Pith Number

pith:APMC4X36

pith:2017:APMC4X36ZKNF5QLIPLSIOIGAAG

not attested not anchored not stored refs pending

Optimal Approximation with Sparsely Connected Deep Neural Networks

Gitta Kutyniok, Helmut B\"olcskei, Philipp Grohs, Philipp Petersen

arxiv:1705.01714 v4 · 2017-05-04 · cs.LG · cs.IT · math.FA · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APMC4X36ZKNF5QLIPLSIOIGAAG}

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	2026-05-18T00:15:52.588526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03d82e5f7eca9a5ec1687ae48720c001a19bfbffb1cdc2220ea02ee7205ef080

Aliases

arxiv: 1705.01714 · arxiv_version: 1705.01714v4 · doi: 10.48550/arxiv.1705.01714 · pith_short_12: APMC4X36ZKNF · pith_short_16: APMC4X36ZKNF5QLI · pith_short_8: APMC4X36

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/APMC4X36ZKNF5QLIPLSIOIGAAG \
  | 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: 03d82e5f7eca9a5ec1687ae48720c001a19bfbffb1cdc2220ea02ee7205ef080

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "667bada4cbbed87854f902e0a593ea088442203a87c3025f54573bb2add644ae",
    "cross_cats_sorted": [
      "cs.IT",
      "math.FA",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2017-05-04T06:45:06Z",
    "title_canon_sha256": "e9d9fc7331c21a258dad7bf298f611525a7ead963bba3068d952b4a9198005ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.01714",
    "kind": "arxiv",
    "version": 4
  }
}