Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T11:55:39.667740Z
Paper Citation Record · LEDGER
As of 10 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 1 inbound Pith citation observation for arXiv:2509.02239.
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 2026-08-05T11:55:39.667740Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-15T11:45:20.771019Z
A source-named dated measurement, never combined with another source.
Source: cited_works
57 of 57 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation acbebccc-7e8c-462f-97a6-e33d22567d11 · outbound
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 97e33197-9429-4883-b190-f3fb101decd7 · outbound
Canonical Forms as Dual Volumes Grassmannian Geometry of Scattering Amplitudes
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f3cdce7a-d6b5-4c2f-86a9-5afb053b5f1e · outbound
Canonical Forms as Dual Volumes Positive geometries and canonical forms
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 93f3e1ff-fdd8-4019-a7c1-8662855e119b · outbound
Canonical Forms as Dual Volumes Adjoints and Canonical Forms of Tree Amplituhedra
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 801587a1-9d5d-4ead-a93c-9268144ad8ee · outbound
Canonical Forms as Dual Volumes Scattering Forms and the Positive Geometry of Kine- matics, Color and the Worldsheet
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation cd29aea0-c51e-47e1-9631-5d6478e44e8e · outbound
Canonical Forms as Dual Volumes The ABJM Amplituhedron
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 24c843d6-b4dc-4a7a-90c4-9e6284e9f79b · outbound
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ced9fc76-4c7d-496b-8208-3d845b135652 · outbound
Canonical Forms as Dual Volumes Cosmological Polytopes and the Wavefunction of the Universe
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation e47a7955-4f91-44ad-8f4c-2ae484e7ff54 · outbound
Canonical Forms as Dual Volumes Stokes polytopes: the pos- itive geometry for ϕ4 interactions
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 778fcc8a-acb2-43eb-8424-112cccde5e33 · outbound
Canonical Forms as Dual Volumes The positive geometry for $\phi^{p}$ interactions
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fb3edd03-f299-4cb0-8297-59a8ab87e9f4 · outbound
Canonical Forms as Dual Volumes On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b112d50c-4787-42be-965b-a2c0b6447691 · outbound
Canonical Forms as Dual Volumes On the Positive Geometry of Quartic Interactions III : One Loop Integrands from Polytopes
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e018fb12-1da6-438c-9dfc-6d0ec6080c37 · outbound
Canonical Forms as Dual Volumes Towards Positive Geometries of Massive Scalar field theories
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 836c39b1-6256-49ff-9bf4-3e1c27d3be1b · outbound
Canonical Forms as Dual Volumes Positive Geometries of S-matrix without Color
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation b046c2e9-9a30-495d-85d3-377ece8cee48 · outbound
Canonical Forms as Dual Volumes Cosmohedra
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 06c9035a-7ada-4cbd-844f-26a76475d02d · outbound
Canonical Forms as Dual Volumes An invitation to positive geometries
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 4930f6b3-bc9b-4340-bf22-0b5c8d3d93ed · outbound
Canonical Forms as Dual Volumes What is Positive Geom- etry?
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation a8213cbc-7e77-488b-8a76-5d80b4275bbc · outbound
Canonical Forms as Dual Volumes Algebraic and Positive Geometry of the Universe: from Particles to Galaxies
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ed08edde-5999-4911-92d6-2ab82cf5c33d · outbound
Canonical Forms as Dual Volumes Eliminating spurious poles from gauge-theoretic amplitudes
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ee4eb79e-b9f0-41b1-a1cb-1a9a195e2439 · outbound
Canonical Forms as Dual Volumes Canonical forms of polytopes from adjoints
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation c97ae7e6-be26-4274-8d1a-72f730050db4 · outbound
Canonical Forms as Dual Volumes Positivity properties of scattering ampli- tudes
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation bdab2150-bef4-40cf-bb45-ff2a2d3345dc · outbound
Canonical Forms as Dual Volumes Laplace transform (PMS-6)
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 7b2069c1-4762-4640-9382-ae507811f16f · outbound
Canonical Forms as Dual Volumes Positive geometry, local triangulations, and the dual of the Amplituhedron
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 6d20a8f8-6e2d-4db6-9f22-52d8c5f6df07 · outbound
Canonical Forms as Dual Volumes Towards the Amplituhedron Volume
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ac1bbf83-b514-49f2-968f-758581e9bd10 · outbound
Canonical Forms as Dual Volumes Positive Amplitudes In The Amplituhedron
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 39f6b0ad-f28c-4914-bb8f-2e7996bca68e · outbound
Canonical Forms as Dual Volumes Multi-loop positivity of the planar N = 4 SYM six-point amplitude
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation a829f4ae-839f-48e3-a6a8-6a551d6f9366 · outbound
Canonical Forms as Dual Volumes Positivity properties of five-point two-loop Wilson loops with Lagrangian insertion
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 297f401e-f280-478b-ba4f-9c84e0d00d6c · outbound
Canonical Forms as Dual Volumes Exterior Cyclic Polytopes and Convexity of Amplituhedra
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2dc4812a-f383-430d-92b7-e238836b91a9 · outbound
