Paper Citation Record · LEDGER

The Role of Integration Cycles in Complex Langevin Simulations

As of 12 August 2026, this Paper Citation Record lists 79 of 79 outbound references and 2 inbound Pith citation observations for arXiv:2412.17137.

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

pith.paper-citation-record.v1
2412.17137 v2

Coverage vector

measured 79 of 79 reference resolution

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measured 81 of 81 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T14:27:43.624486Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T12:51:08.037399Z

Reference resolution

79 of 79 outbound references displayed

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Outbound references

Observation 372bd046-332a-4492-b767-dcbe88231e97 · outbound

This paper cites In order to define the two linearly independent integration cycles for this model, we introduce two variables ξ1 and ξ2 in analogy to (30).

The Role of Integration Cycles in Complex Langevin Simulations In order to define the two linearly independent integration cycles for this model, we introduce two variables ξ1 and ξ2 in analogy to (30)

Reference 1

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Observation fa4ab239-e28d-4b9f-bdc0-c0d800886d85 · outbound

This paper cites However, as is known since [62], the introduction of a nontrivial kernel K ≈ λ−1/2 in (4) can ensure ⟨zn⟩CL = ⟨zn⟩exact for arbitrary λ ̸= 0.

The Role of Integration Cycles in Complex Langevin Simulations However, as is known since [62], the introduction of a nontrivial kernel K ≈ λ−1/2 in (4) can ensure ⟨zn⟩CL = ⟨zn⟩exact for arbitrary λ ̸= 0

Reference 2

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Observation e7902c15-94bd-4dfd-888d-63ad89b92b92 · outbound

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The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 3

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Observation 723cb7c2-6111-4c62-888f-76a24f47a0ab · outbound

This paper cites Schwinger-Dyson equations and line integrals.

The Role of Integration Cycles in Complex Langevin Simulations Schwinger-Dyson equations and line integrals

Reference 4

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Observation 5b1c08f8-8287-4f8b-952b-63d51068f292 · outbound

This paper cites The order of the quantum chromodynamics transition predicted by the standard model of particle physics.

The Role of Integration Cycles in Complex Langevin Simulations The order of the quantum chromodynamics transition predicted by the standard model of particle physics

Reference 5

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Observation bd9f0e97-7415-438e-b6e4-b23cad7dfb4f · outbound

This paper cites Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations.

The Role of Integration Cycles in Complex Langevin Simulations Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

Reference 6

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Observation 7afef7b3-846e-4773-85e8-2a8c8384038c · outbound

This paper cites QCD simulations at small chemical potential.

The Role of Integration Cycles in Complex Langevin Simulations QCD simulations at small chemical potential

Reference 7

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Observation eb68a09f-cd33-4aa0-9183-a4ef0535ee1a · outbound

This paper cites Goksch, Phys.

The Role of Integration Cycles in Complex Langevin Simulations Goksch, Phys

Reference 8

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Observation 8367e8aa-408f-466a-b81e-e8e3689f5457 · outbound

This paper cites A new computational approach to lattice quantum field theories.

The Role of Integration Cycles in Complex Langevin Simulations A new computational approach to lattice quantum field theories

Reference 9

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Observation b329d41f-01e7-4774-b453-a9e66a4118e7 · outbound

This paper cites Parisi, Phys.

The Role of Integration Cycles in Complex Langevin Simulations Parisi, Phys

Reference 10

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Observation 8efe6510-5a68-433e-b2f2-cb7ac1b5362a · outbound

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The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 11

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Observation 1847b7e8-2cb4-40e7-97a2-8ad7475bf108 · outbound

This paper cites High density QCD on a Lefschetz thimble?.

The Role of Integration Cycles in Complex Langevin Simulations High density QCD on a Lefschetz thimble?

Reference 12

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Observation f05e8e34-153b-49b2-8303-fbf3ae74129d · outbound

This paper cites Tensor Networks and their use for Lattice Gauge Theories.

The Role of Integration Cycles in Complex Langevin Simulations Tensor Networks and their use for Lattice Gauge Theories

Reference 13

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Observation 283d0173-d522-4d2b-a620-2722f0a5787f · outbound

This paper cites Imaginary chemical potential and finite fermion density on the lattice.

The Role of Integration Cycles in Complex Langevin Simulations Imaginary chemical potential and finite fermion density on the lattice

Reference 14

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Observation 383437f6-ee84-4eb4-9de9-3c6714df4c72 · outbound

This paper cites The QCD thermal phase transition in the presence of a small chemical potential.

The Role of Integration Cycles in Complex Langevin Simulations The QCD thermal phase transition in the presence of a small chemical potential

Reference 15

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Observation a2a43577-8ca1-4872-9c21-fb827db0bc06 · outbound

This paper cites Parisi and Y.-S.

