Pith Number

pith:HZGSIR3T

pith:2023:HZGSIR3TTBDYO7NY5F45GMLGCZ

not attested not anchored not stored refs pending

High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance

Krishnakumar Balasubramanian, Promit Ghosal, Ye He

arxiv:2304.00707 v2 · 2023-04-03 · math.PR · math.OC · math.ST · stat.ML · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HZGSIR3TTBDYO7NY5F45GMLGCZ}

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

Homogenization of $\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent

Receipt and verification

First computed	2026-07-05T08:04:02.767937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e4d2447739847877db8e979d331661658e5820feb06252937beb36f69e8b07b

Aliases

arxiv: 2304.00707 · arxiv_version: 2304.00707v2 · doi: 10.48550/arxiv.2304.00707 · pith_short_12: HZGSIR3TTBDY · pith_short_16: HZGSIR3TTBDYO7NY · pith_short_8: HZGSIR3T

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/HZGSIR3TTBDYO7NY5F45GMLGCZ \
  | 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: 3e4d2447739847877db8e979d331661658e5820feb06252937beb36f69e8b07b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f82a24fa01220b11917889f795c0a2e9aa2376b8db4f025d8eca9552eaa6192d",
    "cross_cats_sorted": [
      "math.OC",
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-04-03T03:50:00Z",
    "title_canon_sha256": "454c87845dfba098cf83b87994e9c2556c24e2a76e363d20754327cf0dc8f5c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.00707",
    "kind": "arxiv",
    "version": 2
  }
}