Pith Number

pith:3BSJMQ6H

pith:2026:3BSJMQ6HQCHBMQH764JH7TI5XH

not attested not anchored not stored refs pending

Singular perturbations and hierarchical learning in two-layer neural networks

C\'edric Gerbelot, Jean-Christophe Mourrat

arxiv:2607.10869 v1 · 2026-07-12 · cs.LG · math.DS · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3BSJMQ6HQCHBMQH764JH7TI5XH}

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	2026-07-14T01:21:44.385599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8649643c7808e1640fff7127fcd1db9eb5cdff7954acbb22c2a6e19c4743192

Aliases

arxiv: 2607.10869 · arxiv_version: 2607.10869v1 · doi: 10.48550/arxiv.2607.10869 · pith_short_12: 3BSJMQ6HQCHB · pith_short_16: 3BSJMQ6HQCHBMQH7 · pith_short_8: 3BSJMQ6H

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/3BSJMQ6HQCHBMQH764JH7TI5XH \
  | 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: d8649643c7808e1640fff7127fcd1db9eb5cdff7954acbb22c2a6e19c4743192

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f75d1cfb48640bba7f2439e154cc31f558f77e39bee7c8e1026cd1cdd2718ce",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-12T18:10:23Z",
    "title_canon_sha256": "08b2695c359ed8a22b2c694bafe921a47a32fcdb2f54c75218d62b24b9e7a5d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10869",
    "kind": "arxiv",
    "version": 1
  }
}