Paper Citation Record · LEDGER

Minimal surfaces, Knots, and Neural Networks

As of 14 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 2 inbound Pith citation observations for arXiv:2605.26234.

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

pith.paper-citation-record.v1
2605.26234 v2

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T20:08:35.975262Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T00:42:03.269912Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

45 of 45 outbound references displayed

verified exact12
verified fuzzy0
unresolved31
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cfac8d88-a07c-4f79-a451-ea3b1faa1ce2 · outbound

This paper cites Machine learning Sasakian and $G_2$ topology on contact Calabi-Yau $7$-manifolds.

Minimal surfaces, Knots, and Neural Networks Machine learning Sasakian and $G_2$ topology on contact Calabi-Yau $7$-manifolds

Reference 1

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T16:55:50.593188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 022797d1-dedc-4a71-bcad-1302ee70fa2f · outbound

This paper cites an unresolved cited work.

Minimal surfaces, Knots, and Neural Networks Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Unavailable: canonical work link unavailable.

Observation f192f8c0-cce8-4e66-bf40-3d4c71f1552f · outbound

This paper cites High Energy Phys., 2021(5):45,.

Minimal surfaces, Knots, and Neural Networks High Energy Phys., 2021(5):45,

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation e2b14025-1903-4f5a-a89b-88df88da2caa · outbound

This paper cites Anderson.

Minimal surfaces, Knots, and Neural Networks Anderson

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation b7d4747f-f097-4be0-9f25-bd13f7fff7e2 · outbound

This paper cites an unresolved cited work.

Minimal surfaces, Knots, and Neural Networks Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation 2da8f9ad-aecf-4086-94d9-6bb30fc7e436 · outbound

This paper cites Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind.

Minimal surfaces, Knots, and Neural Networks Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation dd7a0789-1aa7-44ff-a0ff-7b0ac7c685bf · outbound

This paper cites Biquard, editor.AdS/CFT correspondence: Einstein metrics and their conformal boundaries.

Minimal surfaces, Knots, and Neural Networks Biquard, editor.AdS/CFT correspondence: Einstein metrics and their conformal boundaries

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation 6a8aed58-2c56-4fb8-9341-736a916f1aec · outbound

This paper cites A Machine Learning Approach to the Nirenberg Problem.

Minimal surfaces, Knots, and Neural Networks A Machine Learning Approach to the Nirenberg Problem

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.599962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3893bdb9-a477-4d1e-b6ef-53dd33930d37 · outbound

This paper cites Asymptotic plateau problem: a survey.

Minimal surfaces, Knots, and Neural Networks Asymptotic plateau problem: a survey

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation 93b6e01b-91c4-4852-9d62-9f3f3048a1ac · outbound

This paper cites Aspects of holographic entanglement entropy using PINNs.

Minimal surfaces, Knots, and Neural Networks Aspects of holographic entanglement entropy using PINNs

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.615811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b5665d2e-5166-462e-90f9-e60bcded90b9 · outbound

This paper cites Douglas, Subramanian Lakshminarasimhan, and Yidi Qi.

Minimal surfaces, Knots, and Neural Networks Douglas, Subramanian Lakshminarasimhan, and Yidi Qi

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation edd9dd7b-6043-4c73-afbf-0f6e13272151 · outbound

This paper cites A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems.

Minimal surfaces, Knots, and Neural Networks A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.606766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fa4db473-1c22-4996-af4d-8611a13da3ac · outbound

This paper cites Robin Graham.

Minimal surfaces, Knots, and Neural Networks Robin Graham

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation 3ef6ec7c-015a-4643-a2c8-8a59792e5a17 · outbound

This paper cites Robin Graham.The ambient metric, volume 178 ofAnnals of Mathematics Studies.

Minimal surfaces, Knots, and Neural Networks Robin Graham.The ambient metric, volume 178 ofAnnals of Mathematics Studies

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25b314f1-1d72-4a85-81d6-2edef2e87000 · outbound

This paper cites Knots, minimal surfaces and J-holomorphic curves.

Minimal surfaces, Knots, and Neural Networks Knots, minimal surfaces and J-holomorphic curves

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.608302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 231be628-9a83-41e9-87ac-8e53c958a654 · outbound

This paper cites Freyd, D.

