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Paper Citation Record · LEDGER

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function

As of 10 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 1 inbound Pith citation observation for arXiv:2501.11150.

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

pith.paper-citation-record.v1
2501.11150 v1

Coverage vector

measured 80 of 80 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-10T18:40:27.849647Z

measured 81 of 81 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T15:45:01.270644Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

80 of 80 outbound references displayed

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  • verified fuzzy0
  • unresolved77
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Outbound references

Observation f5780d00-f525-4a0c-ba19-958432c1ed59 · outbound

This paper cites An Explicit Expression of Generating Function for One-Loop Tensor Reduction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function An Explicit Expression of Generating Function for One-Loop Tensor Reduction

Reference 1

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Observation 9b04ed74-6bcb-4c0c-a2e7-7d96d5ada7fc · outbound

This paper cites Reducing full one-loop amplitudes to scalar integrals at the integrand level.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reducing full one-loop amplitudes to scalar integrals at the integrand level

Reference 2

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source=pdf_text observed=2026-08-10T18:40:27.348536Z digest=sha256:dc202f5cfaf703973ed58519c26197501623bb2f1fce0b9eb14cafa5f2fbd436

Observation e470a67e-4a80-4f34-9961-9e6b7664d424 · outbound

This paper cites On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes

Reference 3

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source=pdf_text observed=2026-08-10T18:40:27.355261Z digest=sha256:3c71f719b8e8cfe2d276859fb3a73efff72372d5cee31aab15cbb55ae8f3a27b

Observation 5217f3b2-5cff-4851-a684-61062fe3106d · outbound

This paper cites Hepta-Cuts of Two-Loop Scattering Amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Hepta-Cuts of Two-Loop Scattering Amplitudes

Reference 4

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source=pdf_text observed=2026-08-10T18:40:27.359988Z digest=sha256:ff45480ff3dceedf9756c8a0becc6ed87e9133388bf6f16c951d5be9e4cb544d

Observation 1ecb6871-2b1a-4b5a-be84-70d0db6e7790 · outbound

This paper cites Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods

Reference 5

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source=pdf_text observed=2026-08-10T18:40:27.364775Z digest=sha256:0c77dee7f0f982905ce6ae02fd8ac152ce354426845431b0d23a4b0b79d967c2

Observation ab756c9e-1b51-4042-8248-d44f9f7aaf55 · outbound

This paper cites Integration-by-parts reductions from unitarity cuts and algebraic geometry.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Integration-by-parts reductions from unitarity cuts and algebraic geometry

Reference 6

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source=pdf_text observed=2026-08-10T18:40:27.370100Z digest=sha256:aa57d3ffb8193f9f292e7346030bb60cdb88b889c1b6407d2398426416b79d1a

Observation 3fb00f9c-da25-4187-916b-4f51bd5f147e · outbound

This paper cites Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry

Reference 7

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source=pdf_text observed=2026-08-10T18:40:27.375698Z digest=sha256:b1b8e6c46bb8eea8e1bd5bd317433340d35138fe938c81094993acfcece065c7

Observation e06f8b75-fc7a-4e77-9cba-39f7956c92a1 · outbound

This paper cites Passarino and M.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Passarino and M

Reference 8

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source=pdf_text observed=2026-08-10T18:40:27.380308Z digest=sha256:2120b5336a8b7521a84e00a2a6442c21edac4a246e5fc6d3398674986a72c4c2

Observation 72c67c31-8bfe-48b6-9864-d46a909bae9a · outbound

This paper cites an unresolved cited work.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Unresolved cited work

Reference 9

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source=pdf_text observed=2026-08-10T18:40:27.384963Z digest=sha256:5d1597547dbed42b272d9def40d2d3217ebc9f7de18c29012f9d043a1ccb4e0f

Observation a2abfdfc-39c4-4062-bd43-adabdb9bdea4 · outbound

This paper cites an unresolved cited work.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Unresolved cited work

