Pith Number

pith:PLY6JTRC

pith:2026:PLY6JTRC5ZTRBVKAOMQMQRRRC2

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Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality

Diego Febbe, Duccio Fanelli, Feliciano Giuseppe Pacifico, Lorenzo Buffoni, Lorenzo Chicchi, Raffaele Marino

Neural-ODEs can approximate arbitrary velocity fields while exactly forcing velocity to zero at any finite set of prescribed points.

arxiv:2605.10613 v1 · 2026-05-11 · cond-mat.dis-nn · cs.LG · physics.bio-ph

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\pithnumber{PLY6JTRC5ZTRBVKAOMQMQRRRC2}

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4 Citations 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 rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points.

C2weakest assumption

That the explicit accommodation for fixed points can be introduced without reducing the expressive power of the underlying Neural-ODE architecture.

C3one line summary

A technique plants exact fixed points in Neural-ODE velocity fields with a rigorous proof that universality is preserved under local constraints.

References

32 extracted · 32 resolved · 2 Pith anchors

[1] Advances in Neural Information Processing Systems (NeurIPS) , year =

[2] Multiplicity of Time Scales in Complex Systems: Challenges for Sciences and Communication II , editor = 2024

[3] Daniel A. Serino and Allen Alvarez Loya and J. W. Burby and Ioannis G. Kevrekidis and Qi Tang , title =. Journal of Computational Physics , volume =. 2025 , doi = 2025

[4] Variazioni e fluttuazioni del numero d'individui in specie animali conviventi , author=. 1927 , publisher= 1927

[5] Golub and Charles F

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-23T03:14:29.043179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7af1e4ce22ee6710d5407320c8463116b770d4f1cfdfe517b3b2fee3cd883a07

Aliases

arxiv: 2605.10613 · arxiv_version: 2605.10613v1 · doi: 10.48550/arxiv.2605.10613 · pith_short_12: PLY6JTRC5ZTR · pith_short_16: PLY6JTRC5ZTRBVKA · pith_short_8: PLY6JTRC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PLY6JTRC5ZTRBVKAOMQMQRRRC2 \
  | 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: 7af1e4ce22ee6710d5407320c8463116b770d4f1cfdfe517b3b2fee3cd883a07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b89d62ab0c165d752f893a141fea340f14dd2888e84ca1d62e279414e5c38c72",
    "cross_cats_sorted": [
      "cs.LG",
      "physics.bio-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-05-11T14:10:31Z",
    "title_canon_sha256": "8f9d3f04e682e7309aa5eb698b3ca52ac8813626251258447d6f4f3504cbc30f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10613",
    "kind": "arxiv",
    "version": 1
  }
}