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Paper Citation Record · LEDGER

Singularities of massless scattering and cluster algebras

As of 21 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 4 inbound Pith citation observations for arXiv:2507.01015.

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

pith.paper-citation-record.v1
2507.01015 v1

Coverage vector

measured 58 of 58 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:09:07.810683Z

measured 62 of 62 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:58:51.604536Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T17:05:50.640634Z

Reference resolution

58 of 58 outbound references displayed

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  • verified fuzzy22
  • unresolved21
  • parse uncertain0
  • malformed identifier0
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External citation measurements

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Outbound references

Observation bf60e181-5f7c-4db6-b2cb-d5542633da83 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 1

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Observation 6a2c37d3-9f90-4886-923f-8b7cbaa778f8 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 2

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Observation 4f97bfc5-48f5-41fd-a3ec-f9a253b82352 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 3

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Observation 83f13ed8-9c4f-4d7e-bf21-f8a5a3b8a4f6 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 4

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Observation a0b34686-cb8d-4267-85e1-d40bca7ba5d8 · outbound

This paper cites Written in terms of spinor brackets, letters V6 to V21 from the non-planar two-loop five-point alphabet are quadratic.

Singularities of massless scattering and cluster algebras Written in terms of spinor brackets, letters V6 to V21 from the non-planar two-loop five-point alphabet are quadratic

Reference 5

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Observation 3323056d-dc0f-43c9-a959-2db3eee2c991 · outbound

This paper cites Each quadratic letter is of the form Qi,j;k,l;m = si,j − sk,l (37) for {i, j, k, l, m} = {1, 2, 3, 4, 5}.

Singularities of massless scattering and cluster algebras Each quadratic letter is of the form Qi,j;k,l;m = si,j − sk,l (37) for {i, j, k, l, m} = {1, 2, 3, 4, 5}

Reference 6

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Observation bb50382a-ec9d-4a47-a632-8f44576dd50e · outbound

This paper cites These are the pairs of quadratics which appear separated by one slot in presently computed two-loop planar data, e.g.

Singularities of massless scattering and cluster algebras These are the pairs of quadratics which appear separated by one slot in presently computed two-loop planar data, e.g

Reference 7

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Observation 9fa1671c-9321-4083-87e8-8525103c29e0 · outbound

This paper cites These appear separated by one slot in non-planar data, with a unique combi- nation sitting between.

Singularities of massless scattering and cluster algebras These appear separated by one slot in non-planar data, with a unique combi- nation sitting between

Reference 8

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Observation 5ee90f54-e25b-45ba-9a74-ea167a672dd1 · outbound

This paper cites Cluster algebras i: Foundations, 2001.

Singularities of massless scattering and cluster algebras Cluster algebras i: Foundations, 2001

Reference 9

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Observation 02a7250b-3850-4025-9099-4004de0e4d7d · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 10

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Observation 162d03f3-6a15-4bb0-9df5-bb9aca2d82fe · outbound

This paper cites Five of the algebraic letters are these naked discriminants.

Singularities of massless scattering and cluster algebras Five of the algebraic letters are these naked discriminants

Reference 11

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Observation c7c3f2ee-b7f4-468e-85af-0f4f87ccbd88 · outbound

This paper cites An example of an origin cluster is shown in Figure 5.

Singularities of massless scattering and cluster algebras An example of an origin cluster is shown in Figure 5

Reference 12

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Observation 23505040-1b54-456c-8fbf-954106c8726e · outbound

This paper cites (18) The map in the other direction, from four-index Pl¨ ucker coordinates to square and angle brackets, is sim- ilarly straightforward.

Singularities of massless scattering and cluster algebras (18) The map in the other direction, from four-index Pl¨ ucker coordinates to square and angle brackets, is sim- ilarly straightforward

Reference 13

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 518ad081-5afb-4f62-9964-f556c509b96c · outbound

This paper cites The only difference is that there are now only 16 different origin clusters, each of which asymptotes to the same ray.

Singularities of massless scattering and cluster algebras The only difference is that there are now only 16 different origin clusters, each of which asymptotes to the same ray

Reference 14

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verified fuzzy
raw_fallback, observed 2026-08-06T21:09:15.764170Z

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Observation 1aab7b11-66c4-41a9-81f1-f419c0b6e2c6 · outbound

This paper cites This class seems to have a realisation in the flag, specifi- cally using the momentum twistor embedding.

Singularities of massless scattering and cluster algebras This class seems to have a realisation in the flag, specifi- cally using the momentum twistor embedding

Reference 15

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Observation 8ef6d288-7639-4571-8e15-7b080d3d1a0e · outbound

This paper cites Since W61 is one of the letters which we fail to reproduce in either embedding of the kinematics, we cannot hope to realise this inside F(2 , 4; 6).