The Role of Integration Cycles in Complex Langevin Simulations Parisi and Y.-S

Reference 16

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Observation aa582ae2-cf4d-4e02-9b00-80588751b509 · outbound

This paper cites Damgaard and H.

The Role of Integration Cycles in Complex Langevin Simulations Damgaard and H

Reference 17

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Observation b32f60d4-5cde-4d1c-90db-ec3228f32b98 · outbound

This paper cites Namiki, Prog.

The Role of Integration Cycles in Complex Langevin Simulations Namiki, Prog

Reference 18

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Observation 39c072a3-f4e7-49d9-9cb1-6b25b3704713 · outbound

This paper cites Karsch and H.

The Role of Integration Cycles in Complex Langevin Simulations Karsch and H

Reference 19

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Observation 74f584e8-cc8a-4a67-85a3-d8a8d8b1e06e · outbound

This paper cites S¨ oderberg, Nucl.

The Role of Integration Cycles in Complex Langevin Simulations S¨ oderberg, Nucl

Reference 20

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Observation 1d511953-3808-47e9-a246-9d75f33bd251 · outbound

This paper cites The Mechanism of Complex Langevin Simulations.

The Role of Integration Cycles in Complex Langevin Simulations The Mechanism of Complex Langevin Simulations

Reference 21

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Observation e3de7185-3b59-40a5-825a-ee1b2c134a52 · outbound

This paper cites Okano, L.

The Role of Integration Cycles in Complex Langevin Simulations Okano, L

Reference 22

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Observation df8a752d-da77-4be8-998d-f4f6d11e8b49 · outbound

This paper cites Ambjørn and S.

The Role of Integration Cycles in Complex Langevin Simulations Ambjørn and S

Reference 23

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This paper cites Ambjørn, M.

The Role of Integration Cycles in Complex Langevin Simulations Ambjørn, M

Reference 24

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The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 25

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This paper cites Fujimura, K.

The Role of Integration Cycles in Complex Langevin Simulations Fujimura, K

Reference 26

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Observation 78de49bb-f71e-4241-b652-c5ed4c1bebb1 · outbound

This paper cites Simulating nonequilibrium quantum fields with stochastic quantization techniques.

The Role of Integration Cycles in Complex Langevin Simulations Simulating nonequilibrium quantum fields with stochastic quantization techniques

Reference 27

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This paper cites Lattice simulations of real-time quantum fields.

The Role of Integration Cycles in Complex Langevin Simulations Lattice simulations of real-time quantum fields

Reference 28

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This paper cites Adaptive stepsize and instabilities in complex Langevin dynamics.

The Role of Integration Cycles in Complex Langevin Simulations Adaptive stepsize and instabilities in complex Langevin dynamics

Reference 29

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This paper cites Gauge cooling in complex Langevin for QCD with heavy quarks.

The Role of Integration Cycles in Complex Langevin Simulations Gauge cooling in complex Langevin for QCD with heavy quarks

Reference 30

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This paper cites Simulating full QCD at nonzero density using the complex Langevin equation.

The Role of Integration Cycles in Complex Langevin Simulations Simulating full QCD at nonzero density using the complex Langevin equation

Reference 31

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This paper cites Progress in complex Langevin simulations of full QCD at nonzero density.

The Role of Integration Cycles in Complex Langevin Simulations Progress in complex Langevin simulations of full QCD at nonzero density

Reference 32

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This paper cites Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion.

The Role of Integration Cycles in Complex Langevin Simulations Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion

Reference 33

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This paper cites Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting.

The Role of Integration Cycles in Complex Langevin Simulations Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting

Reference 34

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This paper cites QCD equation of state via the complex Langevin method.

The Role of Integration Cycles in Complex Langevin Simulations QCD equation of state via the complex Langevin method

Reference 35

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This paper cites The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics.

The Role of Integration Cycles in Complex Langevin Simulations The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics

Reference 36

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This paper cites Complex Langevin and other approaches to the sign problem in quantum many-body physics.

The Role of Integration Cycles in Complex Langevin Simulations Complex Langevin and other approaches to the sign problem in quantum many-body physics

Reference 37

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This paper cites The Complex Langevin method: When can it be trusted?.

The Role of Integration Cycles in Complex Langevin Simulations The Complex Langevin method: When can it be trusted?

Reference 38

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This paper cites Complex Langevin: Etiology and Diagnostics of its Main Problem.

The Role of Integration Cycles in Complex Langevin Simulations Complex Langevin: Etiology and Diagnostics of its Main Problem

Reference 39

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This paper cites Does the complex Langevin method give unbiased results?.

