Pith Number

pith:D4C5ASF3

pith:2026:D4C5ASF3TFTZMWMXRMWM3ODFPD

not attested not anchored not stored refs pending

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width

Defeng Sun, Yang Wang, Yanming Lai

arxiv:2607.10589 v1 · 2026-07-12 · stat.ML · cs.IT · cs.LG · cs.NA · math.IT · math.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{D4C5ASF3TFTZMWMXRMWM3ODFPD}

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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.

Receipt and verification

First computed	2026-07-14T01:21:22.676594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f05d048bb99679659978b2ccdb86578d1bc2ec180c9fda1e9929d797d799270

Aliases

arxiv: 2607.10589 · arxiv_version: 2607.10589v1 · doi: 10.48550/arxiv.2607.10589 · pith_short_12: D4C5ASF3TFTZ · pith_short_16: D4C5ASF3TFTZMWMX · pith_short_8: D4C5ASF3

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/D4C5ASF3TFTZMWMXRMWM3ODFPD \
  | 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: 1f05d048bb99679659978b2ccdb86578d1bc2ec180c9fda1e9929d797d799270

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41c9245c8528a0d5d521d6b3be76485d98fbbd7d22f669edc73eed784905f6dd",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.LG",
      "cs.NA",
      "math.IT",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-12T05:59:12Z",
    "title_canon_sha256": "df985c2f88e650e937daa7627a0e9dcfcf0871e477326b6e6e716eab059cf048"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10589",
    "kind": "arxiv",
    "version": 1
  }
}