Reference 10

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source=pdf_text observed=2026-08-10T18:40:27.389329Z digest=sha256:dd2cd2aef13c7fa3f1d8f51486e97d48831eab4d6605aa1e05dbd9e7bab1e915

Observation c33748e7-ae4c-42f4-832f-f563b3c5cb1e · outbound

This paper cites High-precision calculation of multi-loop Feynman integrals by difference equations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function High-precision calculation of multi-loop Feynman integrals by difference equations

Reference 11

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source=pdf_text observed=2026-08-10T18:40:27.393630Z digest=sha256:97e6a1606d96dc24e9cb61fc9e0c0ea205910132907eb680f980d6bb7885d9b8

Observation c2e89b5b-1fa3-4cb5-8f71-5848799a6b9c · outbound

This paper cites Reduze 2 - Distributed Feynman Integral Reduction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reduze 2 - Distributed Feynman Integral Reduction

Reference 12

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source=pdf_text observed=2026-08-10T18:40:27.398935Z digest=sha256:9d646958618186a1fca254b2a42c576216f5f034257a168fcaf6f576c5b715d8

Observation ed7cbc29-cf57-43e6-9af7-327ffb302319 · outbound

This paper cites Kira - A Feynman Integral Reduction Program.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Kira - A Feynman Integral Reduction Program

Reference 13

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source=pdf_text observed=2026-08-10T18:40:27.403743Z digest=sha256:79452ef4ce9bfd4fb06011bc7d3697f529d659f6c7750a232b46482981c06b90

Observation 9692af63-5b96-4016-b7b1-da563824dc7b · outbound

This paper cites FIRE6: Feynman Integral REduction with Modular Arithmetic.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIRE6: Feynman Integral REduction with Modular Arithmetic

Reference 14

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source=pdf_text observed=2026-08-10T18:40:27.408448Z digest=sha256:0cbee426ecbdbbb550939b36da8aa764abeeeca36837505b4c1b9bceac842547

Observation 5dd621d8-5821-4e9b-bcad-9c1fab8a9163 · outbound

This paper cites A novel approach to integration by parts reduction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function A novel approach to integration by parts reduction

Reference 15

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source=pdf_text observed=2026-08-10T18:40:27.413038Z digest=sha256:a86ecbf5e2a78c904e5f261e42b83d1a00f0277c419e32bd0bc42fea8c0f3a93

Observation 292f07b6-401e-40ac-9dcf-7b7f42be12e3 · outbound

This paper cites Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes

Reference 16

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source=pdf_text observed=2026-08-10T18:40:27.417412Z digest=sha256:2ad9f6ac960816710dbe1b76724193075d21aee8684510891167d456c65bcfd0

Observation ead1cb71-1212-4922-bdb1-b884e3df1138 · outbound

This paper cites One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits

Reference 17

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source=pdf_text observed=2026-08-10T18:40:27.421736Z digest=sha256:366169abef38024836dfd64ddbf844f7059cea926c483296bab6ad9fccf0eb66

Observation a9f283d6-2768-49cd-85c8-cf4cc14e8887 · outbound

This paper cites Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills

Reference 18

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source=pdf_text observed=2026-08-10T18:40:27.427257Z digest=sha256:120d8b7683a3063fe1e5e936d9d65902e64ba54ddbab54874f45b5488e7fa8e5

Observation 049138be-e29b-4297-a0a7-aff99913350b · outbound

This paper cites One-Loop Amplitudes Of Gluons In SQCD.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function One-Loop Amplitudes Of Gluons In SQCD

Reference 19

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source=pdf_text observed=2026-08-10T18:40:27.431994Z digest=sha256:ae14283fdb5c02266f321d14fb119af0466cea61e93bf4d7dcfaff04e61b63bd

Observation 86a5c326-83d4-4c57-9f3b-8307b4c8be74 · outbound

This paper cites The Cut-Constructible Part of QCD Amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function The Cut-Constructible Part of QCD Amplitudes

Reference 20

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source=pdf_text observed=2026-08-10T18:40:27.436388Z digest=sha256:9651ff854ca3b32763f8dcde1d1c82947902e8ca16fd2699f6caefaa3e86dac7

