Pith Number

pith:CXUV5FHR

pith:2026:CXUV5FHRC2AECPJYZCIL2AH2NG

not attested not anchored not stored refs pending

Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

Hanfei Zhou, Lei Shi

CNNs approximate manifold functions and their derivatives at rates set by intrinsic dimension alone.

arxiv:2605.04126 v2 · 2026-05-05 · cs.LG · cs.NA · math.NA

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\usepackage{pith}
\pithnumber{CXUV5FHRC2AECPJYZCIL2AH2NG}

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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

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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.

Claims

C1strongest claim

We establish simultaneous Sobolev approximation results for single- and multichannel CNNs, showing that manifold functions and their derivatives can be approximated with rates governed by the intrinsic dimension and the smoothness gap, rather than by the ambient dimension.

C2weakest assumption

That the CNN architecture can be adapted to the Riemannian manifold structure such that the approximation rates transfer from Euclidean CNN theory without additional manifold-specific error terms that dominate the claimed rates.

C3one line summary

CNNs achieve simultaneous Sobolev approximation on manifolds with intrinsic-dimension rates and enable a PICNN for BVPs via spectral boundary loss that improves stability over standard PINNs.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-23T02:13:24.654670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15e95e94f11680413d38c890bd00fa69b47ac656be38bc2c710f51e5c124e25c

Aliases

arxiv: 2605.04126 · arxiv_version: 2605.04126v2 · doi: 10.48550/arxiv.2605.04126 · pith_short_12: CXUV5FHRC2AE · pith_short_16: CXUV5FHRC2AECPJY · pith_short_8: CXUV5FHR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CXUV5FHRC2AECPJYZCIL2AH2NG \
  | 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: 15e95e94f11680413d38c890bd00fa69b47ac656be38bc2c710f51e5c124e25c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "118df57f213fe0f8330de8ce88cb04103da98af74bf032c696b5ffecc3322a65",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-05T15:35:24Z",
    "title_canon_sha256": "7f34b6eca510e0dbdf42e154c23af053762343e69c40f374c0c9e051ad3b15a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04126",
    "kind": "arxiv",
    "version": 2
  }
}