Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:22:45.509447Z
Paper Citation Record · LEDGER
As of 15 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 0 inbound Pith citation observations for arXiv:1908.09400.
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 2026-08-14T11:22:45.509447Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
69 of 69 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 56b32d75-153b-4b44-9ec2-940de125684a · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete The Art Gallery Problem is $\exists \mathbb{R}$-complete
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 053dd948-48b3-4d04-936f-63d16d0bd432 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Adiprasito, Arnau Padrol, and Louis Theran
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation af99af8e-9711-43d1-94f4-b876cf956d68 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Felzenszwalb, Ross B
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a5fb4d81-fd11-43ad-8c01-060deba0dc9b · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Algorithms in Real Algebraic Geometry , 2nd edition
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1b39516e-4b6a-4a72-9579-6aa15e606257 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete The complexity of computing the minimum rank of a sign pattern matrix
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 99c229f0-2cfe-497b-ad59-c91ae2a13860 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Some provably hard crossing number problems.Discrete Comput
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9a2722b4-f38c-4825-bca0-c67edb1c5f45 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete A catalog of∃R-complete decision problems about Nash equilibria in multi-player games
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7114f4e0-4119-4754-a0b7-b39355fd1fff · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete ∃R-complete decision problems about symmetric Nash equilibria in symmetric multi-player games
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 260170a4-925e-415c-8bec-74fa964c2a4c · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fe4e1cfb-0047-4fe5-9b17-460f334df663 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Complexity and Real Computation
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c35a5dd0-3a8e-4014-b631-bf1c7aebf9bb · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Computational Synthetic Geometry
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6d663e28-649e-4c9f-bd47-15a369d9d094 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Properties of arrangement graphs
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b051fdda-070c-4631-9295-33a11add00c6 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Counting complexity classes for numeric computations ii: Algebraic and semialgebraic sets
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1d5fb468-482b-4c31-8b0f-ea0bf0fafcbd · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Some algebraic and geometric computations in PSPACE.Proc
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8a6fe21d-918b-4d85-892a-07933bb6dd37 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Computational geometry column 62
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 06c19f76-13eb-4b23-92ed-ed2983d5831a · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Intersection Graphs of Rays and Grounded Segments
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4db67211-72a3-4e7c-b0b8-1ab18d6edd05 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Recognition and Complexity of Point Visibility Graphs
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 711c809b-690a-42af-8eeb-a79772571675 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete The Complexity of Simultaneous Geometric Graph Embedding
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7bd64327-60cb-4bc3-a9a2-a20f2fcc9ff8 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Scott Carter
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5f3eb4fb-50ec-456f-b9c3-8e94cdd3faa0 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete The Complexity of Drawing Graphs on Few Lines and Few Planes
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3df00fcb-5448-42db-aa09-df63aa3ad30d · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Algorithmic graph embeddings
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 33f0f355-93a3-4572-8a66-2d414fe6c21c · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Cohen and Uriel G
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5866d56d-98d2-4171-8df6-de2c30637dd9 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Accelerated bend minimization
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e410654d-a835-41b9-9887-018ca81e4ab6 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete A Universality Theorem for Nested Polytopes
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c0f66dc0-d9d4-43e6-a54a-e9bb93003a10 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Dowker and Morwen B
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c2e25359-02cb-4be4-8264-8101e94246a8 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 086206a3-c22e-4575-a4a7-98c62ddb7928 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete A note on minimum-segment drawings of planar graphs
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1b673511-8f91-48a6-b35b-02a82fdcdfb2 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1e1b1ef0-60f7-4fb8-a156-921f3ac338b5 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Vazirani, and Sadra Yazdanbod.∃R-completness for decision version of multi-player (symmetric) Nash equilibria
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 99d86263-aa0f-40f2-9801-8d0f600450d1 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Nachlass
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 40f3a8c7-03d0-4a63-9517-5fa146e2c053 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Nachlass
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f48591b1-a090-44d7-aef8-28325673de82 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f82b92fb-8e29-476e-8377-eb55b5d0fb9f · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Goodman and Richard Pollack
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e0d608fe-0216-4b86-b633-1407d3be9361 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Goodman, Richard Pollack, and Bernd Sturmfels
