0f243ec3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.17087",
    "kind": "arxiv",
    "version": 2
  }
}