Paper Citation Record · LEDGER

Paths and Intersections: Exact Emulators for Planar Graphs

As of 14 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 3 inbound Pith citation observations for arXiv:2507.09620.

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

pith.paper-citation-record.v1
2507.09620 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:02:17.295621Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-12T12:11:39.634286Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T20:40:08.525667Z

Reference resolution

20 of 20 outbound references displayed

verified exact0
verified fuzzy20
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 92eeed4b-6c73-4aa1-9190-653db44efe68 · outbound

This paper cites Steiner point removal in graph metrics.

Paths and Intersections: Exact Emulators for Planar Graphs Steiner point removal in graph metrics

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.972357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 71df2634-62e5-4eac-9127-c862503a5f69 · outbound

This paper cites Covering planar metrics (and beyond): O(1) trees suffice.

Paths and Intersections: Exact Emulators for Planar Graphs Covering planar metrics (and beyond): O(1) trees suffice

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.830502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f556fde8-4cae-4d18-bcd9-5b4e7135cd4c · outbound

This paper cites Shortcut partitions in minor-free graphs: Steiner point removal, distance oracles, tree covers, and more.

Paths and Intersections: Exact Emulators for Planar Graphs Shortcut partitions in minor-free graphs: Steiner point removal, distance oracles, tree covers, and more

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.707454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4adb255d-51da-44f8-9d0a-e9f8483b25b4 · outbound

This paper cites Near-optimal distance emulator for planar graphs.

Paths and Intersections: Exact Emulators for Planar Graphs Near-optimal distance emulator for planar graphs

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.551905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d8a5c04f-53ec-4bf0-a957-7e085ad2db93 · outbound

This paper cites Steiner point removal: distant terminals don't (really) bother.

Paths and Intersections: Exact Emulators for Planar Graphs Steiner point removal: distant terminals don't (really) bother

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.390156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7d1fb6a9-0608-4f34-b346-a261d1194359 · outbound

This paper cites Almost-linear -emulators for planar graphs.

Paths and Intersections: Exact Emulators for Planar Graphs Almost-linear -emulators for planar graphs

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.251385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ce63e2c0-3329-438c-8abc-1a32c56e8be4 · outbound

This paper cites Planar emulators for Monge matrices.

Paths and Intersections: Exact Emulators for Planar Graphs Planar emulators for Monge matrices

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:20.096817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 855fdf5a-33f9-466b-9ad0-0312c809e70f · outbound

This paper cites An O( |T|) lower bound for Steiner point removal.

Paths and Intersections: Exact Emulators for Planar Graphs An O( |T|) lower bound for Steiner point removal

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.926767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ed28dcc2-fc3f-4229-b9ed-6105c331745b · outbound

This paper cites Path and intersections: Characterization of quasi-metrics in directed Okamura-Seymour instances.

Paths and Intersections: Exact Emulators for Planar Graphs Path and intersections: Characterization of quasi-metrics in directed Okamura-Seymour instances

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.786060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5c74ed47-4449-471d-8ed1-0b4a8383ef23 · outbound

This paper cites A tight lower bound for the Steiner point removal problem on trees.

Paths and Intersections: Exact Emulators for Planar Graphs A tight lower bound for the Steiner point removal problem on trees

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.657810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 556bf5a7-7edc-427c-938a-4361290e2f98 · outbound

This paper cites Holiest minimum-cost paths and flows in surface graphs.

Paths and Intersections: Exact Emulators for Planar Graphs Holiest minimum-cost paths and flows in surface graphs

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.520137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a8de26f2-a6f9-4132-9937-a8b900947c91 · outbound

This paper cites A Fourier -f \'e le mechanikai elv algebrai alapja.

Paths and Intersections: Exact Emulators for Planar Graphs A Fourier -f \'e le mechanikai elv algebrai alapja

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.393661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 24d203a0-ceff-4b7e-ae5b-aeb6086d7ef3 · outbound

This paper cites Steiner point removal with distortion O( k) using the relaxed- Voronoi algorithm.

Paths and Intersections: Exact Emulators for Planar Graphs Steiner point removal with distortion O( k) using the relaxed- Voronoi algorithm

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.258065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b77eb263-f1f5-4f15-be82-7803e35b02a2 · outbound

This paper cites Scattering and sparse partitions, and their applications.

Paths and Intersections: Exact Emulators for Planar Graphs Scattering and sparse partitions, and their applications

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:19.114482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4d602a2b-39a7-4558-89eb-d2ca2985081d · outbound

This paper cites Improved guarantees for vertex sparsification in planar graphs.

Paths and Intersections: Exact Emulators for Planar Graphs Improved guarantees for vertex sparsification in planar graphs

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:18.876456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e94ae372-98c7-487b-9dc4-5971a79a6603 · outbound

This paper cites Steiner points in tree metrics don't (really) help.

Paths and Intersections: Exact Emulators for Planar Graphs Steiner points in tree metrics don't (really) help

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:18.657972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5a2b0f6c-ecd6-4f21-8279-e62b495626d1 · outbound

This paper cites Ellis Hershkowitz and Jason Li.

Paths and Intersections: Exact Emulators for Planar Graphs Ellis Hershkowitz and Jason Li

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:18.419780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e031687f-1bec-4904-9197-2a55baeee7c9 · outbound

This paper cites Cutting corners cheaply, or how to remove Steiner points.

Paths and Intersections: Exact Emulators for Planar Graphs Cutting corners cheaply, or how to remove Steiner points

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:18.150001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 87b32596-37b2-4794-ae12-f9944e9f9f43 · outbound

This paper cites Preserving terminal distances using minors.

Paths and Intersections: Exact Emulators for Planar Graphs Preserving terminal distances using minors

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:17.860302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation be73ebff-da71-4e57-9722-ea234a37b048 · outbound

This paper cites Multicommodity flows in planar graphs.

Paths and Intersections: Exact Emulators for Planar Graphs Multicommodity flows in planar graphs

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:02:17.540249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation 212c6796-5e72-4b46-b9a0-fe80afc3e09a · inbound

Paths and Intersections: Recognizing Outerplanar Metrics cites this paper.

Paths and Intersections: Recognizing Outerplanar Metrics Paths and Intersections: Exact Emulators for Planar Graphs

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-04T20:40:08.528589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8c43e349-1bdf-45bd-a30b-f594621cce21 · inbound

Paths and Intersections: Recognizing Outerplanar Metrics cites this paper.

Paths and Intersections: Recognizing Outerplanar Metrics Paths and Intersections: Exact Emulators for Planar Graphs

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-12T12:11:39.634286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23965ab7-9c72-4fae-9d67-0df7407e5df5 · inbound

Paths and Intersections: Minimum Realization of Okamura-Seymour Instances cites this paper.

Paths and Intersections: Minimum Realization of Okamura-Seymour Instances Paths and Intersections: Exact Emulators for Planar Graphs

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-12T06:25:09.946876Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.