From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms | Paper Citation Record

Observation 7e4c1f56-50d9-4986-91d6-15f489fbf771 · outbound

This paper cites doi: 10.1038/s41586-023-06924-6.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms doi: 10.1038/s41586-023-06924-6

Reference 1

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Observation b7aa8189-0744-4fad-afd2-bb9d35bb4125 · outbound

This paper cites Discovering faster matrix multiplication algorithms with reinforcement learning.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Discovering faster matrix multiplication algorithms with reinforcement learning

Reference 2

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This paper cites URL https://openai.com/index/model-disproves-discrete-geometry-conjecture/.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms URL https://openai.com/index/model-disproves-discrete-geometry-conjecture/

Reference 3

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Observation cb53bffc-b7e6-4cef-91e7-ba0e8a716c7c · outbound

This paper cites Trinh, Yuhuai Wu, Quoc V.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Trinh, Yuhuai Wu, Quoc V

Reference 4

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correction dated 2024-02-23. Source: crossref record 10.1038/s41586-024-07115-7->10.1038/s41586-023-06747-5:correction, observed 2026-07-11T03:09:49.232535+00:00. This notice travels one citation hop only.

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This paper cites URL https://aclanthology.org/2025.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms URL https://aclanthology.org/2025

Reference 5

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Observation 5b0f6105-5dbf-44ab-8730-1ae04cc195dc · outbound

This paper cites AI Mathematician: Towards Fully Automated Frontier Mathematical Research.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms AI Mathematician: Towards Fully Automated Frontier Mathematical Research

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-07-03T16:38:40.685226Z

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This paper cites AI mathematician as a partner in advancing mathematical discovery—a case study in homogenization theory.arXiv preprint arXiv:2510.26380, 2025.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms AI mathematician as a partner in advancing mathematical discovery—a case study in homogenization theory.arXiv preprint arXiv:2510.26380, 2025

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-03T16:38:40.671230Z

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This paper cites Trinh, Garrett Bingham, Dawsen Hwang, Yuri Chervonyi, Junehyuk Jung,JoonkyungLee,CarloPagano,SanghyunKim,FedericoPasqualotto,SergeiGukov, Jonathan N.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Trinh, Garrett Bingham, Dawsen Hwang, Yuri Chervonyi, Junehyuk Jung,JoonkyungLee,CarloPagano,SanghyunKim,FedericoPasqualotto,SergeiGukov, Jonathan N

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-03T16:38:40.674734Z

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Observation 267ad632-c486-47f6-a631-25d720fb5c0f · outbound

This paper cites Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-07-03T16:38:40.690480Z

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Observation 9acc518e-f4fd-4964-b399-7aed28f9299c · outbound

This paper cites Generative Language Modeling for Automated Theorem Proving.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Generative Language Modeling for Automated Theorem Proving

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-07-03T16:38:40.693977Z

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Observation d3b3a994-1ad9-4de8-8d2e-846ddc7a3e76 · outbound

This paper cites HyperTree proof search for neural theorem proving.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms HyperTree proof search for neural theorem proving

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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This paper cites Automated.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Automated

Reference 12

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This paper cites URL https: //doi.org/10.1038/s41586-026-10265-5.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms URL https: //doi.org/10.1038/s41586-026-10265-5

Reference 13

Resolution: metadata mismatch; doi, observed 2026-06-27T05:10:34.816107Z

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This paper cites URL https://doi.org/ 10.1038/s41586-026-10644-y.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms URL https://doi.org/ 10.1038/s41586-026-10644-y

Reference 14

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This paper cites E.et al.A multi-agent system for automating scientific discovery.Nature(2026).

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms E.et al.A multi-agent system for automating scientific discovery.Nature(2026)

Reference 15

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This paper cites Advancingmathematicalresearchviahuman-AI interactive theorem proving.arXiv preprint arXiv:2512.09443, 2025.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Advancingmathematicalresearchviahuman-AI interactive theorem proving.arXiv preprint arXiv:2512.09443, 2025

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-03T16:38:40.684073Z

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This paper cites AI co-mathematician: Accelerating mathematicians with agentic AI.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms AI co-mathematician: Accelerating mathematicians with agentic AI

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-07-03T16:38:40.687112Z

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This paper cites Quantum A lgorithm for Linear Systems of Equations.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Quantum A lgorithm for Linear Systems of Equations

Reference 18

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This paper cites Quantum algorithm for systems of linear equations with exponentially improved dependence on precision.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Quantum algorithm for systems of linear equations with exponentially improved dependence on precision

Reference 19

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.796147Z

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This paper cites \ Berry , author Andrew M.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms \ Berry , author Andrew M

Reference 20

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.782986Z

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This paper cites Optimal hamiltonian simulation by quantum signal processing.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Optimal hamiltonian simulation by quantum signal processing

Reference 21

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.794204Z

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This paper cites Hamiltonian simulation by qubitization.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Hamiltonian simulation by qubitization

Reference 22

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.815845Z

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This paper cites Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing , pages =.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing , pages =

Reference 23

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This paper cites Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Linear combination of hamiltonian simulation for nonunitary dynamics with optimal state preparation cost

Reference 24

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.820648Z

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Observation 9dfeaba6-ad3f-4536-8338-c399e8e1ebf8 · outbound

This paper cites Childs, and Lin Lin.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Childs, and Lin Lin

Reference 25

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.792483Z

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This paper cites Childs, Lin Lin, and Lexing Ying.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Childs, Lin Lin, and Lexing Ying

