Paper Citation Record · LEDGER

On volume vectors determined by hypergraphs in thin subsets of Euclidean space

As of 13 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2607.00153.

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

pith.paper-citation-record.v1
2607.00153 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-02T00:56:04.151381Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:16:13.414818Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

39 of 39 outbound references displayed

verified exact26
verified fuzzy3
unresolved1
parse uncertain0
malformed identifier9
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 143273fc-283a-4615-a78e-41b8fb7d5153 · outbound

This paper cites Finite chains inside thin subsets ofR d.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Finite chains inside thin subsets ofR d

Reference 1

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.735770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cbcf0efd-025a-4e08-ac26-e1e25564f239 · outbound

This paper cites Falconer-type results for any finite graph with multiple pins.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Falconer-type results for any finite graph with multiple pins

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:24.074699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cd0c0d6d-b42e-461d-a283-ad577d0d3943 · outbound

This paper cites Nonempty inte- rior of pinned distance and tree sets.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Nonempty inte- rior of pinned distance and tree sets

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:23.754323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9e6f891b-cf1f-4ffd-aa60-0804e317ffc9 · outbound

This paper cites A singular variant of the Falconer distance problem.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space A singular variant of the Falconer distance problem

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:24.078247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 3c7583c8-082e-4525-870a-d01f1bda677a · outbound

This paper cites From weighted paraboloid restriction tok-stars and distance graphs.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space From weighted paraboloid restriction tok-stars and distance graphs

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T10:02:15.136340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ec40724a-bcad-40b6-85fb-98117a484b8c · outbound

This paper cites an unresolved cited work.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-07-06T10:02:15.134651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4a1572ad-300f-4fb6-9ea6-29de46310c98 · outbound

This paper cites Pinned Dot Product Set Estimates.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Pinned Dot Product Set Estimates

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:24.070973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation edb6454a-1d5c-460c-a773-2d4772a1d9e2 · outbound

This paper cites Hall’s marriage theorem.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Hall’s marriage theorem

Reference 8

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.761592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 678e3ccc-ebe5-4dca-a974-af53ae2ef0cc · outbound

This paper cites New improvement to Falconer distance set problem in higher dimensions.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space New improvement to Falconer distance set problem in higher dimensions

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:24.063587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 42e946d4-0794-40dc-8136-1dc2d12a4b2b · outbound

This paper cites SharpL 2 estimates of the Schr¨ odinger maximal func- tion in higher dimensions.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space SharpL 2 estimates of the Schr¨ odinger maximal func- tion in higher dimensions

Reference 10

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.723424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c21b8684-9865-4f67-bb5e-7b9433a8fba8 · outbound

This paper cites Multiparameter projection theorems with applications to sums-products and finite point configurations in the Euclidean set- ting.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Multiparameter projection theorems with applications to sums-products and finite point configurations in the Euclidean set- ting

Reference 11

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.745940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 95f2c893-9aea-4013-905c-e271ddb21d71 · outbound

This paper cites Fourier integral operators, fractal sets, and the regular value theorem.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Fourier integral operators, fractal sets, and the regular value theorem

Reference 12

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.717666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0f8ac1b3-449b-4ece-bf9b-f545b2da126e · outbound

This paper cites On the Hausdorff dimensions of distance sets.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On the Hausdorff dimensions of distance sets

Reference 13

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.733344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a18fbee0-8b1c-49fc-9639-e4de27aade84 · outbound

This paper cites On volumes of simplices in intermediate dimensions.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On volumes of simplices in intermediate dimensions

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-07-02T00:56:24.081425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 962a28d6-34e2-409b-8321-5feb92f89cf0 · outbound

This paper cites Volumes spanned byk-point configurations inR d.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Volumes spanned byk-point configurations inR d

Reference 15

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.737406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 36fcc4b2-a481-4b50-ae5a-a462fb937ae9 · outbound

This paper cites Multilinear generalized Radon transforms and point configurations.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Multilinear generalized Radon transforms and point configurations

Reference 16

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.756799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5e773257-5b48-4390-a083-eb9990761b04 · outbound

This paper cites On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry

Reference 17

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.676810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f954748c-68dc-4e95-8386-bcccd0f84b76 · outbound

This paper cites A group-theoretic viewpoint on Erd¨ os-Falconer problems and the Mattila integral.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space A group-theoretic viewpoint on Erd¨ os-Falconer problems and the Mattila integral

Reference 18

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.739969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a9452222-044c-49b0-b8c5-e1f5f6a1da78 · outbound

This paper cites On necklaces inside thin subsets ofR d.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On necklaces inside thin subsets ofR d

Reference 19

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.738693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d8d8a45d-ea2c-4778-a3be-38877d3459ce · outbound

