Pith Number

pith:PQU4YGP5

pith:2026:PQU4YGP5ZGP3RHIZI3IKH3P5PL

not attested not anchored not stored refs resolved

Topology-Preserving Neural Operator Learning via Hodge Decomposition

Christine Allen-Blanchette, Dongzhe Zheng, Tao Zhong

Hodge orthogonality isolates unlearnable topological degrees of freedom from learnable geometric dynamics in neural operators.

arxiv:2605.13834 v1 · 2026-05-13 · cs.LG · cs.AI · cs.CG

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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

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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

Hodge orthogonality fundamentally resolves spectral interference by isolating unlearnable topological degrees of freedom from learnable geometric dynamics, enabling an additive approximation confined to structure-preserving subspaces.

C2weakest assumption

That the discrete Hodge decomposition cleanly isolates topological components from geometric dynamics in the operator without introducing discretization artifacts or requiring problem-specific tuning on geometric meshes.

C3one line summary

Hodge Spectral Duality provides a topology-preserving neural operator by isolating unlearnable topological components via Hodge orthogonality and operator splitting.

References

14 extracted · 14 resolved · 2 Pith anchors

[1] On the bottleneck of graph neural networks and its practical implications.arXiv:2006.05205 2006

[2] Splitting methods for differential equations.arXiv preprint arXiv:2401.01722,

[3] A note on over-smoothing for graph neural networks 2006

[4] Sim- plicial neural networks.arXiv preprint arXiv:2010.03633 2010

[5] Dey, Soham Mukherjee, Shreyas N

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T02:44:14.962182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c29cc19fdc99fb89d1946d0a3edfd7afd9ade2dee77febbe179ce305aaebcb0

Aliases

arxiv: 2605.13834 · arxiv_version: 2605.13834v1 · doi: 10.48550/arxiv.2605.13834 · pith_short_12: PQU4YGP5ZGP3 · pith_short_16: PQU4YGP5ZGP3RHIZ · pith_short_8: PQU4YGP5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PQU4YGP5ZGP3RHIZI3IKH3P5PL \
  | 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: 7c29cc19fdc99fb89d1946d0a3edfd7afd9ade2dee77febbe179ce305aaebcb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eecf457cba9563fb60422841e79d938c075679f32f7a25bb0b4d7c5e69ec27b3",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T17:56:23Z",
    "title_canon_sha256": "dc23cad76cf1da7a26a7661bb894952a089004993732e46ff3d5b3e7de2a1231"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13834",
    "kind": "arxiv",
    "version": 1
  }
}