Pith Number

pith:HNL4SXOS

pith:2023:HNL4SXOSQEFIOUXMCEFOHL6WZM

not attested not anchored not stored refs pending

Grokking in Linear Estimators -- A Solvable Model that Groks without Understanding

Alon Beck, Noam Levi, Yohai Bar-Sinai

arxiv:2310.16441 v1 · 2023-10-25 · stat.ML · cond-mat.dis-nn · cs.LG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HNL4SXOSQEFIOUXMCEFOHL6WZM}

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

5 papers in Pith

Statistical Properties of Training & Generalization

Noise-Driven Escape from Metastable Phases explains Grokking in Deep Neural Networks

Statistical Properties of Training & Generalization

Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent

Receipt and verification

First computed	2026-07-05T07:40:58.148396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b57c95dd2810a8752ec110ae3afd6cb3911487a12883de69b8751d0d23d8a24

Aliases

arxiv: 2310.16441 · arxiv_version: 2310.16441v1 · doi: 10.48550/arxiv.2310.16441 · pith_short_12: HNL4SXOSQEFI · pith_short_16: HNL4SXOSQEFIOUXM · pith_short_8: HNL4SXOS

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/HNL4SXOSQEFIOUXMCEFOHL6WZM \
  | 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: 3b57c95dd2810a8752ec110ae3afd6cb3911487a12883de69b8751d0d23d8a24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faa62c54dedd59d9528eaca1d33a86149319046b926d75da7027c8f68a874361",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cs.LG",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2023-10-25T08:08:44Z",
    "title_canon_sha256": "9889d638e0682d309227d50ff93e61c7504f50feb83c548c315070c4fa4f063d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.16441",
    "kind": "arxiv",
    "version": 1
  }
}