Paper Citation Record · LEDGER

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus

As of 14 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2507.16599.

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

pith.paper-citation-record.v1
2507.16599 v1

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:19:39.971474Z

measured 11 of 11 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

11 of 11 outbound references displayed

verified exact0
verified fuzzy9
unresolved2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 21aeba6f-ac53-405f-891b-2c812f763cd0 · outbound

This paper cites Semiclassical limits of eigenfunctions on flat n-dimensional tori.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus Semiclassical limits of eigenfunctions on flat n-dimensional tori

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.080145Z

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 8e2d9573-2be6-4c2f-9cbd-8ebfbca0306a · outbound

This paper cites A Counterexample to the Mizohata-Takeuchi Conjecture.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus A Counterexample to the Mizohata-Takeuchi Conjecture

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T15:19:39.947970Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d660cc05-8cd0-4760-890e-c50e43682c6e · outbound

This paper cites 2022, e24.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus 2022, e24

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.065085Z

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 9376ad7e-6a74-4631-b9a3-1e8d4c7bdd2a · outbound

This paper cites On the representations of a number as the sum of three squares.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus On the representations of a number as the sum of three squares

Reference 129

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.072556Z

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 e95b70be-42eb-470f-a982-daf812317d5f · outbound

This paper cites Explicit estimates for the error term in the prime number theorem for arithmetic progressions.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus Explicit estimates for the error term in the prime number theorem for arithmetic progressions

Reference 150

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.032807Z

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 6737e91a-004d-40ae-b1b2-04f45b9a4f62 · outbound

This paper cites L2 to Lp bounds for spectral projectors on thin intervals in Riemannian manifolds.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus L2 to Lp bounds for spectral projectors on thin intervals in Riemannian manifolds

Reference 171

Resolution: unresolved; no resolver link, observed 2026-08-06T15:19:39.951848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6794cd5-464f-44cc-99a3-e66fc71290f4 · outbound

This paper cites Explicit zero-free regions for Dirichlet L-functions.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus Explicit zero-free regions for Dirichlet L-functions

Reference 285

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.024387Z

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 61d11560-7f4e-43ba-a54c-dcaddce66c8e · outbound

This paper cites Restriction of toral eigenfunctions to totally geodesic submanifolds.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus Restriction of toral eigenfunctions to totally geodesic submanifolds

Reference 1985

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.057499Z

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 18c78196-f396-466a-b026-6eabb9671f08 · outbound

This paper cites Fractional perimeters from a fractal perspective.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus Fractional perimeters from a fractal perspective

Reference 1988

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.041348Z

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 bdfd8df3-fa75-44b0-a329-1b2b9fc96161 · outbound

This paper cites A Cantor-Lebesgue theorem for double trigonometric series.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus A Cantor-Lebesgue theorem for double trigonometric series

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.015950Z

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 0745ce63-a4b6-4464-82c9-525f3ad02ad9 · outbound

This paper cites Quantum limits on flat tori.

Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus Quantum limits on flat tori

Reference 2021

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:19:40.048887Z

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

No inbound Pith citation observations are available.