Pith Number

pith:N56MSDUH

pith:2021:N56MSDUHENBVNVSMHD44SD4EME

not attested not anchored not stored refs pending

Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks

Alex Townsend, Annan Yu, Chlo\'e Becquey, Diana Halikias, Matthew Esmaili Mallory

arxiv:2109.11354 v1 · 2021-09-23 · cs.LG · cs.NA · math.CA · math.NA

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\usepackage{pith}
\pithnumber{N56MSDUHENBVNVSMHD44SD4EME}

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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

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Receipt and verification

First computed	2026-07-05T03:16:57.129692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f7cc90e87234356d64c38f9c90f84610bba80377130cbf03c95c7dc8ebff390

Aliases

arxiv: 2109.11354 · arxiv_version: 2109.11354v1 · doi: 10.48550/arxiv.2109.11354 · pith_short_12: N56MSDUHENBV · pith_short_16: N56MSDUHENBVNVSM · pith_short_8: N56MSDUH

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/N56MSDUHENBVNVSMHD44SD4EME \
  | 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: 6f7cc90e87234356d64c38f9c90f84610bba80377130cbf03c95c7dc8ebff390

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c68cee37991b1e6d4dae1623936d8b07faf271e0686b8725e6344b5ca638aaff",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2021-09-23T13:03:53Z",
    "title_canon_sha256": "c5c483cf77969c798a2164a25e2a65a7458df09d95e7a8c24c581b1894da42c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.11354",
    "kind": "arxiv",
    "version": 1
  }
}