Paper Citation Record · LEDGER

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility

As of 19 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2502.04826.

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

pith.paper-citation-record.v1
2502.04826 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T21:27:58.099680Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T15:24:11.775563Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T10:36:07.531660Z

Reference resolution

14 of 14 outbound references displayed

verified exact1
verified fuzzy12
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d8ef59d6-5729-443d-9380-f7b02123a9dd · outbound

This paper cites K AM theory for the Hamiltonian derivative wave equation.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility K AM theory for the Hamiltonian derivative wave equation

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.298941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4a1fb5cc-9789-4ae5-8cab-5085a10b37bf · outbound

This paper cites K AM for reversible derivative wave equations.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility K AM for reversible derivative wave equations

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.287621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 10f34c26-2946-466e-b531-e3f076afc51f · outbound

This paper cites Quasi-periodic solutions of nonlinear wave equations on th ed-dimensional torus.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Quasi-periodic solutions of nonlinear wave equations on th ed-dimensional torus

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.275685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d46c1d73-9a3a-47b0-8308-c0df28ba97dc · outbound

This paper cites Reducibility of klein-gordon equati ons with maximal order perturbations, 2024.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Reducibility of klein-gordon equati ons with maximal order perturbations, 2024

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.263638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4af4b4bb-d015-409b-8e0c-ee8aa4f5e67c · outbound

This paper cites Time periodic solutions of completely resonant klein -gordon equations on S3, 2023.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Time periodic solutions of completely resonant klein -gordon equations on S3, 2023

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.252472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 72e1c987-446e-48c8-ab5d-3222b31a2a8f · outbound

This paper cites Quasi-perio dic standing wave solutions of gravity-capillary water wav es.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Quasi-perio dic standing wave solutions of gravity-capillary water wav es

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.241138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4945920e-61a1-412d-bd50-f4c3f2e018ab · outbound

This paper cites Weakly turbulent instability of anti–de sitter spacetime.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Weakly turbulent instability of anti–de sitter spacetime

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.229166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6eb3eafb-a7bb-4af0-a1f0-6f7bf1c32c32 · outbound

This paper cites Non-linear periodic waves on the Einstein cylinder.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Non-linear periodic waves on the Einstein cylinder

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-08T21:27:58.076412Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7df9a21-2204-45ff-8a34-4daf96f2866f · outbound

This paper cites Time pe riodic solutions and nekhoroshev stability to non-linear m assive klein-gordon equations in anti-de sitter, 2023.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Time pe riodic solutions and nekhoroshev stability to non-linear m assive klein-gordon equations in anti-de sitter, 2023

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.215759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2a7e959e-9248-473a-a641-fdd1482658e1 · outbound

This paper cites Reducibility of first order linear operators on tori via Moser's theorem.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Reducibility of first order linear operators on tori via Moser's theorem

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-08T21:27:58.136649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ce4e5b17-d8a6-406f-b418-fe5062e5343c · outbound

This paper cites Franzoi and A.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Franzoi and A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.203835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 039d3431-d421-49df-b2db-a8ada19b4bf5 · outbound

This paper cites Time-per iodic solutions in an einstein ads–massless-scalar-ﬁeld s ystem.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Time-per iodic solutions in an einstein ads–massless-scalar-ﬁeld s ystem

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.191166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6e9dd560-b497-40ba-b603-11f9b0f00e57 · outbound

This paper cites Quasi-periodic solutions of force d Kirchhoﬀ equation.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility Quasi-periodic solutions of force d Kirchhoﬀ equation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.178131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2b0d702-4ae0-415e-ac35-185bf07c852c · outbound

This paper cites A reducibility result for a class of linear wave equations on Td.

Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility A reducibility result for a class of linear wave equations on Td

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-08T21:27:58.164461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 2398b781-82ae-4bc1-b4a3-fa6a32102d57 · inbound

Weakly turbulent dynamics on Schwarzschild-AdS black hole spacetimes cites this paper.

Weakly turbulent dynamics on Schwarzschild-AdS black hole spacetimes Null coordinates for quasi-periodic $(1+1)$-dimensional wave operators on the circle with applications to reducibility

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-11T10:36:07.534826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.