Paper Citation Record · LEDGER

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation

As of 11 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:2506.02430.

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

pith.paper-citation-record.v1
2506.02430 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:34:27.534612Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-22T09:17:27.349353Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T09:24:46.454225Z

Reference resolution

17 of 17 outbound references displayed

verified exact2
verified fuzzy3
unresolved12
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f1b2c87e-3628-4f7f-bf0c-7c8b2fc39aec · outbound

This paper cites write newline.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:25.453569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05f36e65-3b5f-4c02-b51a-bf0cd691818b · outbound

This paper cites Advanced LIGO.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Advanced LIGO

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:25.565159Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12168253-ae58-467a-889b-31c0a4ce8bba · outbound

This paper cites Advanced Virgo: a 2nd generation interferometric gravitational wave detector.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Advanced Virgo: a 2nd generation interferometric gravitational wave detector

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:25.671300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8af11470-6564-4588-a193-8123db5b1952 · outbound

This paper cites Akutsu et al., Overview of KAGRA: Detector design and construction history , PTEP 2021 (2021), no.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Akutsu et al., Overview of KAGRA: Detector design and construction history , PTEP 2021 (2021), no

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:25.815467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd2ee61c-e82b-451f-9537-861cedad5ad3 · outbound

This paper cites GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:25.928681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20922378-0ce4-4d0b-bfaa-66dc92a51f74 · outbound

This paper cites GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:26.047988Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab201641-a324-4caa-b159-6ce4fb1e2cde · outbound

This paper cites GWTC-2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation GWTC-2.1: Deep Extended Catalog of Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:26.159881Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3277941e-2040-4455-b4ac-8c94d59427f3 · outbound

This paper cites GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:26.319192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1190c2af-b916-4d01-a517-a02ace58f52a · outbound

This paper cites Kramers-Kronig relation in gravitational lensing.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Kramers-Kronig relation in gravitational lensing

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:26.479141Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6dcff52-2d9b-4840-9210-9507da40f4b0 · outbound

This paper cites Tanaka, G.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Tanaka, G

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-07T11:34:28.173007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e4a689e2-24ff-4700-8f2a-8cd4c5b7e4ea · outbound

This paper cites Stern, Elementary theory of the optical properties of solids , vol.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Stern, Elementary theory of the optical properties of solids , vol

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:34:29.255864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2148dc8a-14d1-4be7-a15a-e3dc89168c51 · outbound

This paper cites Small-scale shear: Peeling off diffuse subhalos with gravitational waves.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Small-scale shear: Peeling off diffuse subhalos with gravitational waves

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:26.880702Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51692dde-076c-48ea-827c-0750bc4757e3 · outbound

This paper cites Lensing of gravitational waves: efficient wave-optics methods and validation with symmetric lenses.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Lensing of gravitational waves: efficient wave-optics methods and validation with symmetric lenses

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:27.031181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15167e23-6944-4551-b811-3ccef32067f9 · outbound

This paper cites $\mu$-GLANCE: A Novel Technique to Detect Chromatically and Achromatically Lensed Gravitational Wave Signals.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation $\mu$-GLANCE: A Novel Technique to Detect Chromatically and Achromatically Lensed Gravitational Wave Signals

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T11:34:27.150109Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1c75601-00be-41fd-af73-c2135d4937b4 · outbound

This paper cites On arrival time difference between lensed gravitational waves and light.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation On arrival time difference between lensed gravitational waves and light

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:34:27.827366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5ee4e68d-690a-43e6-9310-e8ee8c3f3a8d · outbound

This paper cites Takahashi, Wave effects in the gravitational lensing of gravitational waves from chirping binaries , 2004.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Takahashi, Wave effects in the gravitational lensing of gravitational waves from chirping binaries , 2004

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:34:29.012602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 93da68b7-39b2-4df9-a8c0-dfbf683a2538 · outbound

This paper cites Schneider, J.

On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation Schneider, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:34:28.779373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 6ddca847-94dd-4697-a771-473d6b12948a · inbound

Wave-optics gravitational wave lensing in modified gravity cites this paper.

Wave-optics gravitational wave lensing in modified gravity On the Phase-Magnitude Relation in Gravitational Lensing: Reformulation and Applications of the Kramers-Kronig relation

Reference 74

Resolution: verified exact; arxiv_id, observed 2026-05-22T09:24:46.456452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.