Pith Number

pith:B2FTCE4G

pith:2020:B2FTCE4G4YBWFEPBSAD2IZGZZA

not attested not anchored not stored refs pending

Nonclosedness of Sets of Neural Networks in Sobolev Spaces

Alex Cloninger, Emily King, Scott Mahan

arxiv:2007.11730 v4 · 2020-07-23 · stat.ML · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B2FTCE4G4YBWFEPBSAD2IZGZZA}

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	2026-07-05T02:10:25.881978Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e8b311386e6036291e19007a464d9c80bdcb8e5dcbecce20742a4dbd682ba96

Aliases

arxiv: 2007.11730 · arxiv_version: 2007.11730v4 · doi: 10.48550/arxiv.2007.11730 · pith_short_12: B2FTCE4G4YBW · pith_short_16: B2FTCE4G4YBWFEPB · pith_short_8: B2FTCE4G

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/B2FTCE4G4YBWFEPBSAD2IZGZZA \
  | 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: 0e8b311386e6036291e19007a464d9c80bdcb8e5dcbecce20742a4dbd682ba96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8582bd9d5fa14999f90ad465a247aa844ec33d1ee11bff1041d3cb7bb3f202e9",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2020-07-23T00:57:25Z",
    "title_canon_sha256": "cf81f1ee1afad15eca7560d37292772ee68afb4c15e357d8b11a95c4b98bdadd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.11730",
    "kind": "arxiv",
    "version": 4
  }
}