Pith Number

pith:JA3NE6CJ

pith:2026:JA3NE6CJ5AWVF47OYFUDAOUT6J

not attested not anchored not stored refs pending

Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks

Greg Ongie, Rahul Parhi

arxiv:2606.14954 v2 · 2026-06-12 · math.FA · cs.LG · math.OC · 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{JA3NE6CJ5AWVF47OYFUDAOUT6J}

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	2026-06-19T16:10:39.777279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4836d27849e82d52f3eec168303a93f27915307ce9b7ba21c93ed75d9ad764aa

Aliases

arxiv: 2606.14954 · arxiv_version: 2606.14954v2 · doi: 10.48550/arxiv.2606.14954 · pith_short_12: JA3NE6CJ5AWV · pith_short_16: JA3NE6CJ5AWVF47O · pith_short_8: JA3NE6CJ

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/JA3NE6CJ5AWVF47OYFUDAOUT6J \
  | 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: 4836d27849e82d52f3eec168303a93f27915307ce9b7ba21c93ed75d9ad764aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "248a35be8123c693aa848fe24115faafdb601eb61dddfc600cc01c1235c112e6",
    "cross_cats_sorted": [
      "cs.LG",
      "math.OC",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-12T20:57:05Z",
    "title_canon_sha256": "845db020a8961953b8f5cffe60c77ec795cf46e01a8edf9ea7ca884fcfe31fd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.14954",
    "kind": "arxiv",
    "version": 2
  }
}