Pith Number

pith:ERTVQSU4

pith:2025:ERTVQSU4UEYSWIOKMI3MD4SGUX

not attested not anchored not stored refs pending

Scaling Laws for Gradient Descent and Sign Descent for Linear Bigram Models under Zipf's Law

Francis Bach, Frederik Kunstner

arxiv:2505.19227 v1 · 2025-05-25 · cs.LG · 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{ERTVQSU4UEYSWIOKMI3MD4SGUX}

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

2 papers in Pith

Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory

Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data

Receipt and verification

First computed	2026-07-05T11:09:26.728726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2467584a9ca1312b21ca6236c1f246a5c27df86b7791ffb4854780c84b5b9294

Aliases

arxiv: 2505.19227 · arxiv_version: 2505.19227v1 · doi: 10.48550/arxiv.2505.19227 · pith_short_12: ERTVQSU4UEYS · pith_short_16: ERTVQSU4UEYSWIOK · pith_short_8: ERTVQSU4

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/ERTVQSU4UEYSWIOKMI3MD4SGUX \
  | 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: 2467584a9ca1312b21ca6236c1f246a5c27df86b7791ffb4854780c84b5b9294

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47ac04ab56cac7634661dd5a1d28f3ffd04ed865b015a61fa74ce2315cef1e6b",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-05-25T16:43:51Z",
    "title_canon_sha256": "f2f4e9cef2198697e0e22f5c18f3ebef5b32e3b6d19691a6e686222c3faec435"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19227",
    "kind": "arxiv",
    "version": 1
  }
}