Pith Number

pith:E4F3FMTE

pith:2026:E4F3FMTEUUPFJE2VFM6N6FG2LC

not attested not anchored not stored refs pending

Sublinearly Structured Deep Neural Networks Achieve Feature Learning Consistency for Compositional Functions

Faming Liang, Sehwan Kim, Yan Sun

arxiv:2606.23477 v1 · 2026-06-22 · stat.ML · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E4F3FMTEUUPFJE2VFM6N6FG2LC}

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	2026-06-23T03:14:20.935818Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

270bb2b264a51e5493552b3cdf14da589ee5ea6cb9768dcfde0db360b523e56e

Aliases

arxiv: 2606.23477 · arxiv_version: 2606.23477v1 · doi: 10.48550/arxiv.2606.23477 · pith_short_12: E4F3FMTEUUPF · pith_short_16: E4F3FMTEUUPFJE2V · pith_short_8: E4F3FMTE

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/E4F3FMTEUUPFJE2VFM6N6FG2LC \
  | 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: 270bb2b264a51e5493552b3cdf14da589ee5ea6cb9768dcfde0db360b523e56e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31fcde721ad256fbeca97e1d6b0c24c90c10d0ad89d75a457df2503b816d6e25",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-06-22T15:24:53Z",
    "title_canon_sha256": "ff594f7320d706fb7a2c64aace608777fe172c66e111b1e5f4fbdb9870bcaffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23477",
    "kind": "arxiv",
    "version": 1
  }
}