Pith Number

pith:ZZIHLJKM

pith:2026:ZZIHLJKMAUIYKUN7DVMZYNU2K5

not attested not anchored not stored refs pending

A Stochastic--Geometric Theory of Scaling Laws in Grokking

Christian Gagn\'e, Ihsan Ullah, Jonas Ngnaw\'e, Karyn Morrissey, R\'ois\'in Luo

arxiv:2606.30388 v1 · 2026-06-29 · stat.ML · cs.AI · 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{ZZIHLJKMAUIYKUN7DVMZYNU2K5}

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	2026-06-30T02:18:13.018105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce5075a54c05118551bf1d599c369a5740bcda805a1fd82bb53c857e75b1e1a0

Aliases

arxiv: 2606.30388 · arxiv_version: 2606.30388v1 · doi: 10.48550/arxiv.2606.30388 · pith_short_12: ZZIHLJKMAUIY · pith_short_16: ZZIHLJKMAUIYKUN7 · pith_short_8: ZZIHLJKM

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/ZZIHLJKMAUIYKUN7DVMZYNU2K5 \
  | 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: ce5075a54c05118551bf1d599c369a5740bcda805a1fd82bb53c857e75b1e1a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19d75901797b7bdfa4090f50be2cc13ac2918a45054916029cf60e53c57cd085",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-06-29T14:43:02Z",
    "title_canon_sha256": "9f2254e6bcab65c182e4d655b7de648de251b9d86229ca6b03952e62c2f2be8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30388",
    "kind": "arxiv",
    "version": 1
  }
}