Pith Number

pith:32FFQ7FK

pith:2026:32FFQ7FKLNADSOTAMEAJMKRYGX

not attested not anchored not stored refs pending

Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves

Alejandro Ribeiro, Claudio Battiloro, Francesca Dominici, Julian Gould, Kartik Tandon, Tanishq Bhatia

Sampling a manifold with a Hilbert bundle induces a cellular sheaf whose Laplacian converges in probability to the connection Laplacian, enabling consistent discrete networks for infinite-dimensional signals.

arxiv:2605.06395 v2 · 2026-05-07 · cs.LG · cs.AI · eess.SP

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\usepackage{pith}
\pithnumber{32FFQ7FKLNADSOTAMEAJMKRYGX}

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Record completeness

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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.

Claims

C1strongest claim

we prove that its sheaf Laplacian converges in probability to the underlying connection Laplacian as the sampling density increases. Notably, this result is a generalization to the infinite-dimensional bundle setting of the Belkin & Niyogi convergence result for the graph Laplacian to the manifold Laplacian

C2weakest assumption

Sampling the manifold induces a Hilbert Cellular Sheaf with edge-wise coupling rules that preserve the necessary structure for the Laplacian convergence to hold in the infinite-dimensional Hilbert bundle case.

C3one line summary

HilbNets discretize Hilbert bundle convolutions through Hilbert Cellular Sheaves whose Laplacians converge to the continuous connection Laplacian, enabling consistent learning across samplings.

Receipt and verification

First computed	2026-05-21T01:04:26.973934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de8a587caa5b40393a606100962a3835f746f59f3fad37bf6a86a5c97cfca67d

Aliases

arxiv: 2605.06395 · arxiv_version: 2605.06395v2 · doi: 10.48550/arxiv.2605.06395 · pith_short_12: 32FFQ7FKLNAD · pith_short_16: 32FFQ7FKLNADSOTA · pith_short_8: 32FFQ7FK

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/32FFQ7FKLNADSOTAMEAJMKRYGX \
  | 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: de8a587caa5b40393a606100962a3835f746f59f3fad37bf6a86a5c97cfca67d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c62159cb5f3bb3fd1b2a466fbbf4d3c2f8a5d8fc25dce127fb02c7b2b66adbcb",
    "cross_cats_sorted": [
      "cs.AI",
      "eess.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-07T15:08:58Z",
    "title_canon_sha256": "ca2ca05275edf19b89e941cd92a1105e1b6c803cbd56ed08dec8975d70b41671"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06395",
    "kind": "arxiv",
    "version": 2
  }
}