Pith Number

pith:Z5APCI36

pith:2025:Z5APCI36GCFTML5I6G3GEJZSH6

not attested not anchored not stored refs pending

GrokAlign: Geometric Characterisation and Acceleration of Grokking

Ahmed Imtiaz Humayun, Randall Balestriero, Richard Baraniuk, Thomas Walker

arxiv:2506.12284 v2 · 2025-06-14 · 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{Z5APCI36GCFTML5I6G3GEJZSH6}

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

1 paper in Pith

Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking

Receipt and verification

First computed	2026-07-05T11:45:58.855432Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf40f1237e308b362fa8f1b66227323f9b9b3f251c2b52625e28cf5d0008d3e0

Aliases

arxiv: 2506.12284 · arxiv_version: 2506.12284v2 · doi: 10.48550/arxiv.2506.12284 · pith_short_12: Z5APCI36GCFT · pith_short_16: Z5APCI36GCFTML5I · pith_short_8: Z5APCI36

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/Z5APCI36GCFTML5I6G3GEJZSH6 \
  | 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: cf40f1237e308b362fa8f1b66227323f9b9b3f251c2b52625e28cf5d0008d3e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c639bd53f266edde8703f9479abaaf7aea49cea66826c7aa9e7308196efc21d",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-06-14T00:16:11Z",
    "title_canon_sha256": "568c24baed188311ebf1fdcbb1c36f1c1f2eeae2bb786d784556af121939e7ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.12284",
    "kind": "arxiv",
    "version": 2
  }
}