Paper Citation Record · LEDGER

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs

As of 16 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2507.11870.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.11870 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:04:31.855309Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

verified exact3
verified fuzzy12
unresolved22
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation babac7c7-8d7c-415f-8c42-7f2f67dbec9e · outbound

This paper cites Aldirany, R.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Aldirany, R

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:37.045316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 042a510f-f481-48f2-b3e0-0c26aa1f7822 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:36.745373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4dd34305-a13b-415d-ae47-7d9331df76b1 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:36.522328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b109ff4c-333b-4dca-ba2d-386556d7dad3 · outbound

This paper cites Chandrasekaran, P.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Chandrasekaran, P

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:36.301317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e3d1e20c-146a-46e3-a19c-f937be5705d3 · outbound

This paper cites Chandrasekaran, P.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Chandrasekaran, P

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:36.119700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 40d8f3e0-e62d-446c-a780-9450f4da40ed · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:35.861877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 89d5adfd-eefc-46a2-916c-ea98e7ce74ea · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:35.676323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 11d1124b-7811-449e-9edc-259ba6814a9a · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:35.515236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e64365bb-eb0a-48e6-9304-b46195419597 · outbound

This paper cites Gómez-Castro.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Gómez-Castro

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:35.219052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4e67b1d1-29f4-4185-9363-a86d8034fdab · outbound

This paper cites Greengard and V.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Greengard and V

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:35.003051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2808d7a3-b66e-4012-9616-7d1304b7bfdb · outbound

This paper cites Multiwavelet-based Operator Learning for Differential Equations.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Multiwavelet-based Operator Learning for Differential Equations

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:28.984914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1db66a0-0d0f-41d9-a0cc-838025997d84 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:34.835404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1dd7dfde-5898-4440-ab8b-ac62a5525b1e · outbound

This paper cites Generating synthetic data for neural operators.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Generating synthetic data for neural operators

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.108661Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 962ca2f7-07ef-4786-a51c-0968c11e1cd5 · outbound

This paper cites Helwig, X.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Helwig, X

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:34.630064Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 80049576-21e1-4578-bad5-ee00371d2ea5 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Adam: A Method for Stochastic Optimization

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.223922Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1965a119-88c4-460e-b577-736c5903686b · outbound

This paper cites Kovachki, Z.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Kovachki, Z

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.270789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0be1e384-b1e3-4c57-bc33-8ab8c5875c21 · outbound

This paper cites Lerer, I.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Lerer, I

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:34.425831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 939548b7-82ff-4ad9-b3fd-c9ea14fde4f1 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.465767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c09207a3-f632-47df-b466-5496ea964b76 · outbound

This paper cites Multipole Graph Neural Operator for Parametric Partial Differential Equations.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Multipole Graph Neural Operator for Parametric Partial Differential Equations

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.557029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f11e181e-1178-48d3-b616-20205d98f6e4 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:34.222143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 23b9a73e-c1a8-4824-b39e-1bedf0e1eca1 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.670632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebb672bc-e62b-437c-bc4f-72d5257c920a · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:34.065242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 497d088c-361b-43d9-86c2-d272c32dc5e5 · outbound

This paper cites Pad\'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Pad\'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:29.782258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a10009c-19fb-4124-b72b-c6aa3ae892ff · outbound

This paper cites FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Reference 24

Resolution: malformed identifier; no resolver link, observed 2026-08-06T17:04:29.844579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b129d997-7943-4817-a66a-a35ab9d42e47 · outbound

This paper cites Raissi, P.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Raissi, P

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:33.907208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a662548e-88de-4841-9f09-e72a913af30f · outbound

This paper cites Raoni’c, R.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Raoni’c, R

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:33.722511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f0c0aedc-dfda-4e27-b53f-19884a24ce95 · outbound

This paper cites Ronneberger, P.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Ronneberger, P

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:33.540470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f5a5495d-f15b-4167-b6e3-1d04ab83cde5 · outbound

This paper cites A Review of Neural Network Solvers for Second-order Boundary Value Problems.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs A Review of Neural Network Solvers for Second-order Boundary Value Problems

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:04:32.565480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4fc59cd1-031d-4821-8347-af78cff9afbd · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:33.390788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3cbad813-693b-4f24-8f03-9ae2f0175d34 · outbound

This paper cites FMM-Net: neural network architecture based on the Fast Multipole Method.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs FMM-Net: neural network architecture based on the Fast Multipole Method

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:04:32.339811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 482fae2a-be44-4bbe-8f04-ebf7f9eb002a · outbound

This paper cites Telgarsky.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Telgarsky

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:30.856681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b69d25f0-578f-46b6-a9db-8e387a8a88d7 · outbound

This paper cites Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:04:32.082181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 50ce88ab-3f14-4a8a-9c1b-ec0aa76f0df1 · outbound

This paper cites Vaswani, N.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Vaswani, N

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:33.233026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b18c85af-e9fe-4b34-8444-3f8e4f748048 · outbound

This paper cites BENO: Boundary-embedded Neural Operators for Elliptic PDEs.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs BENO: Boundary-embedded Neural Operators for Elliptic PDEs

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:31.328960Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b8c928f-0fbb-488f-98e3-5291712dc259 · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:31.486302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e01fce39-afdd-4084-ba69-1509c002ec19 · outbound

This paper cites Transolver: A Fast Transformer Solver for PDEs on General Geometries.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Transolver: A Fast Transformer Solver for PDEs on General Geometries

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T17:04:31.637581Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29ef7f89-5766-495d-9b93-d1da92a54e1e · outbound

This paper cites an unresolved cited work.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:04:33.010800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 13a98cb1-998f-49f7-bb07-5c067566baf1 · outbound

This paper cites Zhang, A.

MNO : A Multi-modal Neural Operator for Parametric Nonlinear BVPs Zhang, A

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:04:32.809392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.