Pith Number

pith:FP3SXFMR

pith:2025:FP3SXFMREDGFAOC2TTTOPMNRXL

not attested not anchored not stored refs pending

Deep Networks are Reproducing Kernel Chains

Christoph Brune, Len Spek, Tjeerd Jan Heeringa

arxiv:2501.03697 v1 · 2025-01-07 · cs.LG · math.FA · 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{FP3SXFMREDGFAOC2TTTOPMNRXL}

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

2 papers in Pith

Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks

Implicit Bias of Mirror Flow in Homogeneous Neural Networks: Sparse and Dense Feature Learning

Receipt and verification

First computed	2026-07-05T09:57:58.600153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bf72b959120cc50385a9ce6e7b1b1baedc557f4834a11955e3bc1d789255fb5

Aliases

arxiv: 2501.03697 · arxiv_version: 2501.03697v1 · doi: 10.48550/arxiv.2501.03697 · pith_short_12: FP3SXFMREDGF · pith_short_16: FP3SXFMREDGFAOC2 · pith_short_8: FP3SXFMR

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/FP3SXFMREDGFAOC2TTTOPMNRXL \
  | 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: 2bf72b959120cc50385a9ce6e7b1b1baedc557f4834a11955e3bc1d789255fb5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10cb34f2bd1c29012f2e439a11a010eb276692c5da6a3c621f9c7895c4db1738",
    "cross_cats_sorted": [
      "math.FA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-01-07T11:01:24Z",
    "title_canon_sha256": "b54c3d1b2891cb79d352b5a9908424203e695ceb20e0371a713fa52bd82e27e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.03697",
    "kind": "arxiv",
    "version": 1
  }
}