Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:09:07.810683Z
Paper Citation Record · LEDGER
As of 8 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 3 inbound Pith citation observations for arXiv:2507.01015.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:09:07.810683Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T23:22:48.010474Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-01T17:05:50.640634Z
58 of 58 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation bf60e181-5f7c-4db6-b2cb-d5542633da83 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6a2c37d3-9f90-4886-923f-8b7cbaa778f8 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4f97bfc5-48f5-41fd-a3ec-f9a253b82352 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 83f13ed8-9c4f-4d7e-bf21-f8a5a3b8a4f6 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a0b34686-cb8d-4267-85e1-d40bca7ba5d8 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3323056d-dc0f-43c9-a959-2db3eee2c991 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bb50382a-ec9d-4a47-a632-8f44576dd50e · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9fa1671c-9321-4083-87e8-8525103c29e0 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5ee90f54-e25b-45ba-9a74-ea167a672dd1 · outbound
Singularities of massless scattering and cluster algebras Cluster algebras i: Foundations, 2001
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 02a7250b-3850-4025-9099-4004de0e4d7d · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 162d03f3-6a15-4bb0-9df5-bb9aca2d82fe · outbound
Singularities of massless scattering and cluster algebras Five of the algebraic letters are these naked discriminants
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c7c3f2ee-b7f4-468e-85af-0f4f87ccbd88 · outbound
Singularities of massless scattering and cluster algebras An example of an origin cluster is shown in Figure 5
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 23505040-1b54-456c-8fbf-954106c8726e · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 518ad081-5afb-4f62-9964-f556c509b96c · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1aab7b11-66c4-41a9-81f1-f419c0b6e2c6 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8ef6d288-7639-4571-8e15-7b080d3d1a0e · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5b51d159-5cc4-4270-870c-820e0e9518dc · outbound
Singularities of massless scattering and cluster algebras Express these in terms of the letters of the planar pentagon al- phabet
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 241d6812-66b4-4b2e-88f0-2ca18e47b0ab · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 41ffa800-0682-4658-b7aa-7d62ecc065f0 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c5d9ecba-1f60-431b-bd79-abfcafecc11e · outbound
Singularities of massless scattering and cluster algebras Summer School in Total Positivity and Quantum Field Theory
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2f5a5ec8-cefb-4b6b-8503-04ba69f235cd · outbound
Singularities of massless scattering and cluster algebras Tropicalised braid automorphisms of grassmannian cluster algebras
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fc2ce32d-3f40-4788-92b0-3d2c5e6c9bf2 · outbound
Singularities of massless scattering and cluster algebras Cluster structures on spinor helicity and momentum twistor varieties
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1195a7c7-fb71-46cf-bcc6-978da668e96d · outbound
Singularities of massless scattering and cluster algebras Symbol alphabets in qcd and flag cluster algebras, 2025
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5b790e70-5d87-4ed5-bc88-c93b3be3ff58 · outbound
Singularities of massless scattering and cluster algebras Adjacency for scattering amplitudes from the Gr\"obner fan
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation df549e62-e5f3-4d01-90ef-76b56a596814 · outbound
Singularities of massless scattering and cluster algebras Dixon, James M
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 250e58b0-a016-4fd1-beed-8e64fa6df554 · outbound
Singularities of massless scattering and cluster algebras Dixon, James M
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c1235a11-0002-4e9a-8778-cf2364a7d184 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7976657d-75bf-4f9f-b5b6-7a8509174e11 · outbound
Singularities of massless scattering and cluster algebras Dixon, James M
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b7accffd-5a13-4288-a43b-cb3f5e70ea1a · outbound
Singularities of massless scattering and cluster algebras Cluster adjacency and the four-loop nmhv heptagon
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation acfd001d-f1f6-496c-aa61-e82b4760ebd7 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c1abed89-545a-48ec-aa7c-82b522adca23 · outbound
Singularities of massless scattering and cluster algebras Tropical grassmannians, clus- ter algebras and scattering amplitudes
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7d4fa3b3-efde-41af-ac68-f9a6c5365d5d · outbound
Singularities of massless scattering and cluster algebras Henn, and Georgios Pap- athanasiou
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ed24367d-24e3-4b00-8e47-f40553f08d08 · outbound
Singularities of massless scattering and cluster algebras Dixon, ¨Omer G¨ urdo˘ gan, Yu-Ting Liu, An- drew J