Canonical Forms as Dual Volumes Barrier functions in interior point methods
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 49594834-939b-46cd-bbdc-407fe8bf03e7 · outbound
Canonical Forms as Dual Volumes 8478 [hep-th]
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 3074cdb5-fa55-4edc-a1eb-5a48f2abc307 · outbound
Canonical Forms as Dual Volumes 11456 [hep-th]
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation dd2275d9-82da-4779-8614-13262b4af1dc · outbound
Canonical Forms as Dual Volumes Positivity certifi- cates via integral representations
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 76ea7f61-469d-445a-9ebe-e8859f6675f4 · outbound
Canonical Forms as Dual Volumes Exponential varieties
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1ca63627-3064-4d2b-9864-65aba3af9d1e · outbound
Canonical Forms as Dual Volumes Complete monotonicity for inverse powers of some combinatorially defined polynomials
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1d5161e8-4bff-465c-b628-669cb9a74949 · outbound
Canonical Forms as Dual Volumes The analysis of linear partial differential operators
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation f3305440-57cd-45b5-8ff0-8cb3016da608 · outbound
Canonical Forms as Dual Volumes An Inequality for Hyperbolic Polynomials
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1c4bbc83-c732-4593-bccf-927ef2d0678e · outbound
Canonical Forms as Dual Volumes Lacunas for hyperbolic differential oper- ators with constant coefficients I
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ee822d1e-de60-47ca-b40b-af026427d68f · outbound
Canonical Forms as Dual Volumes On the fundamental solutions of a class of elliptic quartic operators in dimension 3
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 96da9957-5e5c-416c-974f-7a831807d10f · outbound
Canonical Forms as Dual Volumes A fundamental solution of N. Zeilon’s operator
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 4dfdaf90-5a84-441c-a0eb-b790cd58940e · outbound
Canonical Forms as Dual Volumes Fundamental solutions of real homogeneous cubic operators of principal type in three dimensions
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d5ff7873-64eb-4536-b843-47e4ff2cdb59 · outbound
Canonical Forms as Dual Volumes Deux exemples classiques de repr´ esentation int´ egrale
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ea6ebe20-d8b6-4a15-9092-6a6903657475 · outbound
Canonical Forms as Dual Volumes On the fundamental solutions of a class of hyperbolic quartic op- erators in dimension 3
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d1db0bcd-dc84-4a3a-a159-0af31aee2aec · outbound
Canonical Forms as Dual Volumes Positive geometries and canonical forms via mixed Hodge theory
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 6edb0237-5046-4b6d-922a-fa6b204b5f50 · outbound
Canonical Forms as Dual Volumes Linear hyperbolic partial differential equations with constant co- efficients
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation a70de7a2-719b-4c86-8237-b6f3e2410831 · outbound
Canonical Forms as Dual Volumes Hyperbolic Polynomials and Interior Point Methods for Convex Programming
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 9cc8637b-72fa-49bd-9374-e2e8fccfd49d · outbound
Canonical Forms as Dual Volumes Generalized functions
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2a82c50b-b434-4ba2-bccc-5fdcf1d58ce4 · outbound
Canonical Forms as Dual Volumes Adjoints and Canonical Forms of Polypols
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation fdf7dcbd-b84e-4b41-8cf8-caeddf278626 · outbound
Canonical Forms as Dual Volumes The analysis of linear partial differential operators
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 89cd8038-a5fc-4395-8a1d-cd38bc3a09a9 · outbound
Canonical Forms as Dual Volumes Algebraic boundaries of convex semi-algebraic sets
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 44462c8f-b11f-4123-b20c-a12ee0298501 · outbound
Canonical Forms as Dual Volumes Linear matrix inequality representation of sets
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0adab6f6-b918-4535-ac34-f7bb4c9d3454 · outbound
Canonical Forms as Dual Volumes The Analysis of Linear Partial Differential Operators: Distribu- tion theory and Fourier analysis
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 66bbdc1b-770b-4447-8a37-4a44432c69a3 · outbound
Canonical Forms as Dual Volumes A Note on the Hyperbolicity Cone of the Specialized V´ amos Polynomial
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 7e5c4284-b21f-406c-95dd-03166a71b2a4 · outbound
Canonical Forms as Dual Volumes From polygons and sym- bols to polylogarithmic functions
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 52ef7ed4-9833-4867-913b-4cb9af1429e8 · outbound
Canonical Forms as Dual Volumes Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 31734c65-4a31-40c8-a00a-d2b8be22ff23 · outbound
Canonical Forms as Dual Volumes Classical Polylogarithms for Amplitudes and Wil- son Loops
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f377f3fa-5284-4fc7-a33b-03ef6a066173 · outbound
Canonical Forms as Dual Volumes Byrd and Morris D
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2f19a5fb-a8dc-4aee-9e07-93ece49bc2a8 · outbound
Canonical Forms as Dual Volumes 00951 [hep-th]
Reference 165
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation f980cdb2-b7fa-4bcf-8aab-6f7983ee4ca0 · inbound
Global Convergence of the Return Dynamics in the Class $\mathcal{O}_C$ Canonical Forms as Dual Volumes
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.