Pith Number

pith:5JCX46F5

pith:2024:5JCX46F5TX24HGZWV37R5WB4VU

not attested not anchored not stored refs pending

Accelerated Objective Gap and Gradient Norm Convergence for Gradient Descent via Long Steps

Alex L. Wang, Benjamin Grimmer, Kevin Shu

arxiv:2403.14045 v4 · 2024-03-20 · 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{5JCX46F5TX24HGZWV37R5WB4VU}

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

Optimization Hyper-parameter Laws for Large Language Models

Receipt and verification

First computed	2026-07-05T08:07:16.024088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea457e78bd9df5c39b36aeff1ed83cad1242ef8eb66447689f4ffc986deccede

Aliases

arxiv: 2403.14045 · arxiv_version: 2403.14045v4 · doi: 10.48550/arxiv.2403.14045 · pith_short_12: 5JCX46F5TX24 · pith_short_16: 5JCX46F5TX24HGZW · pith_short_8: 5JCX46F5

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/5JCX46F5TX24HGZWV37R5WB4VU \
  | 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: ea457e78bd9df5c39b36aeff1ed83cad1242ef8eb66447689f4ffc986deccede

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44c8431a8891f45d913e1d6952beefb9916110ed2727b3354cd71696a4a035c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-03-20T23:57:38Z",
    "title_canon_sha256": "79ab3c2bf27fcf6d79a324fb7078a29952e6509667651a7fa2d2c5c4e26a0302"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2403.14045",
    "kind": "arxiv",
    "version": 4
  }
}