Pith Number

pith:PIM7CKWX

pith:2026:PIM7CKWXW5SI7LQSXEWORFIRF5

not attested not anchored not stored refs pending

Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization

Hideaki Iiduka, Naoki Sato, Ryusei Yamada

arxiv:2607.08104 v1 · 2026-07-09 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIM7CKWXW5SI7LQSXEWORFIRF5}

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	2026-07-10T01:19:26.118393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a19f12ad7b7648fae12b92ce895112f715136e7c9a8becd2318eca746082b26

Aliases

arxiv: 2607.08104 · arxiv_version: 2607.08104v1 · doi: 10.48550/arxiv.2607.08104 · pith_short_12: PIM7CKWXW5SI · pith_short_16: PIM7CKWXW5SI7LQS · pith_short_8: PIM7CKWX

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/PIM7CKWXW5SI7LQSXEWORFIRF5 \
  | 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: 7a19f12ad7b7648fae12b92ce895112f715136e7c9a8becd2318eca746082b26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d81f954a4d49feef9882815144027919c76e984fea7e9fb800aaaee4006c02b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-09T04:43:25Z",
    "title_canon_sha256": "5d29d96205ac47b30f8efd258f88ed1e0ede37a29340fd5320ea5790aa2824ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08104",
    "kind": "arxiv",
    "version": 1
  }
}