Paper Citation Record · LEDGER

On the Gauge Invariance of Secondary Gravitational Waves

As of 11 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 4 inbound Pith citation observations for arXiv:2501.13691.

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

pith.paper-citation-record.v1
2501.13691 v3

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T15:49:37.136118Z

measured 38 of 38 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 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T18:40:47.855558Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-17T00:38:45.205286Z

Reference resolution

34 of 34 outbound references displayed

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Outbound references

Observation 17ee15ec-9c1a-4e46-91f2-28936da26b69 · outbound

This paper cites Binary Black Hole Mergers in the first Advanced LIGO Observing Run.

On the Gauge Invariance of Secondary Gravitational Waves Binary Black Hole Mergers in the first Advanced LIGO Observing Run

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.950397Z

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Observation 3ea85426-dc54-424a-a96f-7fe3e5adce45 · 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 Gauge Invariance of Secondary Gravitational Waves GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.956436Z

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Observation 4e3aa44d-df20-428a-98eb-fdeee4e0856f · 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 Gauge Invariance of Secondary Gravitational Waves GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.962841Z

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Observation 9952d2db-17c2-4602-884f-f8c3245692ef · 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 Gauge Invariance of Secondary Gravitational Waves 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 4

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.968644Z

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Observation 2df188a3-33d9-4d89-b440-49b5a62fb7c3 · 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 Gauge Invariance of Secondary Gravitational Waves GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.974209Z

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Observation fe9d9551-5ac3-4ed6-a432-be8241e6b86f · outbound

This paper cites Gravitational wave background as a probe of the primordial black hole abundance.

On the Gauge Invariance of Secondary Gravitational Waves Gravitational wave background as a probe of the primordial black hole abundance

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.979768Z

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Observation d0ccb049-3c4a-4c4c-80b9-085b83a6af92 · outbound

This paper cites Primordial Black Holes - Perspectives in Gravitational Wave Astronomy -.

On the Gauge Invariance of Secondary Gravitational Waves Primordial Black Holes - Perspectives in Gravitational Wave Astronomy -

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.986324Z

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Observation 2f89594c-d249-4dca-ab66-f9d377d830e3 · outbound

This paper cites Pulsar Timing Array Constraints on Primordial Black Holes with NANOGrav 11-Year Data Set.

On the Gauge Invariance of Secondary Gravitational Waves Pulsar Timing Array Constraints on Primordial Black Holes with NANOGrav 11-Year Data Set

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.991654Z

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Observation 8012b722-0082-49b1-ae7d-ebcd0254a5eb · outbound

This paper cites Did NANOGrav see a signal from primordial black hole formation?.

On the Gauge Invariance of Secondary Gravitational Waves Did NANOGrav see a signal from primordial black hole formation?

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:36.997207Z

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Observation 66ca4b13-08bd-4ac5-aa3b-37e682b93504 · outbound

This paper cites NANOGrav Hints to Primordial Black Holes as Dark Matter.

On the Gauge Invariance of Secondary Gravitational Waves NANOGrav Hints to Primordial Black Holes as Dark Matter

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.002618Z

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Observation 9f4ff2c2-bfce-4c59-8a85-684bde9373e8 · outbound

This paper cites A topic review on probing primordial black hole dark matter with scalar induced gravitational waves.

On the Gauge Invariance of Secondary Gravitational Waves A topic review on probing primordial black hole dark matter with scalar induced gravitational waves

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.008929Z

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Observation 40384d83-df21-4fce-9a8c-e8841a78a461 · outbound

This paper cites Scalar induced gravitational waves review.

On the Gauge Invariance of Secondary Gravitational Waves Scalar induced gravitational waves review

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.014969Z

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Observation c87258dc-fdb6-4fdd-a3dd-1683df13db97 · outbound

This paper cites Cosmological Gravitational Waves from Isocurvature Fluctuations.

