Pith Number

pith:Z2WNFDZ2

pith:2026:Z2WNFDZ24K35TH7MERFKAL62TS

not attested not anchored not stored refs pending

The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning

Joan Bruna

arxiv:2607.03347 v1 · 2026-07-03 · 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{Z2WNFDZ24K35TH7MERFKAL62TS}

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

1 paper in Pith

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks

Receipt and verification

First computed	2026-07-07T02:17:38.475539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceacd28f3ae2b7d99fec244aa02fda9cbcf500b3e2ea8aec1cd749474884fee1

Aliases

arxiv: 2607.03347 · arxiv_version: 2607.03347v1 · doi: 10.48550/arxiv.2607.03347 · pith_short_12: Z2WNFDZ24K35 · pith_short_16: Z2WNFDZ24K35TH7M · pith_short_8: Z2WNFDZ2

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/Z2WNFDZ24K35TH7MERFKAL62TS \
  | 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: ceacd28f3ae2b7d99fec244aa02fda9cbcf500b3e2ea8aec1cd749474884fee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdc3ae43a1dbebed6e163b3e30f60bb005ab417be66ceb6f08f7260b5042792e",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-03T14:02:42Z",
    "title_canon_sha256": "072637d6abd8a0bb451ed978168c8565560ccf1d230a13933e6622eedbab7328"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03347",
    "kind": "arxiv",
    "version": 1
  }
}