Paper Citation Record · LEDGER

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index

As of 17 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2608.10518.

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

pith.paper-citation-record.v1
2608.10518 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:28:11.128105Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

26 of 26 outbound references displayed

verified exact0
verified fuzzy21
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6e4bdd09-b585-4a99-95ca-bf95c2f86aff · outbound

This paper cites Catino, P.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Catino, P

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.531611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1bfb86df-63ba-4be1-a2c7-8223336aaf71 · outbound

This paper cites Chodosh and C.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Chodosh and C

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.513582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2bf8336c-9891-4fa2-a31c-d1370ad732fc · outbound

This paper cites Stable minimal hypersurfaces in $\mathbf{R}^5$.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Stable minimal hypersurfaces in $\mathbf{R}^5$

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T14:28:11.024138Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21df7b85-9816-41d7-82fc-117f085b4449 · outbound

This paper cites Cohn-Vossen,K¨ urzeste Wege und Totalkr¨ ummung auf Fl¨ achen, Composi- tio Math.2(1935), 69–133.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Cohn-Vossen,K¨ urzeste Wege und Totalkr¨ ummung auf Fl¨ achen, Composi- tio Math.2(1935), 69–133

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.497754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation afac2746-d8de-4fb9-acb9-ac5cace669d6 · outbound

This paper cites Cohn-Vossen,Totalkr¨ ummung und geod¨ atische Linien auf einfach zusam- menh¨ angenden offenen volst¨ andigen Fl¨ achenst¨ ucken, Recueil Math.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Cohn-Vossen,Totalkr¨ ummung und geod¨ atische Linien auf einfach zusam- menh¨ angenden offenen volst¨ andigen Fl¨ achenst¨ ucken, Recueil Math

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.482151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f3fb79d3-ee24-4372-b877-4c6904716ea3 · outbound

This paper cites do Carmo, Riemannian Geometry, Birkh¨ auser, Boston, MA, 1992.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index do Carmo, Riemannian Geometry, Birkh¨ auser, Boston, MA, 1992

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.466427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 27e62eb9-2331-40f3-b6c6-f8b2bc095e3d · outbound

This paper cites do Carmo and C.K.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index do Carmo and C.K

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.450182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0585aaba-4ab3-4598-8b9c-9a48cb94ebc5 · outbound

This paper cites Fischer-Colbrie,On complete minimal surfaces with finite Morse index in three-manifolds, Invent.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Fischer-Colbrie,On complete minimal surfaces with finite Morse index in three-manifolds, Invent

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T14:28:11.048537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be42e3f2-b4c7-4d25-814e-baaed4fd7afa · outbound

This paper cites Fischer-Colbrie and R.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Fischer-Colbrie and R

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.424829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6cf8b750-2539-4b34-8233-1ea395fe37cc · outbound

This paper cites Grove and K.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Grove and K

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.409838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e3ac1809-2d88-4f90-add5-c27f24cee982 · outbound

This paper cites Harumoto,Topology of complete non-compact surfaces with the finite in- dex of the Schr¨ odinger operator, Master’s thesis, Okayama University, 2026.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Harumoto,Topology of complete non-compact surfaces with the finite in- dex of the Schr¨ odinger operator, Master’s thesis, Okayama University, 2026

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.395166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2ccbb360-ad19-4e56-96a4-8fd98c14754b · outbound

This paper cites Huber,On subharmonic functions and differential geometry in the large, Comment.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Huber,On subharmonic functions and differential geometry in the large, Comment

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T14:28:11.066022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee04d05c-532e-4575-a147-bedeb2ba571f · outbound

This paper cites Itoh and M.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Itoh and M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.370837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1e602f3a-667f-4bc1-a1bc-0383d9d8befc · outbound

This paper cites an unresolved cited work.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-15T14:28:11.355815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation bfcb7b4e-3074-4413-b209-5a58cee12e8c · outbound

This paper cites Kondo and S.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Kondo and S

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.341893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 34be71fa-4b92-438c-9804-fe4fd0c49a14 · outbound

This paper cites Kondo and M.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Kondo and M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.327732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fbd7f6d1-279e-4748-a8a6-c72291a276ff · outbound

This paper cites Kondo and M.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Kondo and M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.313364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation bd77aa45-06fe-4a2f-bb9e-07a8720fa85f · outbound

This paper cites Kondo and M.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Kondo and M

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.298373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 82860638-3c43-4e36-92c2-defd990dc713 · outbound

This paper cites Mao,Volume comparison theorems for manifolds with radial curvature bounded, Czechoslovak Math.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Mao,Volume comparison theorems for manifolds with radial curvature bounded, Czechoslovak Math

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.284149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b8c0d1b2-19c1-4d42-bb21-e577cfd88c17 · outbound

This paper cites Stable minimal hypersurfaces in $\mathbb R^6$.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Stable minimal hypersurfaces in $\mathbb R^6$

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T14:28:11.100863Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87c65439-8cdc-41c4-b213-e1b95688c252 · outbound

This paper cites Shiohama,The role of total curvature on complete noncompact Rieman- nian2-manifolds, Illinois J.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Shiohama,The role of total curvature on complete noncompact Rieman- nian2-manifolds, Illinois J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.269164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f409cb0f-bf5d-491a-8c15-4867929dfea3 · outbound

This paper cites Shiohama, T.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Shiohama, T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.253114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1faddb92-9844-4323-9898-b9840020b12b · outbound

This paper cites Shiohama and M.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Shiohama and M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.238775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6c9302e5-823b-4f77-ac05-3b0b0e96ec3b · outbound

This paper cites Shioya,The ideal boundaries of complete open surfaces, Tohoku Math.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Shioya,The ideal boundaries of complete open surfaces, Tohoku Math

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.224259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0118dbd6-ac21-497c-a8f8-7fbb760b870a · outbound

This paper cites Tanaka,On the cut loci of a von Mangoldt’s surface of revolution, J.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Tanaka,On the cut loci of a von Mangoldt’s surface of revolution, J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.209725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2e3366fa-18ed-4bd7-ac7c-c12f697a92df · outbound

This paper cites Tanaka and K.

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index Tanaka and K

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T14:28:11.194287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.