Paper Citation Record · LEDGER

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds

As of 8 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2507.03079.

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

pith.paper-citation-record.v1
2507.03079 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:39:10.990368Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

49 of 49 outbound references displayed

verified exact3
verified fuzzy8
unresolved38
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f44349ab-5c49-4ce5-810d-7912fc808246 · outbound

This paper cites Hairy Black Holes and Null Circular Geodesics.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Hairy Black Holes and Null Circular Geodesics

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:06.853051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffc6fb9d-b16b-446e-b346-26b13f165808 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:19.010073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b500d3bb-ac36-492b-84e9-244dd96250b3 · outbound

This paper cites Stationary Scalar Clouds Around Rotating Black Holes.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Stationary Scalar Clouds Around Rotating Black Holes

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:07.030115Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f992e07-7f80-436e-a6f2-80269a0bb07e · outbound

This paper cites A no-short scalar hair theorem for rotating Kerr black holes.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds A no-short scalar hair theorem for rotating Kerr black holes

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:39:11.859752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ec55fa90-1fdb-4424-be85-fb6bfdd9d25f · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:18.814721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fa8266f5-304d-4269-8270-56728c8288d0 · outbound

This paper cites How fast can a black hole rotate?.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds How fast can a black hole rotate?

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:39:11.620308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1b071095-ce07-4f30-bb46-9b16e6e48dbe · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:18.544738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8b3f504a-4c78-445c-8f70-0d638d4b642e · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:19.202009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a7738b70-07d6-451f-8f14-22f5cff82137 · outbound

This paper cites Extremal Kerr-Newman black holes with extremely short charged scalar hair.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Extremal Kerr-Newman black holes with extremely short charged scalar hair

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:07.316051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 110012ce-6e2a-4a8d-ad40-b5921746c955 · outbound

This paper cites Rotating black holes can have short bristles.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Rotating black holes can have short bristles

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:07.482057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 199a5e3c-c64e-48ab-a744-dc6bab816c13 · outbound

This paper cites Chandrasekhar, The Mathematical Theory of Black Holes , (Oxford University Press, New York, 1983).

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Chandrasekhar, The Mathematical Theory of Black Holes , (Oxford University Press, New York, 1983)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:18.323676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d0b7d350-f56c-465e-8dad-f087121d33c1 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:07.673354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23060148-617f-4d6a-8505-dc406f6c104c · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:18.113958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5962ddc7-8302-4695-8734-787d1946dabd · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:17.977101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d147bba4-1006-4e87-abc4-6cf79e1d332f · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:17.801181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5ddc1a36-ff4b-4439-bceb-7aba98cc42d0 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:17.531372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b06c178e-2770-4698-bd86-a871e5bfd7ba · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:17.367932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fee335d9-958b-40b7-b188-f854293dea7e · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:17.192926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 57862eb5-c2b7-4549-8958-8ac9af054216 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:16.943113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bd0b2b4e-7374-4b32-ac37-83e4bc14ed38 · outbound

This paper cites Hartman, W.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Hartman, W

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:16.669592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 88ff352e-61d3-4e73-bbe4-55dfc1dbd3a6 · outbound

This paper cites Ronveaux, Heun ’s differential equations.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Ronveaux, Heun ’s differential equations

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:16.459353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fe0e8b27-2391-4e7c-b171-e4c654ad0199 · outbound

This paper cites Classes of Exact Solutions to Regge-Wheeler and Teukolsky Equations.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Classes of Exact Solutions to Regge-Wheeler and Teukolsky Equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:08.457968Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1117c10-1c0b-4de0-a8f4-9a950e25e0ad · outbound

This paper cites Abramowitz and I.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Abramowitz and I

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:16.201941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 56c744ff-79c9-4b0c-ab73-ad3a3c10867e · outbound

This paper cites Weak Cosmic Censorship: As Strong as Ever.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Weak Cosmic Censorship: As Strong as Ever

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:08.674117Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 644baa9b-d50f-42a0-a3fb-9f9c62c62300 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:16.022085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c789b94f-6921-4fc6-b171-12a493dc08c9 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:15.878014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 75ccc382-ee45-448c-bd68-0c63731e4aeb · outbound

This paper cites Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:08.887700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64875096-82d9-4ba7-89fe-9fb716e55e90 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:08.935780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b568e6d-8a84-4e2a-b338-806458b8280f · outbound

This paper cites In particular, one finds the asymptotic functional behavior Kmm(a p µ2 − ω2) = m2[1 + O(m−1)] − a2(µ2 − ω2) [25].

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds In particular, one finds the asymptotic functional behavior Kmm(a p µ2 − ω2) = m2[1 + O(m−1)] − a2(µ2 − ω2) [25]

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:15.754336Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 17742d70-6d24-4fb0-85d8-dedaf78e1da1 · outbound

This paper cites On the instability regime of the rotating Kerr spacetime to massive scalar perturbations.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds On the instability regime of the rotating Kerr spacetime to massive scalar perturbations

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:39:11.286869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b25fb9bf-7094-4bce-b912-e39df7b7a525 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:15.533153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 94ef29b2-cc90-4120-9173-c886e031a157 · outbound

This paper cites (18)] without loss of generality.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds (18)] without loss of generality

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:15.293062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3c02d7b2-f66b-45ed-b904-800d4415eb1a · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:15.060965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d745eecb-45c4-4554-9063-0f117a276df4 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:14.859683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b0f5e91f-462f-4105-8cc5-56eba68abdc3 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:14.666058Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 19a4c9ec-25e2-437d-9413-f6a8c4316283 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:14.449667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fb2b2373-1064-46fd-8df0-f2af5bfa5ac5 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:14.294117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 421aa211-a985-40c8-991b-ba3a0b4623f3 · outbound

This paper cites In addition, we have substituted, without loss of generality, the value 1 for the normalization constant of the linearized scalar eigenfunction (26).

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds In addition, we have substituted, without loss of generality, the value 1 for the normalization constant of the linearized scalar eigenfunction (26)

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:14.101985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 64fabf6e-6e55-40a3-a6be-7b034f121e60 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:13.873861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 104f66ca-67ca-4452-9ebc-d601d4d15d63 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:13.688360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5fac4df1-3e0b-400f-a7c9-0e07d23ec7af · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:13.565307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 893f05f9-f30c-44c4-bcc9-efa0896e9879 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:13.426748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a4f186b8-4a64-41f8-a0bf-6117e5462cd7 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:13.227460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9677e59f-9464-4a87-9af1-ef725e495ed5 · outbound

This paper cites (47), β = τ 2s2 h 1 − r 1 + 2s τ 2i < 0, violates the characteristic inequality (44).

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds (47), β = τ 2s2 h 1 − r 1 + 2s τ 2i < 0, violates the characteristic inequality (44)

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:39:13.007732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 79fa8ca4-0a11-488f-9877-9547235114e9 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-06T20:39:10.581092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fe92eaa-3287-43ec-b97f-72e0ef776ed0 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:12.726899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 161ba1c3-df2a-4279-bab6-0122909dc151 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:12.508838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e010255c-0d97-4f34-8150-34d0861d1d78 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:12.339174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2d72d8b2-c456-466c-b525-ff9a43070b17 · outbound

This paper cites an unresolved cited work.

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:39:12.123744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.