Observation 7022fde1-d43d-46a8-995d-539e42c59f6b · outbound

This paper cites Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes

Reference 21

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source=pdf_text observed=2026-08-10T18:40:27.441712Z digest=sha256:6c07fe4473e36663727a4981815f9a4455d7fa7d760e7aaecb940e3b599a7b3a

Observation 7189d41c-57ec-4a9f-af75-f4eb528ce342 · outbound

This paper cites D-dimensional unitarity cut method.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function D-dimensional unitarity cut method

Reference 22

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source=pdf_text observed=2026-08-10T18:40:27.446129Z digest=sha256:271d92ccc4e9bf8ef90e199a3891a457c635c3fef49e99e4d01cfa0de34b1b21

Observation 9c26939a-d554-4018-a0ed-5742f297ab9f · outbound

This paper cites Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients

Reference 23

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source=pdf_text observed=2026-08-10T18:40:27.450947Z digest=sha256:3725ab3efb3a92ad28e15b81db68e794fa67ccba129f9b4f9b5bb168e1f239d6

Observation 198a638d-a97e-434c-936f-5eb155da5533 · outbound

This paper cites Integral Coefficients for One-Loop Amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Integral Coefficients for One-Loop Amplitudes

Reference 24

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source=pdf_text observed=2026-08-10T18:40:27.455997Z digest=sha256:865179ad12159c41642aee59b147f0933e941a0ffa041477630e19a743bbc2aa

Observation 5bc3bdf0-79fb-4c42-9463-b6b646a0fa82 · outbound

This paper cites Single Cut Integration.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Single Cut Integration

Reference 25

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source=pdf_text observed=2026-08-10T18:40:27.460417Z digest=sha256:95236fe51bbac13d02860480d71c77af5cccb9c36193b4dbb933492c1e3deccf

Observation 0021250f-622b-4ad0-9bc1-4d2cdd6bd6b7 · outbound

This paper cites Full one-loop amplitudes from tree amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Full one-loop amplitudes from tree amplitudes

Reference 26

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source=pdf_text observed=2026-08-10T18:40:27.464931Z digest=sha256:2681fac1df70c016796fa88bdc07ba09ca1fbc3b01104d724f0cd2e35f748a52

Observation 34af0d85-37be-4232-99f8-2443db13cd67 · outbound

This paper cites Feynman Integrals and Intersection Theory.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Feynman Integrals and Intersection Theory

Reference 27

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source=pdf_text observed=2026-08-10T18:40:27.469541Z digest=sha256:78dee1339acac70725ac0d59ce5cc51e435b3fc00696fe9db4ef75e561f2ebb7

Observation 8a9b0017-b45a-4e89-932a-f6c99dc8c507 · outbound

This paper cites Vector Space of Feynman Integrals and Multivariate Intersection Numbers.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Vector Space of Feynman Integrals and Multivariate Intersection Numbers

Reference 28

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source=pdf_text observed=2026-08-10T18:40:27.474403Z digest=sha256:f6fcf81665da986bec3420709ffa3044eb400548d70856ced197019d6c122b35

Observation 17c879cb-dc24-4814-bf46-a96121e59e61 · outbound

This paper cites From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals

Reference 29

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Observation 16cff37a-92bd-4b5d-90a2-bcdad5d9cdb3 · outbound

This paper cites Decomposition of Feynman Integrals by Multivariate Intersection Numbers.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Decomposition of Feynman Integrals by Multivariate Intersection Numbers

Reference 30

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source=pdf_text observed=2026-08-10T18:40:27.485881Z digest=sha256:a9fdf4a899d6f3fa1a3acdf80ed6681b02a4e0c59b78328f90c0a1d8cc1ba833

Observation c2347021-b0d8-49d9-ba09-8a09c83117d0 · outbound

This paper cites Duals of Feynman Integrals, 2: Generalized Unitarity.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Duals of Feynman Integrals, 2: Generalized Unitarity

