Pith Number

pith:F3L5X5BN

pith:2021:F3L5X5BN6HV4A7WLSUSICZQI6N

not attested not anchored not stored refs pending

On the approximation of functions by tanh neural networks

Samuel Lanthaler, Siddhartha Mishra, Tim De Ryck

arxiv:2104.08938 v2 · 2021-04-18 · math.NA · cs.LG · 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{F3L5X5BN6HV4A7WLSUSICZQI6N}

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	2026-07-05T03:38:59.716271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ed7dbf42df1ebc07ecb9524816608f35943fb4740d72d8c170cd5bcc9bd69b3

Aliases

arxiv: 2104.08938 · arxiv_version: 2104.08938v2 · doi: 10.48550/arxiv.2104.08938 · pith_short_12: F3L5X5BN6HV4 · pith_short_16: F3L5X5BN6HV4A7WL · pith_short_8: F3L5X5BN

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/F3L5X5BN6HV4A7WLSUSICZQI6N \
  | 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: 2ed7dbf42df1ebc07ecb9524816608f35943fb4740d72d8c170cd5bcc9bd69b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bc8abaadca2295ebcf3006a9add9988a9d6ea95c97a437fde85c555c7328582",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2021-04-18T19:30:45Z",
    "title_canon_sha256": "518f48e0d0b85dac7ff1a73971643f4bf5eb57273839f362305523d6bb4c06d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.08938",
    "kind": "arxiv",
    "version": 2
  }
}