Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-13T18:06:08.679899Z
Paper Citation Record · LEDGER
Census Dual Graphs: Properties and Random Graph Models
As of 6 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2604.04960.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-02T00:53:21.384733Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
34 of 34 outbound references displayed
- verified exact4
- verified fuzzy29
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 07d8f235-ce5b-4b0b-9a19-2717082ba65e · outbound
This paper cites Geometry of graph partitions via optimal transport.SIAM Journal on Scientific Computing, 42(5):A3340–A3366.
Census Dual Graphs: Properties and Random Graph Models Geometry of graph partitions via optimal transport.SIAM Journal on Scientific Computing, 42(5):A3340–A3366
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.306004Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 9c124ac0-633c-41fc-9c15-52a938ebc705 · outbound
This paper cites Redistricting in triangular and square grids.
Census Dual Graphs: Properties and Random Graph Models Redistricting in triangular and square grids
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.270922Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation df8180b3-443c-405f-9e9b-c6a6fb0db10c · outbound
This paper cites Mattingly.
Census Dual Graphs: Properties and Random Graph Models Mattingly
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.254217Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation dced271b-45b9-4d0f-8d59-6d0666b0dc03 · outbound
This paper cites Autry, Daniel Carter, Gregory Herschlag, Zach Hunter, and Jonathan C.
Census Dual Graphs: Properties and Random Graph Models Autry, Daniel Carter, Gregory Herschlag, Zach Hunter, and Jonathan C
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.292575Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation df0cc05d-3c6c-4901-8940-662cfcedaef1 · outbound
This paper cites Computational redistricting and the voting rights act.Election Law Journal: Rules, Politics, and Policy, 20(4):407–441.
Census Dual Graphs: Properties and Random Graph Models Computational redistricting and the voting rights act.Election Law Journal: Rules, Politics, and Policy, 20(4):407–441
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.301046Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a70d9eed-7b51-4fc2-8378-06bf638ac2ea · outbound
This paper cites Irreducibility of recombination Markov chains in the triangular lattice.Discrete Applied Mathematics, 347:75–130.
Census Dual Graphs: Properties and Random Graph Models Irreducibility of recombination Markov chains in the triangular lattice.Discrete Applied Mathematics, 347:75–130
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.288446Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 057d07ec-1937-4d47-b050-28f30f06ee9a · outbound
This paper cites Spanning trees and redistrict- ing: New methods for sampling and validation.
Census Dual Graphs: Properties and Random Graph Models Spanning trees and redistrict- ing: New methods for sampling and validation
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.284162Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation efa3de06-2719-4889-80ab-89b5a71170c3 · outbound
This paper cites Sampling balanced forests of grids in polynomial time.
Census Dual Graphs: Properties and Random Graph Models Sampling balanced forests of grids in polynomial time
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.258566Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation bc7d78d3-2201-4978-896d-ccfa1779d93f · outbound
This paper cites On the Complexity of Sampling Redistricting Plans.
Census Dual Graphs: Properties and Random Graph Models On the Complexity of Sampling Redistricting Plans
Reference 9
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T18:08:15.445003Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8c634957-f9fb-488a-b84f-120c782bf9c3 · outbound
This paper cites Stephanopoulos.
Census Dual Graphs: Properties and Random Graph Models Stephanopoulos
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.266380Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c1ef71b4-13bd-4061-b4d7-db57f099e05f · outbound
This paper cites Dey, and Jonathan Shewchuk.Delaunay Mesh Generation, chap- ter 2.
Census Dual Graphs: Properties and Random Graph Models Dey, and Jonathan Shewchuk.Delaunay Mesh Generation, chap- ter 2
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.296397Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 6f56921b-8448-4f9e-9521-dc2dbb216b43 · outbound
This paper cites Separating effect from significance in Markov chain tests.Statistics and Public Policy, 7(1):101–114.
Census Dual Graphs: Properties and Random Graph Models Separating effect from significance in Markov chain tests.Statistics and Public Policy, 7(1):101–114
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.275873Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation db755758-652a-4963-95dd-b4976c93c974 · outbound
This paper cites Assessing significance in a Markov chain without mixing.Proceedings of the National Academy of Sciences, 114(11):2860–2864.
Census Dual Graphs: Properties and Random Graph Models Assessing significance in a Markov chain without mixing.Proceedings of the National Academy of Sciences, 114(11):2860–2864
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.262575Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 3cec4717-cd11-44ea-98b7-7258ff2a8153 · outbound
This paper cites Compactness statistics for spanning tree recombination.
Census Dual Graphs: Properties and Random Graph Models Compactness statistics for spanning tree recombination
Reference 14
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T18:08:15.447711Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8e509ae4-f585-42fa-8ee2-37f268b15a9c · outbound
This paper cites Census TopDown: The Impacts of Differential Privacy on Redistricting.
Census Dual Graphs: Properties and Random Graph Models Census TopDown: The Impacts of Differential Privacy on Redistricting
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.280023Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 8f032742-3040-4028-ab39-03960ad703a5 · outbound
This paper cites Introduction to discrete markov chain monte carlo for redistricting, June 16.
Census Dual Graphs: Properties and Random Graph Models Introduction to discrete markov chain monte carlo for redistricting, June 16
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.231659Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 649d526f-398a-471d-bee4-df8c7e5a167f · outbound
This paper cites Redistricting reform in Virginia: Districting criteria in context.Virginia Policy Review, XII:120–146, Spring 2019.
Census Dual Graphs: Properties and Random Graph Models Redistricting reform in Virginia: Districting criteria in context.Virginia Policy Review, XII:120–146, Spring 2019
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.235966Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation ed27a173-0175-4290-8ab7-d0e968dcf46c · outbound
This paper cites Recombination: A Family of Markov Chains for Redistricting.Harvard Data Science Review, 3(1), mar 31 2021.