Reference 31

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source=pdf_text observed=2026-08-10T18:40:27.490605Z digest=sha256:9823205625e20f2c59e66de952178869edccdd7405b783c02533b1d3f7f38f78

Observation bf423bc8-15b9-4e5b-9214-22422ea9155c · outbound

This paper cites Duals of Feynman Integrals, I: Differential Equations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Duals of Feynman Integrals, I: Differential Equations

Reference 32

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source=pdf_text observed=2026-08-10T18:40:27.494793Z digest=sha256:276a19dab9cd0bbffd58e5fee6ef52444611c3db74d72f1e0af2083b08d368a6

Observation 1e32334f-64aa-4100-a78e-fea044710e15 · outbound

This paper cites CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes

Reference 33

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source=pdf_text observed=2026-08-10T18:40:27.499271Z digest=sha256:cc16b40a5b440fd1e853243be1c44c92a55523294f8bfa10d65c51507f9bfaec

Observation 90ab8306-0c52-4c11-a542-f5538584b4c2 · outbound

This paper cites Kira 1.2 Release Notes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Kira 1.2 Release Notes

Reference 34

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source=pdf_text observed=2026-08-10T18:40:27.503576Z digest=sha256:ede2fd125fd553b74a2a077eefbdf40b29a20099cd066274406b7814e9dc73e1

Observation 6799542f-0f94-44f2-8b29-1865722b0db8 · outbound

This paper cites Integral Reduction with Kira 2.0 and Finite Field Methods.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Integral Reduction with Kira 2.0 and Finite Field Methods

Reference 35

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source=pdf_text observed=2026-08-10T18:40:27.508403Z digest=sha256:d77d63473c041004f7b4e3fa1b3e0b0604538811e9774045b6a129afc7fd2297

Observation cc06234d-5d90-48c5-bfe4-bed3c5e51689 · outbound

This paper cites Algorithm FIRE -- Feynman Integral REduction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Algorithm FIRE -- Feynman Integral REduction

Reference 36

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source=pdf_text observed=2026-08-10T18:40:27.512287Z digest=sha256:5e16edc3ae98ece9e8b4ca89b739b70a01fd329ee5a88e4c8b548f5d95910277

Observation 78858e15-7437-4337-b181-ec13c4b44bb9 · outbound

This paper cites FIRE4, LiteRed and accompanying tools to solve integration by parts relations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIRE4, LiteRed and accompanying tools to solve integration by parts relations

Reference 37

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source=pdf_text observed=2026-08-10T18:40:27.516290Z digest=sha256:3503e87a64daffd068395d507d9d594e02ebedf878c9b1bd67bd88b43a22fba1

Observation bc81c9e5-4762-45e1-8310-8129607ac3e4 · outbound

This paper cites FIRE5: a C++ implementation of Feynman Integral REduction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIRE5: a C++ implementation of Feynman Integral REduction

Reference 38

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source=pdf_text observed=2026-08-10T18:40:27.520700Z digest=sha256:ade85aad8243f517ed0731881611d08c6e3f3d351e187ec17e9b00ea274fa636

Observation f820580a-770a-468f-84ca-434f93499624 · outbound

This paper cites Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA).

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)

Reference 39

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source=pdf_text observed=2026-08-10T18:40:27.525342Z digest=sha256:fd7236a8ce2be11e3dd7e53332e6d94d0aff3a6fd73c6dcc69934f44c01d8db9

Observation 90b29060-2eda-43ab-911e-ce11eca29f90 · outbound

This paper cites FIESTA 2: parallelizeable multiloop numerical calculations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIESTA 2: parallelizeable multiloop numerical calculations

Reference 40

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source=pdf_text observed=2026-08-10T18:40:27.529622Z digest=sha256:1e9a1584211f1db2c6a59cead2afffabd09356472960039c10f0f9804f77d4bc

Observation c3967c70-9ab2-4b55-b692-3adb40b621ae · outbound

This paper cites FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions

Reference 41

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source=pdf_text observed=2026-08-10T18:40:27.534238Z digest=sha256:921a044e41cc24fbea49230068804578ecd7f29b0de7fec77b71c40a463478b7