This paper cites Configuration sets with nonempty interior.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Configuration sets with nonempty interior

Reference 20

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.706027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 65d2feb7-b9f7-4c1d-9103-ef54ca2945e8 · outbound

This paper cites Nishihara,L p-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application, Math.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Nishihara,L p-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application, Math

Reference 21

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.712186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 314727ba-fde5-4bf2-ad9e-496e9a088159 · outbound

This paper cites Onk-point configuration sets with nonempty interior.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Onk-point configuration sets with nonempty interior

Reference 22

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.743245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 11bcced9-5c1f-4a93-b0da-0baaf9d2d3b3 · outbound

This paper cites Realizing trees of configurations in thin sets.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Realizing trees of configurations in thin sets

Reference 23

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.699320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7ab4037c-e16b-4be2-8f9e-05a023591e63 · outbound

This paper cites On Falconer’s distance set problem in the plane.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On Falconer’s distance set problem in the plane

Reference 24

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.768483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fd33dad5-93d5-4c2a-8a6b-153f09d4dd50 · outbound

This paper cites In: Proc.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space In: Proc

Reference 25

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.714862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 54d81445-2f6a-4069-9514-12bd226951df · outbound

This paper cites The VC-dimension and point configurations inR d.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space The VC-dimension and point configurations inR d

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:24.067442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8218d836-0730-4911-938e-824afb3ebf99 · outbound

This paper cites On the Mattila-Sj¨ olin theorem for distance sets.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On the Mattila-Sj¨ olin theorem for distance sets

Reference 27

Resolution: malformed identifier; arxiv_id, observed 2026-07-02T00:56:23.719239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 79f8e24f-41b8-4fb2-9072-bfc84ab1b2aa · outbound

This paper cites Pinned simplices and connections to product of sets on paraboloids.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Pinned simplices and connections to product of sets on paraboloids

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T10:02:15.134387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation acee9550-c68d-452b-beec-e7f4fd70b579 · outbound

This paper cites Gaspar and M.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Gaspar and M

Reference 29

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.759148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 26e93049-3384-4af4-b9fb-caefa8480b36 · outbound

This paper cites On thek-volume rigidity of a simplicial complex inR d.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On thek-volume rigidity of a simplicial complex inR d

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:23.727669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c39ae0e5-41c0-4c82-957a-cd3ffbace082 · outbound

This paper cites Euclidean dis- tance geometry and applications.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Euclidean dis- tance geometry and applications

Reference 31

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.765634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation af4af728-b04f-458d-ac0e-d848c1d8a037 · outbound

This paper cites Integrable geodesic flows on surfaces.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Integrable geodesic flows on surfaces

Reference 32

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.730917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 754dc9e9-5e1a-4d52-bf70-4600ff05bcbb · outbound

This paper cites an unresolved cited work.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.734243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4e231a88-506e-4d55-aba6-33cd6c59d8bd · outbound

This paper cites and Tian, J.-F.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space and Tian, J.-F

Reference 34

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.696197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 12ba4af5-18e9-47d8-87ea-f8c5a0a8d9e8 · outbound

This paper cites On the dimension and smoothness of radial projections.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On the dimension and smoothness of radial projections

Reference 35

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.741037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d0fa0e9b-1739-473a-8d56-38715d656e54 · outbound

This paper cites Finite point configurations and the regular value theorem in a fractal setting.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space Finite point configurations and the regular value theorem in a fractal setting

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-07-06T10:02:15.132949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5285d87e-e97b-4e18-bb51-bb309b0d4cca · outbound

This paper cites A Mattila-Sj¨ olin theorem for simplices in low dimensions.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space A Mattila-Sj¨ olin theorem for simplices in low dimensions

Reference 37

Resolution: malformed identifier; doi_truncated, observed 2026-07-02T00:56:23.770831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 144ec0bb-c1d7-4799-84fe-cca6dae1022c · outbound

This paper cites A Mattila-Sj¨ olin theorem for triangles.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space A Mattila-Sj¨ olin theorem for triangles

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-07-02T00:56:23.750006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0c01da2f-1d1e-471c-bd0d-a3138e37e182 · outbound

This paper cites On the volumes of simplices determined by a subset ofR d.

On volume vectors determined by hypergraphs in thin subsets of Euclidean space On the volumes of simplices determined by a subset ofR d

Reference 39

Resolution: verified exact; doi, observed 2026-07-02T00:56:23.711984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation a255cd59-95b4-49bc-b078-2600a99e3e4e · inbound

Pinned nonempty interior and volumes of simplices cites this paper.

Pinned nonempty interior and volumes of simplices On volume vectors determined by hypergraphs in thin subsets of Euclidean space

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T10:16:13.414818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.