Pith Number

pith:NPJSTJXT

pith:2025:NPJSTJXTZVRAWLMWCXK3EMH7KZ

not attested not anchored not stored refs pending

A posteriori analysis of neural network approximations

Sergio Rojas, Thomas F\"uhrer

arxiv:2507.06017 v1 · 2025-07-08 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NPJSTJXTZVRAWLMWCXK3EMH7KZ}

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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

1 paper in Pith

Neural network approximation in discrete dual norms with adaptive test spaces

Receipt and verification

First computed	2026-07-05T11:33:39.996603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bd329a6f3cd620b2d9615d5b230ff566bd8e613efcde86f8cb2cdacf9369fc0

Aliases

arxiv: 2507.06017 · arxiv_version: 2507.06017v1 · doi: 10.48550/arxiv.2507.06017 · pith_short_12: NPJSTJXTZVRA · pith_short_16: NPJSTJXTZVRAWLMW · pith_short_8: NPJSTJXT

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/NPJSTJXTZVRAWLMWCXK3EMH7KZ \
  | 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: 6bd329a6f3cd620b2d9615d5b230ff566bd8e613efcde86f8cb2cdacf9369fc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfdebdd9437f2da7f3523839ffc6fab34f25109dfc1a2747488ed26d26d93115",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-08T14:23:55Z",
    "title_canon_sha256": "144bdca07ddbf16aac714d3a71f0fffd973b6cee87a1e9f76f090dc0e707b8a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06017",
    "kind": "arxiv",
    "version": 1
  }
}