Minimal surfaces, Knots, and Neural Networks Freyd, D

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2997bad6-012d-4490-8436-75287d36f500 · outbound

This paper cites Computer-assisted proofs in pde: a survey.SeMA Journal, 76(3):459–484, 2019.

Minimal surfaces, Knots, and Neural Networks Computer-assisted proofs in pde: a survey.SeMA Journal, 76(3):459–484, 2019

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation e6d35068-7885-47d5-96c6-efee71bb4c9d · outbound

This paper cites Robin Graham and John M.

Minimal surfaces, Knots, and Neural Networks Robin Graham and John M

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation 171d6c46-fbb9-4723-9bc6-4ee741ee6995 · outbound

This paper cites SIAM, Philadelphia, PA, 2nd edition, 2008.

Minimal surfaces, Knots, and Neural Networks SIAM, Philadelphia, PA, 2nd edition, 2008

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 139bc70b-6560-444b-ab47-4dab36762c1d · outbound

This paper cites Metric Flows with Neural Networks.

Minimal surfaces, Knots, and Neural Networks Metric Flows with Neural Networks

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.601332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6b188728-3457-4d4e-a458-ee0ab2315eef · outbound

This paper cites Approximating Continuous Functions by ReLU Nets of Minimal Width, 2018.

Minimal surfaces, Knots, and Neural Networks Approximating Continuous Functions by ReLU Nets of Minimal Width, 2018

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6a92e82-8c50-46ec-beef-c2e8fb3c1ff4 · outbound

This paper cites Physics-informed neural network solves minimal surfaces in curved spacetime.

Minimal surfaces, Knots, and Neural Networks Physics-informed neural network solves minimal surfaces in curved spacetime

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.587716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9d196625-a2ee-4997-97af-43891abdb0f9 · outbound

This paper cites Minimising Willmore Energy via Neural Flow.

Minimal surfaces, Knots, and Neural Networks Minimising Willmore Energy via Neural Flow

Reference 23

Resolution: metadata mismatch; local_arxiv, observed 2026-07-01T16:55:50.609487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f64884b3-81b3-4d2d-bf62-6ef9f70a1012 · outbound

This paper cites AInstein: Numerical Einstein Metrics via Machine Learning.

Minimal surfaces, Knots, and Neural Networks AInstein: Numerical Einstein Metrics via Machine Learning

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.621874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ba0d9c76-a095-49b2-bfec-9f2b365be43f · outbound

This paper cites Multilayer feedforward networks are universal approx- imators.Neural Networks, 2(5):359–366, 1989.

Minimal surfaces, Knots, and Neural Networks Multilayer feedforward networks are universal approx- imators.Neural Networks, 2(5):359–366, 1989

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation 036b4685-23ad-4925-b2dc-1cc68562c4e4 · outbound

This paper cites Neural network approximations for Calabi-Yau metrics.arXiv, 08:105, 2022.

Minimal surfaces, Knots, and Neural Networks Neural network approximations for Calabi-Yau metrics.arXiv, 08:105, 2022

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation ae03c27e-6ae8-403d-953f-699d720e45d7 · outbound

This paper cites an unresolved cited work.

Minimal surfaces, Knots, and Neural Networks Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation 12d2cd48-111a-44fa-b0c3-f99bfffb467f · outbound

This paper cites an unresolved cited work.

Minimal surfaces, Knots, and Neural Networks Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

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Observation a2df3ef4-e041-42e9-8ba8-403d8246d0aa · outbound

This paper cites Universal approximation with deep narrow networks, 2020.

Minimal surfaces, Knots, and Neural Networks Universal approximation with deep narrow networks, 2020

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation 060b1bb7-c432-48a0-832f-eb5d75220c29 · outbound

This paper cites Kingma and Jimmy Ba.

Minimal surfaces, Knots, and Neural Networks Kingma and Jimmy Ba

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 236ced75-ace8-413d-8c46-3837fd5443ae · outbound

This paper cites Learning Size and Shape of Calabi-Yau Spaces.

Minimal surfaces, Knots, and Neural Networks Learning Size and Shape of Calabi-Yau Spaces

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.611085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fabd09ef-31a0-4499-87fd-e405c94eebdb · outbound

This paper cites an unresolved cited work.

Minimal surfaces, Knots, and Neural Networks Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Unavailable: canonical work link unavailable.

