Pith Number

pith:2NEW4YQU

pith:2019:2NEW4YQUFSMB2HNVF4CJWUO52H

not attested not anchored not stored refs pending

The Barron Space and the Flow-induced Function Spaces for Neural Network Models

Chao Ma, Lei Wu, Weinan E

arxiv:1906.08039 v2 · 2019-06-18 · cs.LG · math.PR · 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{2NEW4YQUFSMB2HNVF4CJWUO52H}

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.

Cited by

2 papers in Pith

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations

Receipt and verification

First computed	2026-07-05T02:26:45.674270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3496e62142c981d1db52f049b51ddd1e63a3f8b32ec340834e839119cf60dac

Aliases

arxiv: 1906.08039 · arxiv_version: 1906.08039v2 · doi: 10.48550/arxiv.1906.08039 · pith_short_12: 2NEW4YQUFSMB · pith_short_16: 2NEW4YQUFSMB2HNV · pith_short_8: 2NEW4YQU

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/2NEW4YQUFSMB2HNVF4CJWUO52H \
  | 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: d3496e62142c981d1db52f049b51ddd1e63a3f8b32ec340834e839119cf60dac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b738efb2f2f385df63d618530ecb50bc67e888dad7fe4380a85d019afe525bb",
    "cross_cats_sorted": [
      "math.PR",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2019-06-18T12:07:01Z",
    "title_canon_sha256": "706f3b36ce8310523847a7d8996d89dc00a5f1ccdaa36c31556f45bbe89d1ffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.08039",
    "kind": "arxiv",
    "version": 2
  }
}