Pith Number

pith:CQ4NHSAS

pith:2026:CQ4NHSAS62NFQZUTGZ6KDO43L4

not attested not anchored not stored refs pending

How Width and Data Shape Generalization Scaling Laws in Quadratic Neural Networks

Emanuele Troiani, Florent Krzakala, Julius Girardin, Lenka Zdeborov\'a, Vittorio Erba, Yizhou Xu

arxiv:2606.28242 v1 · 2026-06-26 · cs.LG · cond-mat.dis-nn · cs.AI · 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{CQ4NHSAS62NFQZUTGZ6KDO43L4}

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	2026-06-29T01:15:10.236204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1438d3c812f69a586693367ca1bb9b5f2a20209da02d0b8b6478ad44ca59b25a

Aliases

arxiv: 2606.28242 · arxiv_version: 2606.28242v1 · doi: 10.48550/arxiv.2606.28242 · pith_short_12: CQ4NHSAS62NF · pith_short_16: CQ4NHSAS62NFQZUT · pith_short_8: CQ4NHSAS

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/CQ4NHSAS62NFQZUTGZ6KDO43L4 \
  | 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: 1438d3c812f69a586693367ca1bb9b5f2a20209da02d0b8b6478ad44ca59b25a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f0c3e701bbdb4f993460fa247cbc4555ea8422cce465a9b7fd2a97272def4d7",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cs.AI",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-26T16:27:46Z",
    "title_canon_sha256": "a5adeaa3fee8824f93b1deb35ecc137206ceaf30851e260a95c1471210ea9909"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28242",
    "kind": "arxiv",
    "version": 1
  }
}