The Role of Integration Cycles in Complex Langevin Simulations Does the complex Langevin method give unbiased results?

Reference 40

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This paper cites The argument for justification of the complex Langevin method and the condition for correct convergence.

The Role of Integration Cycles in Complex Langevin Simulations The argument for justification of the complex Langevin method and the condition for correct convergence

Reference 41

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The Role of Integration Cycles in Complex Langevin Simulations Complex Langevin and boundary terms

Reference 42

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This paper cites Controlling Complex Langevin simulations of lattice models by boundary term analysis.

The Role of Integration Cycles in Complex Langevin Simulations Controlling Complex Langevin simulations of lattice models by boundary term analysis

Reference 43

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This paper cites Complex Langevin: Correctness criteria, boundary terms and spectrum.

The Role of Integration Cycles in Complex Langevin Simulations Complex Langevin: Correctness criteria, boundary terms and spectrum

Reference 44

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This paper cites Analytic Continuation Of Chern-Simons Theory.

The Role of Integration Cycles in Complex Langevin Simulations Analytic Continuation Of Chern-Simons Theory

Reference 45

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This paper cites A New Look At The Path Integral Of Quantum Mechanics.

The Role of Integration Cycles in Complex Langevin Simulations A New Look At The Path Integral Of Quantum Mechanics

Reference 46

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The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 47

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The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 48

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Observation cb5cb503-dc1c-4240-9d3f-b78a1b43c40b · outbound

This paper cites Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals.

The Role of Integration Cycles in Complex Langevin Simulations Complex Probabilities on R^N as Real Probabilities on C^N and an Application to Path Integrals

Reference 49

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This paper cites Existence of positive representations for complex weights.

The Role of Integration Cycles in Complex Langevin Simulations Existence of positive representations for complex weights

Reference 50

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Observation f22a69ff-c273-42c0-9ea4-3e78fb527f25 · outbound

This paper cites Real time evolution of scalar fields with kernelled Complex Langevin equation.

The Role of Integration Cycles in Complex Langevin Simulations Real time evolution of scalar fields with kernelled Complex Langevin equation

Reference 51

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Observation 796aaa40-a70e-4f89-96b4-959e01273c7d · outbound

This paper cites Towards learning optimized kernels for complex Langevin.

The Role of Integration Cycles in Complex Langevin Simulations Towards learning optimized kernels for complex Langevin

Reference 52

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This paper cites Lattice real-time simulations with learned optimal kernels.

The Role of Integration Cycles in Complex Langevin Simulations Lattice real-time simulations with learned optimal kernels

Reference 53

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This paper cites Testing dynamical stabilization of Complex Langevin simulations of QCD.

The Role of Integration Cycles in Complex Langevin Simulations Testing dynamical stabilization of Complex Langevin simulations of QCD

Reference 54

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This paper cites Kernels and integration cycles in complex Langevin simulations.

The Role of Integration Cycles in Complex Langevin Simulations Kernels and integration cycles in complex Langevin simulations

Reference 55

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This paper cites Garc ´ ıa, Z.

The Role of Integration Cycles in Complex Langevin Simulations Garc ´ ıa, Z

Reference 56

Resolution: verified exact; raw_fallback, observed 2026-08-11T05:52:05.831848Z

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Observation a997982a-9a85-4620-8628-a048271d3122 · outbound

This paper cites Complex Langevin Equations and Schwinger-Dyson Equations.

The Role of Integration Cycles in Complex Langevin Simulations Complex Langevin Equations and Schwinger-Dyson Equations

Reference 57

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Observation 6db1b719-2d15-41fa-ad94-f6a6535689d8 · outbound

This paper cites Complexified Path Integrals and the Phases of Quantum Field Theory.

The Role of Integration Cycles in Complex Langevin Simulations Complexified Path Integrals and the Phases of Quantum Field Theory

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.574551Z

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Unavailable: canonical work link unavailable.

Observation 73d062d8-6fbf-4cc9-a8d9-52e4ac97af8b · outbound

This paper cites an unresolved cited work.

The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 59

Resolution: verified exact; doi, observed 2026-08-11T05:52:05.667427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a3b59203-b593-43cd-908b-7735718102d5 · outbound

This paper cites an unresolved cited work.

The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 60

Resolution: verified exact; doi, observed 2026-08-11T05:52:05.658279Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3de68f97-cb04-4afa-abbb-0d2acf3d33ad · outbound

This paper cites Ukawa and M.

The Role of Integration Cycles in Complex Langevin Simulations Ukawa and M

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.250130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1f9f06c0-a49d-43fb-a53e-bd704df321ae · outbound

This paper cites L’Ecuyer, R.

