Pith Number

pith:XXUSS5MZ

pith:2024:XXUSS5MZFH6DKIX4MMCJFZIE3C

not attested not anchored not stored refs pending

A Proof of the Exact Convergence Rate of Gradient Descent

Jungbin Kim

arxiv:2412.04427 v2 · 2024-12-05 · 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{XXUSS5MZFH6DKIX4MMCJFZIE3C}

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

A Theory of Composition and Duality of Extremal Optimal Fixed-Point Algorithms

Receipt and verification

First computed	2026-07-05T10:39:24.068085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bde929759929fc3522fc630492e504d8a4737ebdf8c9f0b7a630df9b48fd54d6

Aliases

arxiv: 2412.04427 · arxiv_version: 2412.04427v2 · doi: 10.48550/arxiv.2412.04427 · pith_short_12: XXUSS5MZFH6D · pith_short_16: XXUSS5MZFH6DKIX4 · pith_short_8: XXUSS5MZ

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/XXUSS5MZFH6DKIX4MMCJFZIE3C \
  | 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: bde929759929fc3522fc630492e504d8a4737ebdf8c9f0b7a630df9b48fd54d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd5a56d718cb3fd87097fd22f1eae4c1d779884be6ecdee508cfd2c324feb00a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-12-05T18:51:26Z",
    "title_canon_sha256": "d99332bbaff480be899dc04aa93ea4bbdd165481e5742d81b41f7c51b16affcc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.04427",
    "kind": "arxiv",
    "version": 2
  }
}