Observation 7a0986cf-a44c-4b52-9030-1f6cc5a844b2 · outbound

This paper cites FIESTA 4: optimized Feynman integral calculations with GPU support.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIESTA 4: optimized Feynman integral calculations with GPU support

Reference 42

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source=pdf_text observed=2026-08-10T18:40:27.538838Z digest=sha256:389f08cea074fe28ea54a7d4227db3796e14fab8ce85d04e9cb2c360ae0aad64

Observation 81323a8f-b1fa-4c08-9946-8e18beac275c · outbound

This paper cites FIESTA5: numerical high-performance Feynman integral evaluation.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FIESTA5: numerical high-performance Feynman integral evaluation

Reference 43

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source=pdf_text observed=2026-08-10T18:40:27.543507Z digest=sha256:2c721b4a71d8a42d6fe95a919ea1abc6bd6df759898fafce24c617baa23e5d36

Observation 75b91077-fab6-41b8-9fc3-a9292ae4227d · outbound

This paper cites Reconstructing Rational Functions with $\texttt{FireFly}$.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reconstructing Rational Functions with $\texttt{FireFly}$

Reference 44

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source=pdf_text observed=2026-08-10T18:40:27.547814Z digest=sha256:a35414d9c3e7cb044148af3c55b6c46f4b85bcdc2b85742dc61469bb21199362

Observation 5598a651-e4a8-4465-9390-d7a6ba3ab34f · outbound

This paper cites Interpolation of Dense and Sparse Rational Functions and other Improvements in $\texttt{FireFly}$.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Interpolation of Dense and Sparse Rational Functions and other Improvements in $\texttt{FireFly}$

Reference 45

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source=pdf_text observed=2026-08-10T18:40:27.552040Z digest=sha256:a2ee8f166e92756738cec852f1b0f44417991dd5e32a951a0014d75f3f8913c0

Observation 27821a1e-6102-4d66-962e-43fefbc25afd · outbound

This paper cites Reduze - Feynman Integral Reduction in C++.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reduze - Feynman Integral Reduction in C++

Reference 46

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source=pdf_text observed=2026-08-10T18:40:27.556732Z digest=sha256:abb7237b888636d0bc066471e1402b05ad5d9cc5d57cf6ea2da3a7f525a374bc

Observation 78596372-2799-47ba-ae2b-ccdf6cd48260 · outbound

This paper cites Presenting LiteRed: a tool for the Loop InTEgrals REDuction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Presenting LiteRed: a tool for the Loop InTEgrals REDuction

Reference 47

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source=pdf_text observed=2026-08-10T18:40:27.561732Z digest=sha256:1ad9ceb25956ef9cdb2b8fcff4caecda6296abba30ee48bb925b16d7d361cc46

Observation a14e1aea-691c-4155-9a3a-65e0d6c7cce0 · outbound

This paper cites NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals

Reference 48

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source=pdf_text observed=2026-08-10T18:40:27.566575Z digest=sha256:125c4e810da6cc3f6409d0a8bd6828a3965d24ee68f7bc4c647cb64421310e84

Observation 54acf38f-e91a-436a-989a-1c56c0ec2b5d · outbound

This paper cites Complete reduction of integrals in two-loop five-light-parton scattering amplitudes.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Complete reduction of integrals in two-loop five-light-parton scattering amplitudes

Reference 49

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source=pdf_text observed=2026-08-10T18:40:27.571009Z digest=sha256:6b5d248f0a4e1032381e84a05fe838e99967d16c43be2e5aad4852650c0661b9

Observation c8721347-0cf8-4a07-818e-a1449f6232cd · outbound

This paper cites Blade: A package for block-triangular form improved Feynman integrals decomposition.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Blade: A package for block-triangular form improved Feynman integrals decomposition