Singularities of massless scattering and cluster algebras Since W61 is one of the letters which we fail to reproduce in either embedding of the kinematics, we cannot hope to realise this inside F(2 , 4; 6)

Reference 16

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Observation 5b51d159-5cc4-4270-870c-820e0e9518dc · outbound

This paper cites Express these in terms of the letters of the planar pentagon al- phabet.

Singularities of massless scattering and cluster algebras Express these in terms of the letters of the planar pentagon al- phabet

Reference 17

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Observation 241d6812-66b4-4b2e-88f0-2ca18e47b0ab · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 18

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Observation 41ffa800-0682-4658-b7aa-7d62ecc065f0 · outbound

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Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 19

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Observation c5d9ecba-1f60-431b-bd79-abfcafecc11e · outbound

This paper cites Summer School in Total Positivity and Quantum Field Theory.

Singularities of massless scattering and cluster algebras Summer School in Total Positivity and Quantum Field Theory

Reference 20

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Observation 2f5a5ec8-cefb-4b6b-8503-04ba69f235cd · outbound

This paper cites Tropicalised braid automorphisms of grassmannian cluster algebras.

Singularities of massless scattering and cluster algebras Tropicalised braid automorphisms of grassmannian cluster algebras

Reference 21

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Observation fc2ce32d-3f40-4788-92b0-3d2c5e6c9bf2 · outbound

This paper cites Cluster structures on spinor helicity and momentum twistor varieties.

Singularities of massless scattering and cluster algebras Cluster structures on spinor helicity and momentum twistor varieties

Reference 22

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Observation 1195a7c7-fb71-46cf-bcc6-978da668e96d · outbound

This paper cites Symbol alphabets in qcd and flag cluster algebras, 2025.

Singularities of massless scattering and cluster algebras Symbol alphabets in qcd and flag cluster algebras, 2025

Reference 23

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Observation 5b790e70-5d87-4ed5-bc88-c93b3be3ff58 · outbound

This paper cites Adjacency for scattering amplitudes from the Gr\"obner fan.

Singularities of massless scattering and cluster algebras Adjacency for scattering amplitudes from the Gr\"obner fan

Reference 24

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Observation df549e62-e5f3-4d01-90ef-76b56a596814 · outbound

This paper cites Dixon, James M.

Singularities of massless scattering and cluster algebras Dixon, James M

Reference 25

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Observation 250e58b0-a016-4fd1-beed-8e64fa6df554 · outbound

This paper cites Dixon, James M.

Singularities of massless scattering and cluster algebras Dixon, James M

Reference 26

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doi, observed 2026-08-06T21:09:10.670438Z

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Observation c1235a11-0002-4e9a-8778-cf2364a7d184 · outbound

This paper cites Here we review the recovery of the symbol letters using both F(2 , n− 4; n) and F(2, 4; n) in the case n = 5.

Singularities of massless scattering and cluster algebras Here we review the recovery of the symbol letters using both F(2 , n− 4; n) and F(2, 4; n) in the case n = 5

Reference 27

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Observation 7976657d-75bf-4f9f-b5b6-7a8509174e11 · outbound

This paper cites Dixon, James M.

Singularities of massless scattering and cluster algebras Dixon, James M

Reference 28

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source=pdf_text observed=2026-08-06T21:09:04.933435Z digest=sha256:c9f6066cebed51f4fb2c4237986ad84adab2261ad538bd07a3fc1a8f9f2c1c9e

Observation b7accffd-5a13-4288-a43b-cb3f5e70ea1a · outbound

This paper cites Cluster adjacency and the four-loop nmhv heptagon.

Singularities of massless scattering and cluster algebras Cluster adjacency and the four-loop nmhv heptagon

Reference 29

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doi, observed 2026-08-06T21:09:10.443374Z

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Observation acfd001d-f1f6-496c-aa61-e82b4760ebd7 · outbound

This paper cites an unresolved cited work.

Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 30

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Observation c1abed89-545a-48ec-aa7c-82b522adca23 · outbound

This paper cites Tropical grassmannians, clus- ter algebras and scattering amplitudes.

Singularities of massless scattering and cluster algebras Tropical grassmannians, clus- ter algebras and scattering amplitudes

Reference 31

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Observation 7d4fa3b3-efde-41af-ac68-f9a6c5365d5d · outbound

This paper cites Henn, and Georgios Pap- athanasiou.

Singularities of massless scattering and cluster algebras Henn, and Georgios Pap- athanasiou

Reference 32

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Observation ed24367d-24e3-4b00-8e47-f40553f08d08 · outbound

This paper cites Dixon, ¨Omer G¨ urdo˘ gan, Yu-Ting Liu, An- drew J.

