Pith Number

pith:NG4N36PS

pith:2021:NG4N36PSG7CJKSDJM7MIZVRZTB

not attested not anchored not stored refs pending

The Connection Between Approximation, Depth Separation and Learnability in Neural Networks

Eran Malach, Gilad Yehudai, Ohad Shamir, Shai Shalev-Shwartz

arxiv:2102.00434 v2 · 2021-01-31 · cs.LG · cs.NE · 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{NG4N36PSG7CJKSDJM7MIZVRZTB}

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	2026-07-05T02:58:39.054272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69b8ddf9f237c495486967d88cd6399863e499bdd185f64111da51fd8fe52546

Aliases

arxiv: 2102.00434 · arxiv_version: 2102.00434v2 · doi: 10.48550/arxiv.2102.00434 · pith_short_12: NG4N36PSG7CJ · pith_short_16: NG4N36PSG7CJKSDJ · pith_short_8: NG4N36PS

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/NG4N36PSG7CJKSDJM7MIZVRZTB \
  | 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: 69b8ddf9f237c495486967d88cd6399863e499bdd185f64111da51fd8fe52546

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ffe8840bf19d388cd17b9479dd544ed073c7d7616028331eac3fc21783eaefb",
    "cross_cats_sorted": [
      "cs.NE",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-01-31T11:32:30Z",
    "title_canon_sha256": "05cc640b749e8c966ebec6243ab94d496ea31d686827f5422db63926c96faab0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.00434",
    "kind": "arxiv",
    "version": 2
  }
}