Reference 50

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source=pdf_text observed=2026-08-10T18:40:27.575076Z digest=sha256:5416bbd5a1ad8b7813549b87bf35d406d6663724be07c3c85c3791cde77a39d6

Observation 69cc74e3-4a78-4ee8-b67d-992ea8c0e8e0 · outbound

This paper cites Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices

Reference 51

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source=pdf_text observed=2026-08-10T18:40:27.580230Z digest=sha256:1085804e9d4547c1588f8d354b4090d2d3c38ed92d390b7be32d9025046b0124

Observation 3d94818c-bbc4-44c9-9f86-80db93007222 · outbound

This paper cites OPITeR: A program for tensor reduction of multi-loop Feynman Integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function OPITeR: A program for tensor reduction of multi-loop Feynman Integrals

Reference 52

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source=pdf_text observed=2026-08-10T18:40:27.584501Z digest=sha256:2bfd7fcd4fa7be44487f722fadce6737cea06f18e2503aae4243702735de1c8c

Observation 7723ae65-4737-4407-a4fd-9fcb30542af6 · outbound

This paper cites Semi-automatic Calculations of Multi-loop Feynman Amplitudes with AmpRed.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Semi-automatic Calculations of Multi-loop Feynman Amplitudes with AmpRed

Reference 53

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source=pdf_text observed=2026-08-10T18:40:27.589182Z digest=sha256:004980ec492997d0e54c2401b31cdcd6c42800b5250c6cfc5f99aec2e8bdf86e

Observation a81dbbe0-ad0d-4aa6-97c8-e06f7960a593 · outbound

This paper cites FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs

Reference 54

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source=pdf_text observed=2026-08-10T18:40:27.593147Z digest=sha256:ab26d681358a3b847d67f34781b86bc4e21099a811a51b43d117aa3434784444

Observation 494f0dcd-3968-42fe-8ff1-c46197e9ead2 · outbound

This paper cites Balancing act: multivariate rational reconstruction for IBP.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Balancing act: multivariate rational reconstruction for IBP

Reference 55

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source=pdf_text observed=2026-08-10T18:40:27.598561Z digest=sha256:584071cb638839506e114c0a141b8d72df7971204a3be22dba09492bfd0d0c4e

Observation d4693634-2be1-4e9c-b4f3-0f79923e13ca · outbound

This paper cites How to choose master integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function How to choose master integrals

Reference 56

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source=pdf_text observed=2026-08-10T18:40:27.602632Z digest=sha256:84061a62b854f746333125056e5ee64b8447e774430fe7bc52b728ceef4ca358

Observation 0c3b32fd-22ae-4f25-8f0d-bf933af5b990 · outbound

This paper cites Factorization of denominators in integration-by-parts reductions.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Factorization of denominators in integration-by-parts reductions

Reference 57

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source=pdf_text observed=2026-08-10T18:40:27.606676Z digest=sha256:17b61d8465c12646aa4df348e412229f43f4d9f47a13614832f674ada201e72b

Observation 4e56e89a-e91c-49ed-bcbb-48a74b57b48a · outbound

This paper cites Automatic Integral Reduction for Higher Order Perturbative Calculations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Automatic Integral Reduction for Higher Order Perturbative Calculations

Reference 58

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source=pdf_text observed=2026-08-10T18:40:27.610620Z digest=sha256:60953a4ba8d4bb82b4179d49ebd8d4e5b3b33ed9829f09e3ded9629c66f621b6

Observation 1e3763af-d188-4024-a544-8902d234340d · outbound

This paper cites Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD

Reference 59

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source=pdf_text observed=2026-08-10T18:40:27.614618Z digest=sha256:ee18056a493cc0ce6b9fa7145e120f79cdeda1783a7ee19d6d1c686a6a87cb07

Observation 430d5dcf-ad0a-4c58-b170-184d54c97ee7 · outbound

This paper cites Scalar one-loop integrals for QCD.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Scalar one-loop integrals for QCD

Reference 60

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source=pdf_text observed=2026-08-10T18:40:27.618992Z digest=sha256:c6e02d335a629b035f5e262297e2a0019e738375e628381899919cfe6a2a5232

