Pith Number

pith:LKR7LU7Y

pith:2026:LKR7LU7YBSR3NMJAAKZVBQLK44

not attested not anchored not stored refs pending

Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse

Guido Mont\'ufar, Shuang Liang, Tom Jacobs

arxiv:2607.03613 v1 · 2026-07-03 · 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{LKR7LU7YBSR3NMJAAKZVBQLK44}

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	2026-07-07T02:17:57.470032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5aa3f5d3f80ca3b6b12002b350c16ae720f5d2c050dedcee49a49f04468252b4

Aliases

arxiv: 2607.03613 · arxiv_version: 2607.03613v1 · doi: 10.48550/arxiv.2607.03613 · pith_short_12: LKR7LU7YBSR3 · pith_short_16: LKR7LU7YBSR3NMJA · pith_short_8: LKR7LU7Y

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/LKR7LU7YBSR3NMJAAKZVBQLK44 \
  | 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: 5aa3f5d3f80ca3b6b12002b350c16ae720f5d2c050dedcee49a49f04468252b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e78e89f6d0e1cdb97596da68cec9efa32b5bb32677a8aa4267a68a68998a8eb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-03T22:03:13Z",
    "title_canon_sha256": "1772e42cf24d4fe1bb0478613b7027822502ef4f5aea671a8028d3aa5caf8bc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03613",
    "kind": "arxiv",
    "version": 1
  }
}