Singularities of massless scattering and cluster algebras Dixon, ¨Omer G¨ urdo˘ gan, Yu-Ting Liu, An- drew J

Reference 33

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Observation c3c9f275-b6c4-48bb-9334-db6767bd81a8 · outbound

This paper cites The other rational letters missed in in the momentum twistor embedding are all permutations of this letter, and so the entire rational alphabet is recovered.

Singularities of massless scattering and cluster algebras The other rational letters missed in in the momentum twistor embedding are all permutations of this letter, and so the entire rational alphabet is recovered

Reference 34

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-06T21:09:04.278181Z digest=sha256:3254b2f51ce68a132c3d24493625b0e6c7fd400fdd4bcd4e8044f95d12148ea7

Observation f8f1d414-005b-4295-a3b8-deaa1ad4ff63 · outbound

This paper cites An Exceptional Cluster Algebra for Higgs plus Jet Production.

Singularities of massless scattering and cluster algebras An Exceptional Cluster Algebra for Higgs plus Jet Production

Reference 35

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Source-reported events for the cited work

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Observation d942b962-314b-49d5-8585-07d2d76b0e70 · outbound

This paper cites For six particles, both partial flag varieties turn out to be F(2 , 4; 6).

Singularities of massless scattering and cluster algebras For six particles, both partial flag varieties turn out to be F(2 , 4; 6)

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Observation 4f5a159c-20da-44c6-806b-41f18c094542 · outbound

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Singularities of massless scattering and cluster algebras Unresolved cited work

Reference 37

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Observation e011764a-81cc-47af-85da-2a40a1035a91 · outbound

This paper cites Paulos, Marcus Spradlin, and Anastasia Volovich.

Singularities of massless scattering and cluster algebras Paulos, Marcus Spradlin, and Anastasia Volovich

Reference 38

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Observation 6d536432-cee9-478d-82d9-cc84c46a7f3f · outbound

This paper cites Dixon, James Drummond, Thomas Har- rington, Andrew J.

Singularities of massless scattering and cluster algebras Dixon, James Drummond, Thomas Har- rington, Andrew J

Reference 39

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Observation 377074aa-d798-4aef-a6eb-92050f0c6168 · outbound

This paper cites Algebraic singularities of scat- tering amplitudes from tropical geometry, 2021.

Singularities of massless scattering and cluster algebras Algebraic singularities of scat- tering amplitudes from tropical geometry, 2021

Reference 40

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Observation 28cd6672-dc81-442f-8827-18d2dd9a743d · outbound

This paper cites How tropical are seven- and eight-particle amplitudes? Journal of High Energy Physics , 2020(8), August 2020.

Singularities of massless scattering and cluster algebras How tropical are seven- and eight-particle amplitudes? Journal of High Energy Physics , 2020(8), August 2020

Reference 41

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Observation aad3d6b6-e3a3-4ad5-b099-f193486c0867 · outbound

This paper cites Singulari- ties of eight- and nine-particle amplitudes from cluster algebras and tropical geometry.

Singularities of massless scattering and cluster algebras Singulari- ties of eight- and nine-particle amplitudes from cluster algebras and tropical geometry

Reference 42

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation ca005ceb-071b-45ad-819a-681f1a029765 · outbound

This paper cites Bourjaily, Andrew J.

Singularities of massless scattering and cluster algebras Bourjaily, Andrew J

Reference 43

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Observation d110bba7-6dc7-4f8a-bbae-140850db8c2c · outbound

This paper cites Introduction to Cluster Algebras. Chapters 1-3.

Singularities of massless scattering and cluster algebras Introduction to Cluster Algebras. Chapters 1-3

Reference 44

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Observation d57d1c4d-9bb0-41db-a09d-719d8b1c818c · outbound

This paper cites Cluster Adjacency Properties of Scattering Ampli- tudes in N = 4 Supersymmetric Yang-Mills The- ory.

Singularities of massless scattering and cluster algebras Cluster Adjacency Properties of Scattering Ampli- tudes in N = 4 Supersymmetric Yang-Mills The- ory

Reference 45

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Observation ae9e57e5-548c-41d7-8bc1-d2c790d40f93 · outbound

This paper cites Partial flag varieties and preprojective algebras.

Singularities of massless scattering and cluster algebras Partial flag varieties and preprojective algebras

Reference 46

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Observation bf6fbca0-b226-45bb-9392-152c56d988b1 · outbound

This paper cites Bootstrapping pentagon functions.

Singularities of massless scattering and cluster algebras Bootstrapping pentagon functions

Reference 48

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation e3ee30a7-3d0f-4c8a-a7d4-b533b37f36b1 · outbound

This paper cites Dixon, Enrico Herrmann, Ben Page, and Mao Zeng.