Census Dual Graphs: Properties and Random Graph Models Recombination: A Family of Markov Chains for Redistricting.Harvard Data Science Review, 3(1), mar 31 2021
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.227465Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 67d651ae-3927-4786-894b-30b422a5ec52 · outbound
This paper cites Sur la sph` ere vide.
Census Dual Graphs: Properties and Random Graph Models Sur la sph` ere vide
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.214761Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 5dcef59d-5ec0-4604-8be4-753375101a7c · outbound
This paper cites The (homological) persistence of gerry- mandering.Foundations of Data Science, 4(4):581–622.
Census Dual Graphs: Properties and Random Graph Models The (homological) persistence of gerry- mandering.Foundations of Data Science, 4(4):581–622
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.219152Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 29e031f3-46a2-4655-8ee0-23337ac212e8 · outbound
This paper cites an unresolved cited work.
Census Dual Graphs: Properties and Random Graph Models Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-05-14T04:36:39.184197Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 456b0dfa-ccf0-41d8-b291-631ec2093171 · outbound
This paper cites Discrete geometry for electoral geography.
Census Dual Graphs: Properties and Random Graph Models Discrete geometry for electoral geography
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T18:08:15.453230Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation b434aa41-6993-495e-a2bd-43e53a18f36b · outbound
This paper cites Empirical analysis of political districting splitability via uniform spanning trees in polynomial time.Scripps Senior Theses.
Census Dual Graphs: Properties and Random Graph Models Empirical analysis of political districting splitability via uniform spanning trees in polynomial time.Scripps Senior Theses
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.223263Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 77181878-312f-4977-a9d1-bb157553d528 · outbound
This paper cites Automated redistrict- ing simulation using Markov chain Monte Carlo.Journal of Computational and Graphical Statistics, 29(4):715–728.
Census Dual Graphs: Properties and Random Graph Models Automated redistrict- ing simulation using Markov chain Monte Carlo.Journal of Computational and Graphical Statistics, 29(4):715–728
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.244480Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation aa51b62d-09ec-4ad5-bb81-09de29d422d1 · outbound
This paper cites Random graph models for dual graphs.Scripps Senior Theses.
Census Dual Graphs: Properties and Random Graph Models Random graph models for dual graphs.Scripps Senior Theses
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.250301Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation ad2656f9-695d-430c-8de0-de47d572b45e · outbound
This paper cites Mattingly.
Census Dual Graphs: Properties and Random Graph Models Mattingly
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.202132Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation a72082df-d676-4e5d-8fee-d32e959bc9f1 · outbound
This paper cites An unbiased estimate for the mean of a {0,1} random variable with relative error distribution independent of the mean.
Census Dual Graphs: Properties and Random Graph Models An unbiased estimate for the mean of a {0,1} random variable with relative error distribution independent of the mean
Reference 28
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T20:40:48.716094Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation b3a47733-c950-466b-b154-8928c44c2a18 · outbound
This paper cites Sequential Monte Carlo for sampling balanced and compact redistricting plans.Annals of Applied Statistics, 17(4):3300–3323.
Census Dual Graphs: Properties and Random Graph Models Sequential Monte Carlo for sampling balanced and compact redistricting plans.Annals of Applied Statistics, 17(4):3300–3323
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.193741Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 46d4e62e-7d67-4412-926c-d2f9921b1483 · outbound
This paper cites Procaccia and Jamie Tucker-Foltz.
Census Dual Graphs: Properties and Random Graph Models Procaccia and Jamie Tucker-Foltz
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.188707Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 08db7bde-38e2-45c3-8d9e-91ed97b1cbef · outbound
This paper cites Spanning tree bounds for grid graphs.The Electronic Journal of Combina- torics, 31.
Census Dual Graphs: Properties and Random Graph Models Spanning tree bounds for grid graphs.The Electronic Journal of Combina- torics, 31
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.198211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation c85d43ab-b6a1-4e41-9c8a-a0815ad2ee97 · outbound
This paper cites Political districting to minimize cut edges.Mathe- matical Programming Computation, 14:623–672.
Census Dual Graphs: Properties and Random Graph Models Political districting to minimize cut edges.Mathe- matical Programming Computation, 14:623–672
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.206347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 55f23cea-ebdd-48f3-a8da-ab30e0c20bb8 · outbound
This paper cites Wilson.Graph Theory and Spanning Trees.
Census Dual Graphs: Properties and Random Graph Models Wilson.Graph Theory and Spanning Trees
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.240190Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 56119162-9f82-4dfc-bb76-f3a0284a8dd2 · outbound
This paper cites Number of spanning trees on a lattice.Journal of Physics A: Mathematical and General, 10(6):L113, jun 1977.
Census Dual Graphs: Properties and Random Graph Models Number of spanning trees on a lattice.Journal of Physics A: Mathematical and General, 10(6):L113, jun 1977
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.210658Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Observation 6c4bafb8-f506-4765-9c04-ce5f0fee4d5d · outbound
This paper cites Mathematically quantifying non-responsiveness of the 2021 Georgia Congressional districting plan.
Census Dual Graphs: Properties and Random Graph Models Mathematically quantifying non-responsiveness of the 2021 Georgia Congressional districting plan
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T04:36:39.180202Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.
Pith citing papers
Observation 23d618c2-db63-40b6-b3fd-c2e274291c38 · inbound
Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance cites this paper.
Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance Census Dual Graphs: Properties and Random Graph Models
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T00:53:21.384733Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.