Pith Number

pith:TQ63Y7DF

pith:2021:TQ63Y7DFIKXYFROXEPFY2UWCN2

not attested not anchored not stored refs pending

Characterization of the Variation Spaces Corresponding to Shallow Neural Networks

Jinchao Xu, Jonathan W. Siegel

arxiv:2106.15002 v2 · 2021-06-28 · 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{TQ63Y7DFIKXYFROXEPFY2UWCN2}

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	2026-07-05T04:12:49.838915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c3dbc7c6542af82c5d723cb8d52c26eb305e94d57d43db09e292ece32b1730f

Aliases

arxiv: 2106.15002 · arxiv_version: 2106.15002v2 · doi: 10.48550/arxiv.2106.15002 · pith_short_12: TQ63Y7DFIKXY · pith_short_16: TQ63Y7DFIKXYFROX · pith_short_8: TQ63Y7DF

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/TQ63Y7DFIKXYFROXEPFY2UWCN2 \
  | 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: 9c3dbc7c6542af82c5d723cb8d52c26eb305e94d57d43db09e292ece32b1730f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6da4a478d96301ed12d491d3d64c2e6d090b927cbe065e6423eb41088f4587c7",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2021-06-28T22:11:14Z",
    "title_canon_sha256": "d3da76e4cecf420eaf30fcfe1248a4fb47db3b1da60195ab603ab6604d8f928b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.15002",
    "kind": "arxiv",
    "version": 2
  }
}