Pith Number

pith:C2KNAYKA

pith:2025:C2KNAYKAWDB3EAFP3H4QFV5K7B

not attested not anchored not stored refs pending

Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking)

Charles London, Clementine C J Domine, Niclas Goring, Seok Hyeong Lee, Seungjai Lee, Wonyl Choi, Yeachan Park, Yoonsoo Nam

arxiv:2502.21009 v2 · 2025-02-28 · stat.ML · cs.LG · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C2KNAYKAWDB3EAFP3H4QFV5K7B}

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

There Will Be a Scientific Theory of Deep Learning

Receipt and verification

First computed	2026-07-05T11:09:45.663681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1694d06140b0c3b200afd9f902d7aaf8520df980df077a3b8ec40cf4c9c9f455

Aliases

arxiv: 2502.21009 · arxiv_version: 2502.21009v2 · doi: 10.48550/arxiv.2502.21009 · pith_short_12: C2KNAYKAWDB3 · pith_short_16: C2KNAYKAWDB3EAFP · pith_short_8: C2KNAYKA

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/C2KNAYKAWDB3EAFP3H4QFV5K7B \
  | 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: 1694d06140b0c3b200afd9f902d7aaf8520df980df077a3b8ec40cf4c9c9f455

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fc9182e163b5f8b30124808577d20fc5efe0e12057fd483759b9e5cefaee726",
    "cross_cats_sorted": [
      "cs.LG",
      "physics.data-an"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-02-28T12:52:11Z",
    "title_canon_sha256": "9be48d887daf1c736dd1b466afc5f1331f412bd1bd712745e9f2fa830f9a3718"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.21009",
    "kind": "arxiv",
    "version": 2
  }
}