Paper Citation Record · LEDGER

Asymptotic structure. VI. Distant paths across a disc

As of 21 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 6 inbound Pith citation observations for arXiv:2509.07174.

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

pith.paper-citation-record.v1
2509.07174 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:21:58.512157Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:14:47.178089Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T20:16:29.542125Z

Reference resolution

15 of 15 outbound references displayed

verified exact0
verified fuzzy6
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0997d5ad-bca4-4488-8dea-aaff6273be3e · outbound

This paper cites A Menger-type theorem for two induced paths.

Asymptotic structure. VI. Distant paths across a disc A Menger-type theorem for two induced paths

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.444504Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24bd365d-80f3-46de-b5e3-230da1b8ba9a · outbound

This paper cites The metric Menger problem.

Asymptotic structure. VI. Distant paths across a disc The metric Menger problem

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.450375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5fe6ae79-3dd0-435a-b778-8e645b1ff537 · outbound

This paper cites On the complexity of testing for odd holes and induced odd paths.

Asymptotic structure. VI. Distant paths across a disc On the complexity of testing for odd holes and induced odd paths

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.455362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d16fac2f-8e44-4937-85f9-340f7ab22c24 · outbound

This paper cites The monadic second-order logic of graphs. I. Recognizable sets of finite graphs.

Asymptotic structure. VI. Distant paths across a disc The monadic second-order logic of graphs. I. Recognizable sets of finite graphs

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:21:58.846505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3ecfb954-e6d0-41e0-970d-7011deea3a50 · outbound

This paper cites On Induced Versions of Menger's Theorem on Sparse Graphs.

Asymptotic structure. VI. Distant paths across a disc On Induced Versions of Menger's Theorem on Sparse Graphs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.465212Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52c8bbe5-f6e9-4bcd-b7ad-94136b5271fe · outbound

This paper cites Graph minors and metric spaces.

Asymptotic structure. VI. Distant paths across a disc Graph minors and metric spaces

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.471193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eeced106-996b-46ab-b61b-4140f5e81c3b · outbound

This paper cites On an induced version of Menger’s theorem.

Asymptotic structure. VI. Distant paths across a disc On an induced version of Menger’s theorem

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.476102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a361f9a-dcac-4721-a5f5-a5d3cc60d9b0 · outbound

This paper cites On the complexity of combinatorial problems.

Asymptotic structure. VI. Distant paths across a disc On the complexity of combinatorial problems

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:21:58.830815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b0141955-7bc4-4f83-b8f9-0ec399ef0610 · outbound

This paper cites The induced disjoint paths problem.

Asymptotic structure. VI. Distant paths across a disc The induced disjoint paths problem

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:21:58.816139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7e566757-bd9e-4949-ae01-583cf4465645 · outbound

This paper cites Zur allgemeinen kurventheorie.

Asymptotic structure. VI. Distant paths across a disc Zur allgemeinen kurventheorie

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.489747Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38a3236a-111d-4beb-9063-f7c6b2ab0585 · outbound

This paper cites A counterexample to the coarse Menger conjecture.

Asymptotic structure. VI. Distant paths across a disc A counterexample to the coarse Menger conjecture

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.494080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17176410-ecb4-4db5-a05e-63c0209ef4b0 · outbound

This paper cites Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture.

Asymptotic structure. VI. Distant paths across a disc Asymptotic structure. IV. A counterexample to the weak coarse Menger conjecture

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:21:58.498849Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecf0edbf-1ae7-412a-bbe5-c6a1db59de5b · outbound

This paper cites Asymptotic structure. V. The coarse Menger conjecture in bounded pathwidth.

Asymptotic structure. VI. Distant paths across a disc Asymptotic structure. V. The coarse Menger conjecture in bounded pathwidth

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:21:58.792432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d03290ad-a016-4335-b012-5117dec5892a · outbound

This paper cites Graph minors. VI. Disjoint paths across a disc.

Asymptotic structure. VI. Distant paths across a disc Graph minors. VI. Disjoint paths across a disc

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:21:58.777896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b3e47098-0f02-4ca9-b1ac-e9907fdf7ad4 · outbound

This paper cites Graph minors. XIII. The disjoint paths problem.

Asymptotic structure. VI. Distant paths across a disc Graph minors. XIII. The disjoint paths problem

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:21:58.761888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation bbc8848e-47ff-4f1a-b46d-ae124bd97982 · inbound

Asymptotic structure. V. The coarse Menger conjecture in bounded path-width cites this paper.

Asymptotic structure. V. The coarse Menger conjecture in bounded path-width Asymptotic structure. VI. Distant paths across a disc

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T16:14:47.178089Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e95ffec5-c728-4c89-81e2-cbbb790f6f15 · inbound

Coarse Menger property of quasi-minor excluded graphs and length spaces cites this paper.

Coarse Menger property of quasi-minor excluded graphs and length spaces Asymptotic structure. VI. Distant paths across a disc

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:51:27.106986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 346d9214-54ef-4203-8962-8748f230458b · inbound

A coarse Menger's Theorem for planar and bounded genus graphs cites this paper.

A coarse Menger's Theorem for planar and bounded genus graphs Asymptotic structure. VI. Distant paths across a disc

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-05-13T02:37:08.138141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3df14502-e357-4ed4-ac19-6e09b1bd9d99 · inbound

A coarse Menger theorem for hyperbolic graphs, finitely presented groups, and more cites this paper.

A coarse Menger theorem for hyperbolic graphs, finitely presented groups, and more Asymptotic structure. VI. Distant paths across a disc

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-03T21:28:58.894559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 74578743-b016-43a2-af9a-5ba3a036b92b · inbound

A coarse block-cut tree theorem cites this paper.

A coarse block-cut tree theorem Asymptotic structure. VI. Distant paths across a disc

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-07-09T20:16:29.543408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1e27adc9-bc3f-4e93-8f80-e803790670a2 · inbound

Quasi-isometries, contractions, and intersection graphs cites this paper.

Quasi-isometries, contractions, and intersection graphs Asymptotic structure. VI. Distant paths across a disc

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-14T04:21:13.829181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.