Pith Number

pith:DICK4HXK

pith:2025:DICK4HXKUYXQT64FU4FNQUADEE

not attested not anchored not stored refs pending

Convergence of First-Order Algorithms with Momentum from the Perspective of an Inexact Gradient Descent Method

Boris Mordukhovich, Dat Ba Tran, Pham Duy Khanh

arxiv:2505.03050 v1 · 2025-05-05 · 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{DICK4HXKUYXQT64FU4FNQUADEE}

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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

Worst-case convergence analysis of relatively inexact gradient descent on smooth convex functions

Receipt and verification

First computed	2026-07-05T10:58:51.848498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a04ae1eeaa62f09fb85a70ad850032139be76836464c97cddecbe395f08f743

Aliases

arxiv: 2505.03050 · arxiv_version: 2505.03050v1 · doi: 10.48550/arxiv.2505.03050 · pith_short_12: DICK4HXKUYXQ · pith_short_16: DICK4HXKUYXQT64F · pith_short_8: DICK4HXK

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/DICK4HXKUYXQT64FU4FNQUADEE \
  | 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: 1a04ae1eeaa62f09fb85a70ad850032139be76836464c97cddecbe395f08f743

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebcbd9e7807d304fab9be2b69ee6db329c1b9e960f114e1b92d9b2ed867e53b7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-05-05T22:13:58Z",
    "title_canon_sha256": "d3bccdcde5f2b55ddff0c1363d09995fb84e2d53a58e696507ffd07d7829bc6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.03050",
    "kind": "arxiv",
    "version": 1
  }
}