Observation fc6fd110-0355-4dca-9a93-57064c0c8ce9 · outbound

This paper cites QCDLoop: a comprehensive framework for one-loop scalar integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function QCDLoop: a comprehensive framework for one-loop scalar integrals

Reference 61

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verified exact
local_arxiv, observed 2026-08-10T18:40:28.174000Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T18:40:27.623422Z digest=sha256:e47a826290d557ad954e43d9b6a0c067c453898d906ec44839da7b56a4c9b00d

Observation 57491be1-8ae4-4464-abe1-d6b8593eb7ec · outbound

This paper cites Reduction of one-loop tensor 5-point integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reduction of one-loop tensor 5-point integrals

Reference 62

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source=pdf_text observed=2026-08-10T18:40:27.628672Z digest=sha256:28e41074bc72554f74e657708e46d1cfbf322c08ab4013ea2f11b61453000f79

Observation bbe37e34-1012-4525-b01d-225fae254c04 · outbound

This paper cites Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations

Reference 63

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source=pdf_text observed=2026-08-10T18:40:27.768847Z digest=sha256:9c5f0178d4215b88e0585334e8a8fdb353ffb237f77debad7713da481664d860

Observation ff236a57-2b3c-432c-a43e-89a698cc8b84 · outbound

This paper cites Adaptive Integrand Decomposition in parallel and orthogonal space.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Adaptive Integrand Decomposition in parallel and orthogonal space

Reference 64

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source=pdf_text observed=2026-08-10T18:40:27.774658Z digest=sha256:549a5be1fbf854a01504e1f13b88b81f527379f46c4d9d155c3900a838c32a02

Observation b491a604-2b71-42d0-8a7f-6a3ec3083f60 · outbound

This paper cites Analytic Tadpole Coefficients of One-loop Integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Analytic Tadpole Coefficients of One-loop Integrals

Reference 65

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source=pdf_text observed=2026-08-10T18:40:27.779418Z digest=sha256:58259cf5683bb09c4ddd1b7cec868f1a4a64356d950ffceba21619509862e2d1

Observation d99e4843-8b7d-4571-b7a5-3114ffbec396 · outbound

This paper cites One-loop Feynman Integral Reduction by Differential Operators.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function One-loop Feynman Integral Reduction by Differential Operators

Reference 66

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source=pdf_text observed=2026-08-10T18:40:27.783871Z digest=sha256:78ba6d2802601743a03d9430aa3772a672600a0258b1fbaadf233c34a5cc9940

Observation c664c609-f0cb-4ed9-b434-baf5897211a5 · outbound

This paper cites Reduction of General One-loop Integrals Using Auxiliary Vector.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reduction of General One-loop Integrals Using Auxiliary Vector

Reference 67

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source=pdf_text observed=2026-08-10T18:40:27.788452Z digest=sha256:b482556d7b22fd2c7326293e9b3c9502409a408375aa9ec7b81d269a81323a79

Observation c416d348-745a-4bf5-ab0d-a4b4e60cef0a · outbound

This paper cites PV-Reduction of Sunset Topology with Auxiliary Vector.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function PV-Reduction of Sunset Topology with Auxiliary Vector

Reference 68

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source=pdf_text observed=2026-08-10T18:40:27.793472Z digest=sha256:28e285b5e054c44358bf80955ba7b263ca61bb4ee2751fc043ecdcdbc94dbcb9

Observation 81b309cd-2f83-42fa-b407-bed7c46ec2f7 · outbound

This paper cites Universal Treatment of Reduction for One-Loop Integrals in Projective Space.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Universal Treatment of Reduction for One-Loop Integrals in Projective Space

Reference 69

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source=pdf_text observed=2026-08-10T18:40:27.797862Z digest=sha256:73ffb4902b055ecbeccba107e9a668da7916bedd5d468484568aee4885532ee1