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9390270a-0d6b-4d2c-aa34-894960ddb50f · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Goodman, Richard Pollack, and Bernd Sturmfels
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 160e6bb1-cea8-4d23-aa6c-fa23a793f9fe · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Arrangements and Spreads
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8146d0e3-902d-4aca-ba65-0af9114aaab0 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Guibas and Jorge Stolfi
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ab78f5ac-c3be-48d0-aa4c-d1ceb14b36e5 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Satisfiability of cross product terms is complete for real nondeterministic polytime Blum-Shub-Smale machines
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c8078be9-bff3-40bd-b61c-c53cd7c567eb · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete On the complexity of the planar slope number problem
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 35743fd6-f36c-4d92-86fa-4f37598af13b · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3df5523b-16d7-433d-b795-47c7f38bf1f8 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Min-cost flow in unit-capacity planar graphs
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation dae68b10-e8c0-4136-8bae-9316332bd10e · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Intersection graphs of segments.J
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 01effab4-b9ec-4026-9956-d09b1ec79e46 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Mnev-Sturmfels universality for schemes
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1448c71a-e723-4dcb-9132-7184db219ac5 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Die teilung der projektiven ebene durch gerade und pseudogerade
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f6aa601d-b646-448a-b5f4-91f47b2ab0f3 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Intersection graphs of segments and $\exists\mathbb{R}$
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 04a58e19-62bb-4773-8765-e95df23d22e4 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Integer realizations of disk and segment graphs
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 74ef08a8-ceda-4764-a4ed-33182f1c4f46 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a4bdced8-9fbc-4be9-97f5-93213616e9b3 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d02322ee-e234-4ef2-9552-1e4d022ac75d · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Muller and Franco P
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9009c062-8fa9-456d-adf8-940eee3c4ad0 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Delaunay triangulations with disconnected realization spaces
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7bd46bfd-6d8e-47c5-aa87-f231c5842fdb · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Recognising multidimensional euclidean preferences
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3d8edc67-7c4a-4f2d-8490-3a1f621e4c8b · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete On the computational complexity and geometry of the first-order theory of the reals, Part I
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5946a929-c324-4030-a1c0-ff012d3d0943 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Mnëv’s universality theorem revisited
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b17006d5-42df-430a-996f-4c0529f18d99 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Realization spaces of polytopes
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 153026eb-96da-444f-8178-a803f432a5c3 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Kombinatorische Realisierbarkeitskriterien für orientierte Matroide
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 96bb5b07-b4a2-4100-b377-74a8bbe15986 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Teilungen der Ebene durch Geraden oder topologische Geraden.Math
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7035659d-bdf2-4815-9dc1-adb7128321dd · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Complexity of some geometric and topological problems
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6ee5ae38-f3b2-4938-8b42-87ded05af3fc · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Realizability of graphs and linkages
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e6920614-97f3-4454-9037-7436c874b45d · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Fixed points, Nash equilibria, and the existential theory of the reals
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ab377bd8-01cd-4ca4-a4c0-2986120ea1a0 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete The Complexity of Tensor Rank
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d93db723-9a68-4c76-9bd5-28af69b5d7bf · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete The nonnegative rank of a matrix: Hard problems, easy solutions
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 59bbb66b-6405-499a-a3c2-8eab8ecf6421 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 97100d5b-3416-438d-aa2e-76acf768a201 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Geometrie der Lage
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3f7520cc-bd66-404e-87a3-5b70288f9f54 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete On knots I
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 31f45b96-8ea7-4bd4-99ba-bda6e7db81c8 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete On embedding a graph in the grid with the minimum numberof bends
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f44b723d-b073-493b-b87e-6cf88b568c18 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8211892b-64f8-41dc-864f-990e8194bf36 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Murphy’s law in algebraic geometry: Badly-behaved deformation spaces
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b17d3451-5766-439d-81f4-072a0ec79e62 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Edge-based data structures for solid modeling in curved-surface environments
Reference 68
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b11055ed-79d7-48f2-910f-fd4355f31f40 · outbound
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete Unresolved cited work
Reference 1355
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
No inbound Pith citation observations are available.