Pith Number

pith:7K2QE2R2

pith:2024:7K2QE2R2THVVL73MQO7LJ5ABBM

not attested not anchored not stored refs pending

Wide Neural Networks Trained with Weight Decay Provably Exhibit Neural Collapse

Arthur Jacot, Marco Mondelli, Peter S\'uken\'ik, Zihan Wang

arxiv:2410.04887 v1 · 2024-10-07 · cs.LG · math.OC · 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{7K2QE2R2THVVL73MQO7LJ5ABBM}

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

Structure Before Collapse: Transient semantic geometry in next-token prediction

Receipt and verification

First computed	2026-07-05T09:16:57.722678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fab5026a3a99eb55ff6c83beb4f4010b244859b72c720d03a7b7766638da935b

Aliases

arxiv: 2410.04887 · arxiv_version: 2410.04887v1 · doi: 10.48550/arxiv.2410.04887 · pith_short_12: 7K2QE2R2THVV · pith_short_16: 7K2QE2R2THVVL73M · pith_short_8: 7K2QE2R2

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/7K2QE2R2THVVL73MQO7LJ5ABBM \
  | 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: fab5026a3a99eb55ff6c83beb4f4010b244859b72c720d03a7b7766638da935b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "149ab51452a915be5b96ebfe564ea085232f839882c4d344cd553901a0d96aac",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-10-07T10:16:40Z",
    "title_canon_sha256": "25fda723d4aa8621091c1ffe39089ec25f40e86c5adb5be10f25e68e8a7a83ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.04887",
    "kind": "arxiv",
    "version": 1
  }
}