On the Gauge Invariance of Secondary Gravitational Waves Cosmological Gravitational Waves from Isocurvature Fluctuations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.020315Z

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Observation 31e11866-9df2-43e7-8c0b-1289efadbb41 · outbound

This paper cites Relativistic second-order perturbations of the Einstein-de Sitter Universe.

On the Gauge Invariance of Secondary Gravitational Waves Relativistic second-order perturbations of the Einstein-de Sitter Universe

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.025540Z

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Observation dc5c54ca-54d7-413d-b4f3-1a75efdb94f8 · outbound

This paper cites Second-order Perturbations of the Friedmann World Model.

On the Gauge Invariance of Secondary Gravitational Waves Second-order Perturbations of the Friedmann World Model

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.031664Z

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Observation 33117fdd-6443-49f1-9f4d-4dd15307e7da · outbound

This paper cites Second-order perturbations of the Schwarzschild spacetime: practical, covariant and gauge-invariant formalisms.

On the Gauge Invariance of Secondary Gravitational Waves Second-order perturbations of the Schwarzschild spacetime: practical, covariant and gauge-invariant formalisms

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.037345Z

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Observation cec5ce6d-26f2-40d9-9efa-cf5c4de94b98 · outbound

This paper cites Analytic integral solutions for induced gravitational waves.

On the Gauge Invariance of Secondary Gravitational Waves Analytic integral solutions for induced gravitational waves

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.043742Z

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Observation b76e10cd-cf46-466c-94ca-3d4108179c27 · outbound

This paper cites On the gauge dependence of gravitational waves generated at second order from scalar perturbations.

On the Gauge Invariance of Secondary Gravitational Waves On the gauge dependence of gravitational waves generated at second order from scalar perturbations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.049860Z

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Observation e25cbe2e-8c2e-4009-bc49-fb68175631b4 · outbound

This paper cites On the Gauge Invariance of Cosmological Gravitational Waves.

On the Gauge Invariance of Secondary Gravitational Waves On the Gauge Invariance of Cosmological Gravitational Waves

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.055242Z

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Observation 915ba8e0-9612-46e1-bb50-c2db65e4323a · outbound

This paper cites Gauge Independence of Induced Gravitational Waves.

On the Gauge Invariance of Secondary Gravitational Waves Gauge Independence of Induced Gravitational Waves

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.060523Z

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Observation a0d347fd-8191-439e-ab66-8be5ebc79986 · outbound

This paper cites Scalar Induced Gravitational Waves in Different Gauges.

On the Gauge Invariance of Secondary Gravitational Waves Scalar Induced Gravitational Waves in Different Gauges

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.065928Z

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Observation e359f58f-cfab-434e-b5ba-f99e4d5a1bce · outbound

This paper cites Gauge transformation of scalar induced gravitational waves.

On the Gauge Invariance of Secondary Gravitational Waves Gauge transformation of scalar induced gravitational waves

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.072449Z

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Observation f91624ed-b31b-4f80-952f-77e06042cb8d · outbound

This paper cites Gauge transformation of scalar induced tensor perturbation during matter domination.

On the Gauge Invariance of Secondary Gravitational Waves Gauge transformation of scalar induced tensor perturbation during matter domination

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.077694Z

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Observation 48f53659-a2ec-45a5-95c1-3be1418c17f0 · outbound

This paper cites Gauge Dependence of Gravitational Waves Induced by Primordial Isocurvature Fluctuations.

On the Gauge Invariance of Secondary Gravitational Waves Gauge Dependence of Gravitational Waves Induced by Primordial Isocurvature Fluctuations

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.083479Z

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Observation 3b40db05-a271-43f7-aaeb-ef215ed76994 · outbound

This paper cites Gauge dependence of gravitational waves generated from scalar perturbations.

On the Gauge Invariance of Secondary Gravitational Waves Gauge dependence of gravitational waves generated from scalar perturbations

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.089335Z

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Observation 160e4d0d-a00a-42d8-bec4-d004942b3321 · outbound

This paper cites Approximate gauge independence of the induced gravitational wave spectrum.