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c3c9f275-b6c4-48bb-9334-db6767bd81a8 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f8f1d414-005b-4295-a3b8-deaa1ad4ff63 · outbound
Singularities of massless scattering and cluster algebras An Exceptional Cluster Algebra for Higgs plus Jet Production
Reference 35
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d942b962-314b-49d5-8585-07d2d76b0e70 · outbound
Singularities of massless scattering and cluster algebras For six particles, both partial flag varieties turn out to be F(2 , 4; 6)
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4f5a159c-20da-44c6-806b-41f18c094542 · outbound
Singularities of massless scattering and cluster algebras Unresolved cited work
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e011764a-81cc-47af-85da-2a40a1035a91 · outbound
Singularities of massless scattering and cluster algebras Paulos, Marcus Spradlin, and Anastasia Volovich
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6d536432-cee9-478d-82d9-cc84c46a7f3f · outbound
Singularities of massless scattering and cluster algebras Dixon, James Drummond, Thomas Har- rington, Andrew J
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 377074aa-d798-4aef-a6eb-92050f0c6168 · outbound
Singularities of massless scattering and cluster algebras Algebraic singularities of scat- tering amplitudes from tropical geometry, 2021
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 28cd6672-dc81-442f-8827-18d2dd9a743d · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation aad3d6b6-e3a3-4ad5-b099-f193486c0867 · outbound
Singularities of massless scattering and cluster algebras Singulari- ties of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ca005ceb-071b-45ad-819a-681f1a029765 · outbound
Singularities of massless scattering and cluster algebras Bourjaily, Andrew J
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d110bba7-6dc7-4f8a-bbae-140850db8c2c · outbound
Singularities of massless scattering and cluster algebras Introduction to Cluster Algebras. Chapters 1-3
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d57d1c4d-9bb0-41db-a09d-719d8b1c818c · outbound
Singularities of massless scattering and cluster algebras Cluster Adjacency Properties of Scattering Ampli- tudes in N = 4 Supersymmetric Yang-Mills The- ory
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae9e57e5-548c-41d7-8bc1-d2c790d40f93 · outbound
Singularities of massless scattering and cluster algebras Partial flag varieties and preprojective algebras
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bf6fbca0-b226-45bb-9392-152c56d988b1 · outbound
Singularities of massless scattering and cluster algebras Bootstrapping pentagon functions
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e3ee30a7-3d0f-4c8a-a7d4-b533b37f36b1 · outbound
Singularities of massless scattering and cluster algebras Dixon, Enrico Herrmann, Ben Page, and Mao Zeng
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8f48a0f4-5037-40da-acea-776fc52305b3 · outbound
Singularities of massless scattering and cluster algebras Dixon, Enrico Herrmann, Ben Page, and Mao Zeng
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5e495ec9-447c-49ba-946c-3cedce9b6e5d · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6421f0f4-376f-450e-9f81-49b5894b3b3c · outbound
Singularities of massless scattering and cluster algebras Abreu, J
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 00731f55-84c2-4bc0-9dca-f2fc940801cc · outbound
Singularities of massless scattering and cluster algebras Complete function space for planar two-loop six-particle scattering amplitudes
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 54469486-55a0-4f26-865b-9f5306824ebe · outbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ad7c6f5b-ae1a-4d12-94d0-ee979327c5e5 · outbound
Singularities of massless scattering and cluster algebras The tropical totally positive Grassmannian
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c1df0678-6b41-46aa-a604-ce67545c3bfd · outbound
Singularities of massless scattering and cluster algebras An Analytic Computation of Three-Loop Five-Point Feynman Integrals
Reference 58
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b237f438-8722-4049-abc5-19bbeb767f8f · outbound
Singularities of massless scattering and cluster algebras Grassmannians and Cluster Algebras
Reference 2003
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9b1b2793-167f-4b2d-8ef5-30d7602c1a6c · outbound
Singularities of massless scattering and cluster algebras URL http: //dx.doi.org/10.1103/PhysRevLett.126.091603
Reference 7114
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b3e3089c-4fd6-4ab3-8216-192878438d86 · outbound
Singularities of massless scattering and cluster algebras URL http://dx
Reference 8479
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ea0441d7-55bf-4060-a7b2-144ec2d15684 · inbound
Geometric Landau Analysis and Symbol Bootstrap Singularities of massless scattering and cluster algebras
Reference 103
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4db6d7c9-52a0-48b4-bee0-ed1aa944065e · inbound
Novel cluster-algebraic letters for 5- and 6-point QCD processes Singularities of massless scattering and cluster algebras
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fd57f4da-87d6-4ac8-84bb-e266cc0cba35 · inbound
Bootstrapping two-loop six-gluon amplitudes in QCD Singularities of massless scattering and cluster algebras
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.