Pith Number

pith:IL642OS3

pith:2026:IL642OS3LJC2BPPS6S67XRY54Q

not attested not anchored not stored refs pending

In-Expectation Convergence of Stochastic Gradient Methods under Heavy-Tailed Noise

Zijian Liu

arxiv:2606.00520 v1 · 2026-05-30 · math.OC · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IL642OS3LJC2BPPS6S67XRY54Q}

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	2026-06-02T01:03:57.109031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42fdcd3a5b5a45a0bdf2f4bdfbc71de432e0f48884bf49a93c3f949db756bd55

Aliases

arxiv: 2606.00520 · arxiv_version: 2606.00520v1 · doi: 10.48550/arxiv.2606.00520 · pith_short_12: IL642OS3LJC2 · pith_short_16: IL642OS3LJC2BPPS · pith_short_8: IL642OS3

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/IL642OS3LJC2BPPS6S67XRY54Q \
  | 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: 42fdcd3a5b5a45a0bdf2f4bdfbc71de432e0f48884bf49a93c3f949db756bd55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e63ee07c0b553120164bbc7326ec87eb410304846f1dc50ea4fbbea243110ac3",
    "cross_cats_sorted": [
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-30T04:27:47Z",
    "title_canon_sha256": "b267953960e9d94f647d7d42e4c8f3d7610f26c1219914f364cd6809b4b38f4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.00520",
    "kind": "arxiv",
    "version": 1
  }
}