Observation b47c0033-8d4e-4950-9dc9-91c6352b759e · outbound

This paper cites Reduction with Degenerate Gram matrix for One-loop Integrals.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Reduction with Degenerate Gram matrix for One-loop Integrals

Reference 70

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source=pdf_text observed=2026-08-10T18:40:27.802279Z digest=sha256:a6d6b21ceb760d5960b92648b757f5aac346f19bbf0dfb4befa848058af99b5d

Observation 7c87969f-d1a1-41fb-8746-9620fcbe8166 · outbound

This paper cites Nontrivial One-loop Recursive Reduction Relation.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Nontrivial One-loop Recursive Reduction Relation

Reference 71

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source=pdf_text observed=2026-08-10T18:40:27.806724Z digest=sha256:bcc077274f8e7c730aea82b027d122eee0244ad8e4876644f7a08d27c5289049

Observation dc78125b-289c-405b-a8ca-b5380eb8c048 · outbound

This paper cites Tensor Loop Reduction via the Baikov Representation and an Auxiliary Vector.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Tensor Loop Reduction via the Baikov Representation and an Auxiliary Vector

Reference 72

Resolution
verified exact
local_arxiv, observed 2026-08-10T18:40:28.017083Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T18:40:27.811329Z digest=sha256:79ad21b2bc96583bfcb260fc9f29564653231f4e4933876ea2902a1fb354ead2

Observation 45a01ef3-33b6-4028-bcb2-1593660875dd · outbound

This paper cites Generation Function For One-loop Tensor Reduction.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Generation Function For One-loop Tensor Reduction

Reference 73

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source=pdf_text observed=2026-08-10T18:40:27.815773Z digest=sha256:7fa2981ef2cb5c03d0079d06397f1e60798970458c863549e7cd85aade503feb

Observation f3330ed9-998e-4db8-b5ec-849242c78698 · outbound

This paper cites Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms

Reference 74

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verified exact
local_arxiv, observed 2026-08-10T18:40:27.981726Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-10T18:40:27.820851Z digest=sha256:0165ec3bcfcceb04505a1d942b440ee9101eb8ffb863945f06041206ea4ae68d

Observation e7a0b694-dbca-44fd-bb63-1169f66c181f · outbound

This paper cites Direct Solution of Integration-by-Parts Systems.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Direct Solution of Integration-by-Parts Systems

Reference 75

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source=pdf_text observed=2026-08-10T18:40:27.825753Z digest=sha256:963cfa0d8e8323187b01c1fd21485856e072ce9947bba0baee5c266e844782e2

Observation d8410580-74e0-433a-98b9-6fc300e72393 · outbound

This paper cites Exploring the linear space of Feynman integrals via generating functions.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Exploring the linear space of Feynman integrals via generating functions

Reference 76

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source=pdf_text observed=2026-08-10T18:40:27.830481Z digest=sha256:14c351b11e5f5fb4f01f40d9249bd143dd8cb75425c8e1cad1578ba369104ad7

Observation 713b7457-73ea-4aab-86e7-b17ff4729415 · outbound

This paper cites General One-loop Generating Function by IBP relations.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function General One-loop Generating Function by IBP relations

Reference 77

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This paper cites Solving arbitrary one-loop reduction via generating function.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Solving arbitrary one-loop reduction via generating function

Reference 78

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Observation b862c7f1-ca6e-485a-a565-c181c4f3cbac · outbound

This paper cites Systematic integral evaluation for spin-resummed binary dynamics.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Systematic integral evaluation for spin-resummed binary dynamics

Reference 79

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Observation 7bc5bfba-a2fa-4f52-b743-96919e42cea5 · outbound

This paper cites Spinning waveforms in cubic effective field theories of gravity.

Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function Spinning waveforms in cubic effective field theories of gravity

Reference 80

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Observation 3bfc30f1-77d2-4340-8610-e519bc0d7966 · inbound

Tensor Reduction of Sunset by Generating Function cites this paper.

Tensor Reduction of Sunset by Generating Function Direct Expression for One-Loop Tensor Reduction with Lorentz Indices via Generating Function

Reference 43

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