The Role of Integration Cycles in Complex Langevin Simulations L’Ecuyer, R

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.243337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bc7c35ff-c289-4ccc-9610-a4049efdfe1a · outbound

This paper cites an unresolved cited work.

The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 63

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:52:06.236555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation abe980c5-fe55-48db-bb28-7bd68477adeb · outbound

This paper cites Vingelmann, and F.

The Role of Integration Cycles in Complex Langevin Simulations Vingelmann, and F

Reference 64

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0fb890eb-a127-4790-be02-c3dea2aac72b · outbound

This paper cites Okamoto, K.

The Role of Integration Cycles in Complex Langevin Simulations Okamoto, K

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.222279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4041e716-f87d-4599-840c-859a824563c5 · outbound

This paper cites Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane.

The Role of Integration Cycles in Complex Langevin Simulations Lefschetz thimbles and stochastic quantisation: Complex actions in the complex plane

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.595081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfda6ae1-d914-4f5a-860e-a5dda5f6f761 · outbound

This paper cites Some remarks on Lefschetz thimbles and complex Langevin dynamics.

The Role of Integration Cycles in Complex Langevin Simulations Some remarks on Lefschetz thimbles and complex Langevin dynamics

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.597612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f013b4f0-4d95-4db2-a53b-3d6bac3f8721 · outbound

This paper cites Lefschetz thimble-inspired weight regularizations for complex Langevin simulations.

The Role of Integration Cycles in Complex Langevin Simulations Lefschetz thimble-inspired weight regularizations for complex Langevin simulations

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.600476Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20edbbb8-d9f2-45ee-bcd0-94d4a5a151b8 · outbound

This paper cites Okano, L.

The Role of Integration Cycles in Complex Langevin Simulations Okano, L

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.215010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ba1a0985-3b3f-4247-ad28-bcf97474e7c7 · outbound

This paper cites van Rossum and J.

The Role of Integration Cycles in Complex Langevin Simulations van Rossum and J

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.207936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6aa2893e-5d78-4872-ad90-7ad38b19c6b3 · outbound

This paper cites van der Walt, S.

The Role of Integration Cycles in Complex Langevin Simulations van der Walt, S

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.201009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a825e28d-1f85-49db-9893-c26c1ad25f7e · outbound

This paper cites Virtanen, R.

The Role of Integration Cycles in Complex Langevin Simulations Virtanen, R

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.194048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d4a01375-446c-4a94-9f4e-de8976077fdf · outbound

This paper cites McKinney, Proceedings of the 9th Python in Science Conference (Scipy 2010) , 51 (2010).

The Role of Integration Cycles in Complex Langevin Simulations McKinney, Proceedings of the 9th Python in Science Conference (Scipy 2010) , 51 (2010)

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:52:06.187171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5bb2778a-4112-4808-99f8-1ef944a16feb · outbound

This paper cites an unresolved cited work.

The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.618554Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8442256e-87b5-4e6c-80a6-44717ab4dc28 · outbound

This paper cites Crameri, Zenodo 10.5281/zenodo.8409685 (2023).

The Role of Integration Cycles in Complex Langevin Simulations Crameri, Zenodo 10.5281/zenodo.8409685 (2023)

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.621607Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81687b59-2fd8-42bb-b6e0-17be1b7cb1ca · outbound

This paper cites an unresolved cited work.

The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 76

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:52:06.174611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 634145e1-40db-4149-a165-d5dd92f12a66 · outbound

This paper cites Dos and don'ts of reduced chi-squared.

The Role of Integration Cycles in Complex Langevin Simulations Dos and don'ts of reduced chi-squared

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.627361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b43a411-72cf-4a97-8847-58d81bb8b433 · outbound

This paper cites Optimal whitening and decorrelation.

The Role of Integration Cycles in Complex Langevin Simulations Optimal whitening and decorrelation

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.629919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cae273c3-b533-440e-87ac-c2a7d9fdb461 · outbound

This paper cites an unresolved cited work.

The Role of Integration Cycles in Complex Langevin Simulations Unresolved cited work

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-11T05:52:05.633038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 5fc91293-8e0d-407f-ada1-790d9ed5d4c1 · inbound

Correctness criteria for complex Langevin cites this paper.

Correctness criteria for complex Langevin The Role of Integration Cycles in Complex Langevin Simulations

Reference 50

Resolution: verified exact; arxiv_id, observed 2026-05-10T14:30:31.703531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d86ab5b0-fb22-44c2-b92f-72fe6c195fbb · inbound

The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations cites this paper.

The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations The Role of Integration Cycles in Complex Langevin Simulations

Reference 81

Resolution: verified exact; arxiv_id, observed 2026-05-11T12:51:08.043515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.