Pith Number

pith:7WXDY6ME

pith:2024:7WXDY6METDSIF2HLDIYUQHTTDZ

not attested not anchored not stored refs pending

Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition

Danica J. Sutherland, Lei Wu, Mohamad Amin Mohamadi, Zhiyuan Li

arxiv:2407.12332 v1 · 2024-07-17 · 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{7WXDY6METDSIF2HLDIYUQHTTDZ}

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

3 papers in Pith

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

Topological Signatures of Grokking

Receipt and verification

First computed	2026-07-05T08:45:03.020215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdae3c798498e482e8eb1a31481e731e583839d4587d060dbadf8ee3e4d31f78

Aliases

arxiv: 2407.12332 · arxiv_version: 2407.12332v1 · doi: 10.48550/arxiv.2407.12332 · pith_short_12: 7WXDY6METDSI · pith_short_16: 7WXDY6METDSIF2HL · pith_short_8: 7WXDY6ME

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/7WXDY6METDSIF2HLDIYUQHTTDZ \
  | 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: fdae3c798498e482e8eb1a31481e731e583839d4587d060dbadf8ee3e4d31f78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd3f286e3c11d5898e820be62ab2aaf792a3e086e0b618b2ede58b016d8fee80",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-07-17T06:15:30Z",
    "title_canon_sha256": "ce53d89f308c52112a6e76df45ca91ff08f7f8602a486853339720d6d8c33ded"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.12332",
    "kind": "arxiv",
    "version": 1
  }
}