Reference 26

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.814181Z

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This paper cites An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-06-27T05:10:34.771838Z

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This paper cites Arbitrary Boundary Conditions and Constraints in Quantum Algorithms for Differential Equations via Penalty Projections.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Arbitrary Boundary Conditions and Constraints in Quantum Algorithms for Differential Equations via Penalty Projections

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:10:34.834447Z

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This paper cites Optimal quantum simulation of linear non-unitary dynamics.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Optimal quantum simulation of linear non-unitary dynamics

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-06-27T05:10:34.823791Z

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This paper cites Fourier transform-based linear combination of Hamiltonian simulation.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Fourier transform-based linear combination of Hamiltonian simulation

Reference 30

Resolution: metadata mismatch; arxiv_id, observed 2026-06-27T05:10:34.827087Z

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Observation e85734dd-515d-4f11-9ff1-b09406c56bec · outbound

This paper cites Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs

Reference 31

Resolution: metadata mismatch; arxiv_id, observed 2026-06-27T05:10:34.808436Z

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Observation a4aab81d-1965-4986-9056-0836a4c88dd4 · outbound

This paper cites Quantum algorithms based on the Block-Encoding framework for matrix functions by contour integrals.Quantum Information and Computation, 22(11–12):965–979, 2022.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Quantum algorithms based on the Block-Encoding framework for matrix functions by contour integrals.Quantum Information and Computation, 22(11–12):965–979, 2022

Reference 32

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.801157Z

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Observation ed3c6a44-d591-4b70-a363-a963e7dc5942 · outbound

This paper cites Quantum algorithm for linear matrix equations.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Quantum algorithm for linear matrix equations

Reference 33

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T16:38:40.687987Z

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This paper cites Wilde, and Zhicheng Zhang.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Wilde, and Zhicheng Zhang

Reference 34

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.836453Z

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Observation 376b1314-34a6-4ead-8f59-06a9dfbf95eb · outbound

This paper cites J.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms J

Reference 35

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This paper cites Kenney and Alan J.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Kenney and Alan J

Reference 36

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.780602Z

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Observation 44968dcc-969f-443c-98c1-dd957de52e38 · outbound

This paper cites Oxford University Press, Oxford, 1995.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Oxford University Press, Oxford, 1995

Reference 37

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 38

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Observation 25df1f84-e79d-4f93-a54a-f2b8359f54d8 · outbound

This paper cites Solving the algebraic riccati equation with the matrix sign function.Linear Algebra and Its Applications, 85:267–279, 1987.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Solving the algebraic riccati equation with the matrix sign function.Linear Algebra and Its Applications, 85:267–279, 1987

Reference 39

Resolution: verified exact; doi, observed 2026-06-27T05:10:34.810374Z

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 40

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 41

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 42

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 43

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Do not try to force a single answer

Reference 44

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This paper cites Instead of implementing𝑓 by a high-degree QSVT polynomial, implement a linear combination of shifted inverses.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Instead of implementing𝑓 by a high-degree QSVT polynomial, implement a linear combination of shifted inverses

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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Observation c59c5f2a-be08-4c8d-b7a6-5e2fbc38fd8f · outbound

This paper cites For example, if𝐴is stable, 𝑋= ∫ ∞ 0 𝑒𝑡 𝐴𝑄𝑒 𝑡 𝐴† 𝑑𝑡.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms For example, if𝐴is stable, 𝑋= ∫ ∞ 0 𝑒𝑡 𝐴𝑄𝑒 𝑡 𝐴† 𝑑𝑡

Reference 46

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 47

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 48

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 49

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 50

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Observation 179806cf-abab-4d7b-81a4-70286672f95d · outbound

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 51

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This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 52

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 53

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This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 54

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 55

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 56

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 57

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 58

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 59

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 60

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Main deliverable: Reusable block-encoded approximate inverses, Schur complements, or effective operators for downstream quantum algorithms

Reference 61

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 62

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Quantumly, poles near the spectrum are expensive because shifted systems become ill-conditioned

Reference 63

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Rational methods are compelling only if the savings in approximation order survive the cost of shifted inverses

Reference 64

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Observation a766f325-01fc-43b7-b296-765b45aee195 · outbound

This paper cites If𝐴is Hermitian, this can be reduced to real block systems such as 𝐴−𝑎𝐼 𝑏𝐼 −𝑏𝐼 𝐴−𝑎𝐼 −1.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms If𝐴is Hermitian, this can be reduced to real block systems such as 𝐴−𝑎𝐼 𝑏𝐼 −𝑏𝐼 𝐴−𝑎𝐼 −1

Reference 65

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms rational approximation to block-encoding

Reference 66

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Observation c14ff0ff-47c9-436d-bf77-f4b28c1ed25d · outbound

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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 67

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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Observation 93dd710a-5f7d-40a0-a5a8-a4920a8600d4 · outbound

This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 68

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Observation d4f57f08-dce5-401c-b2d5-846749abeed3 · outbound

This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 69

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This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 70

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Observation 3bcb5fe3-b0a5-496c-8e7f-95f00750443a · outbound

This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 71

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Observation 857da072-5fd2-4d39-bb75-c2d2e2039cd3 · outbound

This paper cites an unresolved cited work.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms Unresolved cited work

Reference 72

Resolution: unresolved; no resolver link, observed 2026-06-27T05:07:24.992096Z

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Observation e5d9a167-eee7-49da-aec6-04fd9cd782bd · outbound

This paper cites explicitly implementable contractions with costs,.

From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms explicitly implementable contractions with costs,

Reference 73

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