Observation 866d202d-ccb1-47ed-a3f0-364e4c5f4d81 · outbound

This paper cites Machine Learning Gravity Compactifications on Negatively Curved Manifolds.

Minimal surfaces, Knots, and Neural Networks Machine Learning Gravity Compactifications on Negatively Curved Manifolds

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.612430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dce14e18-ad91-47b1-90d4-3deeddd4f5da · outbound

This paper cites Variations of renormalized volume for minimal submanifolds of Poincaré-Einstein manifolds.

Minimal surfaces, Knots, and Neural Networks Variations of renormalized volume for minimal submanifolds of Poincaré-Einstein manifolds

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation bf45e86f-070b-49da-971d-98d7a921a3c7 · outbound

This paper cites Mazzeo.Hodge cohomology of negatively curved manifolds.

Minimal surfaces, Knots, and Neural Networks Mazzeo.Hodge cohomology of negatively curved manifolds

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation 1477b75e-3484-4a51-9aaf-def982af2510 · outbound

This paper cites Mazzeo and Richard B.

Minimal surfaces, Knots, and Neural Networks Mazzeo and Richard B

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Observation 6c22f9e3-a417-45ee-9fa9-33fe5bf33ee4 · outbound

This paper cites an unresolved cited work.

Minimal surfaces, Knots, and Neural Networks Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

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Unavailable: canonical work link unavailable.

Observation 5bf9aae4-4eb3-472a-a759-9488e109770d · outbound

This paper cites Updating quasi-Newton matrices with limited storage.Mathematics of Computation, 35(151):773–782, 1980.

Minimal surfaces, Knots, and Neural Networks Updating quasi-Newton matrices with limited storage.Mathematics of Computation, 35(151):773–782, 1980

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afe9e9c4-f5ec-44ce-b859-e2516f71764e · outbound

This paper cites Non-uniqueness and symmetries for the nirenberg problem using computer assistance.

Minimal surfaces, Knots, and Neural Networks Non-uniqueness and symmetries for the nirenberg problem using computer assistance

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.598775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 04d380e9-064d-4a71-9b7c-885a49377f76 · outbound

This paper cites Raissi, P.

Minimal surfaces, Knots, and Neural Networks Raissi, P

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ddfce9d-ddc7-46f7-9217-01b4e0ba529a · outbound

This paper cites Biharmonic maps between conformally compact manifolds.Calc.

Minimal surfaces, Knots, and Neural Networks Biharmonic maps between conformally compact manifolds.Calc

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9583e466-48cc-4241-a868-ced2dab3bc13 · outbound

This paper cites Isometric embeddings of conformally compact manifolds into hyperbolic spaces.International Mathematics Research Notices, 2026(10):rnag098, 05 2026.

Minimal surfaces, Knots, and Neural Networks Isometric embeddings of conformally compact manifolds into hyperbolic spaces.International Mathematics Research Notices, 2026(10):rnag098, 05 2026

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 335b58e8-1973-46fe-a14a-a96af3a6136b · outbound

This paper cites Discovery of unstable singularities.

Minimal surfaces, Knots, and Neural Networks Discovery of unstable singularities

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.583729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 609fbba6-ab80-421a-86fc-22fa9fe383d2 · outbound

This paper cites Convergence conditions for ascent methods.SIAM Review, 11(2):226–235, 1969.

Minimal surfaces, Knots, and Neural Networks Convergence conditions for ascent methods.SIAM Review, 11(2):226–235, 1969

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-29T20:08:35.975262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ef99e6c-7e18-4182-b223-1818e002f566 · outbound

This paper cites Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks.

Minimal surfaces, Knots, and Neural Networks Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-07-01T16:55:50.618879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 5f13bdf8-84b2-4261-b109-453bee639d5a · inbound

Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks cites this paper.

Black Hole Black Boxes: Numerical Black Hole Metrics via AInstein Neural Networks Minimal surfaces, Knots, and Neural Networks

Reference 42

Resolution: unresolved; no resolver link, observed 2026-07-11T06:56:17.499687Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f4a7b60-775a-40f1-9dad-97f44457cb1c · inbound

A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem cites this paper.

A user's guide to PINNs in geometric analysis: lessons from the asymptotic Plateau problem Minimal surfaces, Knots, and Neural Networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T00:42:03.269912Z

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Unavailable: canonical work link unavailable.