Singularities of massless scattering and cluster algebras Dixon, Enrico Herrmann, Ben Page, and Mao Zeng

Reference 49

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Observation 8f48a0f4-5037-40da-acea-776fc52305b3 · outbound

This paper cites Dixon, Enrico Herrmann, Ben Page, and Mao Zeng.

Singularities of massless scattering and cluster algebras Dixon, Enrico Herrmann, Ben Page, and Mao Zeng

Reference 50

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Observation 5e495ec9-447c-49ba-946c-3cedce9b6e5d · outbound

This paper cites Pentagon Wilson loop with Lagrangian insertion at two loops in N = 4 super Yang-Mills theory, 2022.

Singularities of massless scattering and cluster algebras Pentagon Wilson loop with Lagrangian insertion at two loops in N = 4 super Yang-Mills theory, 2022

Reference 51

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Observation 6421f0f4-376f-450e-9f81-49b5894b3b3c · outbound

This paper cites Abreu, J.

Singularities of massless scattering and cluster algebras Abreu, J

Reference 52

Resolution
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Observation 00731f55-84c2-4bc0-9dca-f2fc940801cc · outbound

This paper cites Complete function space for planar two-loop six-particle scattering amplitudes.

Singularities of massless scattering and cluster algebras Complete function space for planar two-loop six-particle scattering amplitudes

Reference 53

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source=pdf_text observed=2026-08-06T21:09:07.255068Z digest=sha256:b988b8a114976ce3356f73e8937e3f141f7e844d7bf80deb8aee0d98a261d05d

Observation 54469486-55a0-4f26-865b-9f5306824ebe · outbound

This paper cites Hexagonal Wilson loop with Lagrangian insertion at two loops in $\mathcal{N}=4$ super Yang-Mills theory.

Singularities of massless scattering and cluster algebras Hexagonal Wilson loop with Lagrangian insertion at two loops in $\mathcal{N}=4$ super Yang-Mills theory

Reference 55

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Observation ad7c6f5b-ae1a-4d12-94d0-ee979327c5e5 · outbound

This paper cites The tropical totally positive Grassmannian.

Singularities of massless scattering and cluster algebras The tropical totally positive Grassmannian

Reference 57

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Observation c1df0678-6b41-46aa-a604-ce67545c3bfd · outbound

This paper cites An Analytic Computation of Three-Loop Five-Point Feynman Integrals.

Singularities of massless scattering and cluster algebras An Analytic Computation of Three-Loop Five-Point Feynman Integrals

Reference 58

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Observation b237f438-8722-4049-abc5-19bbeb767f8f · outbound

This paper cites Grassmannians and Cluster Algebras.

Singularities of massless scattering and cluster algebras Grassmannians and Cluster Algebras

Reference 2003

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Observation 9b1b2793-167f-4b2d-8ef5-30d7602c1a6c · outbound

This paper cites URL http: //dx.doi.org/10.1103/PhysRevLett.126.091603.

Singularities of massless scattering and cluster algebras URL http: //dx.doi.org/10.1103/PhysRevLett.126.091603

Reference 7114

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Observation b3e3089c-4fd6-4ab3-8216-192878438d86 · outbound

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Singularities of massless scattering and cluster algebras URL http://dx

Reference 8479

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Pith citing papers

Observation ea0441d7-55bf-4060-a7b2-144ec2d15684 · inbound

Geometric Landau Analysis and Symbol Bootstrap cites this paper.

Geometric Landau Analysis and Symbol Bootstrap Singularities of massless scattering and cluster algebras

Reference 103

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Observation 4db6d7c9-52a0-48b4-bee0-ed1aa944065e · inbound

Novel cluster-algebraic letters for 5- and 6-point QCD processes cites this paper.

Novel cluster-algebraic letters for 5- and 6-point QCD processes Singularities of massless scattering and cluster algebras

Reference 33

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source=pdf_text observed=2026-08-02T18:05:13.216113Z digest=sha256:c20a8bfaf34110b4472d801e36e8c2068bc1ffcde0ccec98f1fab955e55d830a

Observation fd57f4da-87d6-4ac8-84bb-e266cc0cba35 · inbound

Bootstrapping two-loop six-gluon amplitudes in QCD cites this paper.

Bootstrapping two-loop six-gluon amplitudes in QCD Singularities of massless scattering and cluster algebras

Reference 25

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 91c09dc7-1672-468d-87d0-bb44a6b717ce · inbound

Cluster Algebras, Cube Roots, and Energy Correlators in $\mathcal{N}=4$ SYM cites this paper.

Cluster Algebras, Cube Roots, and Energy Correlators in $\mathcal{N}=4$ SYM Singularities of massless scattering and cluster algebras

Reference 8

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