Pith Number

pith:BYKUX7DB

pith:2021:BYKUX7DBMH4UD2VGSVR76I5D4T

not attested not anchored not stored refs pending

On the Cryptographic Hardness of Learning Single Periodic Neurons

Ilias Zadik, Joan Bruna, Min Jae Song

arxiv:2106.10744 v2 · 2021-06-20 · cs.LG · cs.CC · math.PR · math.ST · stat.ML · 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{BYKUX7DBMH4UD2VGSVR76I5D4T}

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	2026-07-05T03:14:56.103343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e154bfc6161f941eaa69563ff23a3e4c7e31b5614260223fd15db28f133b3ce

Aliases

arxiv: 2106.10744 · arxiv_version: 2106.10744v2 · doi: 10.48550/arxiv.2106.10744 · pith_short_12: BYKUX7DBMH4U · pith_short_16: BYKUX7DBMH4UD2VG · pith_short_8: BYKUX7DB

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/BYKUX7DBMH4UD2VGSVR76I5D4T \
  | 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: 0e154bfc6161f941eaa69563ff23a3e4c7e31b5614260223fd15db28f133b3ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ae8bf64c92caa49b63b0d4af8a061251134354ad232cf9824dacfc353a515d7",
    "cross_cats_sorted": [
      "cs.CC",
      "math.PR",
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-06-20T20:03:52Z",
    "title_canon_sha256": "90208347d5563d856d6f1c9ab47a48ba17704eeddd0c885d91fd9ace9d4394ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.10744",
    "kind": "arxiv",
    "version": 2
  }
}