Pith Number

pith:65VBXAJ2

pith:2026:65VBXAJ2N42GEUGTUYGEYPHAEK

not attested not anchored not stored refs pending

Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima

Lachlan Ewen MacDonald, Ren\'e Vidal

arxiv:2607.08380 v1 · 2026-07-09 · cs.LG · math.DS · 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{65VBXAJ2N42GEUGTUYGEYPHAEK}

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.

Receipt and verification

First computed	2026-07-10T01:19:48.593930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f76a1b813a6f346250d3a60c4c3ce02293c938c1c414764d9bfa444fe9505e93

Aliases

arxiv: 2607.08380 · arxiv_version: 2607.08380v1 · doi: 10.48550/arxiv.2607.08380 · pith_short_12: 65VBXAJ2N42G · pith_short_16: 65VBXAJ2N42GEUGT · pith_short_8: 65VBXAJ2

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/65VBXAJ2N42GEUGTUYGEYPHAEK \
  | 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: f76a1b813a6f346250d3a60c4c3ce02293c938c1c414764d9bfa444fe9505e93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b4945b6bde0d8976827bd2c8afe40ecf943eb7462e1501f7f0b27c7982dd740",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-09T11:58:44Z",
    "title_canon_sha256": "0bad4c74a9f1b2a90144cefb5d19a957cc966ec2bf4d63a8ec70af24e6dd86e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08380",
    "kind": "arxiv",
    "version": 1
  }
}