On the Gauge Invariance of Secondary Gravitational Waves Approximate gauge independence of the induced gravitational wave spectrum

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.094559Z

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Observation 4a02c4cf-56f4-48ea-8380-d0e3894b9d4d · outbound

This paper cites On the energy of gravitational waves.

On the Gauge Invariance of Secondary Gravitational Waves On the energy of gravitational waves

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-10T15:49:37.345697Z

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

Observation 9a490487-8f94-4e64-b24e-5c6e4f2e798b · outbound

This paper cites Newman and R.

On the Gauge Invariance of Secondary Gravitational Waves Newman and R

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:49:37.855205Z

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Observation 97c0ca72-04de-49dc-b458-d8a3b530f4e0 · outbound

This paper cites Semianalytic Calculation of Gravitational Wave Spectrum Nonlinearly Induced from Primordial Curvature Perturbations.

On the Gauge Invariance of Secondary Gravitational Waves Semianalytic Calculation of Gravitational Wave Spectrum Nonlinearly Induced from Primordial Curvature Perturbations

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.110531Z

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Observation d183af17-db17-4482-8bde-7e4e56ecbe2c · outbound

This paper cites Induced gravitational waves in a general cosmological background.

On the Gauge Invariance of Secondary Gravitational Waves Induced gravitational waves in a general cosmological background

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.115671Z

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Observation b02d9c18-3c9e-493f-af20-ec490d35877d · outbound

This paper cites From formation to evaporation: Induced gravitational wave probes of the primordial black hole reheating scenario.

On the Gauge Invariance of Secondary Gravitational Waves From formation to evaporation: Induced gravitational wave probes of the primordial black hole reheating scenario

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.121134Z

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Observation c8a59f1c-7651-4276-b9c7-5d7605c2dd64 · outbound

This paper cites Gravitational waves from dark matter isocurvature.

On the Gauge Invariance of Secondary Gravitational Waves Gravitational waves from dark matter isocurvature

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.126201Z

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Observation f0ee49dd-72c2-48c0-80b4-3a0a4e1bd5d8 · outbound

This paper cites Maggiore, Gravitational Waves.

On the Gauge Invariance of Secondary Gravitational Waves Maggiore, Gravitational Waves

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.131376Z

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Observation 5ad3437d-7632-436c-86a2-fde6316f668d · outbound

This paper cites Relativistic conservation laws and integral constraints for large cosmological perturbations.

On the Gauge Invariance of Secondary Gravitational Waves Relativistic conservation laws and integral constraints for large cosmological perturbations

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-10T15:49:37.136118Z

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Pith citing papers

Observation 57c93ac4-72be-4a94-8ded-05076cfbaeb7 · inbound

General SIGW source for reheating dynamics cites this paper.

General SIGW source for reheating dynamics On the Gauge Invariance of Secondary Gravitational Waves

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-03T18:40:47.855558Z

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Observation 74b2bc5a-0956-4c01-9c90-75630b0eac65 · inbound

Isocurvature Induced Gravitational Waves at Pulsar Timing Arrays cites this paper.

Isocurvature Induced Gravitational Waves at Pulsar Timing Arrays On the Gauge Invariance of Secondary Gravitational Waves

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-17T00:38:45.206991Z

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

Observation 195ea31c-4780-41e3-9022-4419bbebce0a · inbound

Observable Gravitational Wave Strain at Second Order cites this paper.

Observable Gravitational Wave Strain at Second Order On the Gauge Invariance of Secondary Gravitational Waves

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-03T15:50:31.321091Z

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Observation c11434ed-39a0-4b08-bbc1-8fb3e2d5d275 · inbound

Scalar-induced gravitational waves from a box-shaped curvature power spectrum cites this paper.

Scalar-induced gravitational waves from a box-shaped curvature power spectrum On the Gauge Invariance of Secondary Gravitational Waves

Reference 141

Resolution: unresolved; no resolver link, observed 2026-07-14T09:40:09.826288Z

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