Paper Citation Record · LEDGER

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants

As of 19 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2507.12725.

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

pith.paper-citation-record.v1
2507.12725 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:53:18.327282Z

measured 30 of 30 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 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

30 of 30 outbound references displayed

verified exact0
verified fuzzy20
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ce59f6d2-552f-4303-b034-6ec9f1b72903 · outbound

This paper cites Bartsch, T.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Bartsch, T

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:23.169809Z

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 4d4cdd1b-75cd-431a-b5d6-c5d3d6d1b427 · outbound

This paper cites Beckner, Sharp inequalities and geometric manifolds.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Beckner, Sharp inequalities and geometric manifolds

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:23.022758Z

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 75c27d5c-e007-47c0-9a57-1bf0a6fb1cb0 · outbound

This paper cites Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:22.917273Z

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 60cf624c-a234-429c-8acc-2d9ffffb3e51 · outbound

This paper cites Bianchi and H.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Bianchi and H

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:22.762705Z

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 41a30dad-34cd-4c6e-85bc-2f9433038ae3 · outbound

This paper cites Brezis and E.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Brezis and E

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:22.571089Z

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 d51f2d32-0c27-476f-91ed-8f2b79bc1dc5 · outbound

This paper cites Carlen, Duality and stability for functional inequalities , Ann.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Carlen, Duality and stability for functional inequalities , Ann

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:22.431380Z

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 06869cb9-b93d-4308-ae73-d9b7086e1b6c · outbound

This paper cites Carlen, Stability for the logarithmic Hardy-Littlewood-Sobolev inequality with application to the Keller-Segel equation, J.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Carlen, Stability for the logarithmic Hardy-Littlewood-Sobolev inequality with application to the Keller-Segel equation, J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:22.346729Z

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 72d38ebb-dd4e-4d76-8767-a0c56646f0c4 · outbound

This paper cites Carlen and M.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Carlen and M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:22.199645Z

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 c25596c9-244a-4c86-b934-c76929bcffbf · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:21.937772Z

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 d75c6c3c-852c-4211-ba0e-51d1f4e1fe01 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:21.672730Z

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 e6f32d60-003c-461e-828c-be4d5f1e3b70 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:21.448875Z

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 bd525b9b-7c26-47e4-887c-5f122bfaa059 · outbound

This paper cites Optimal stability of Hardy-Littlewood-Sobolev and Sobolev inequalities of arbitrary orders with dimension-dependent constants.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Optimal stability of Hardy-Littlewood-Sobolev and Sobolev inequalities of arbitrary orders with dimension-dependent constants

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T16:53:17.056635Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd033469-dcd6-4dee-83af-fb14293f343a · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:21.213333Z

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 42a3c0a8-489d-4535-8dec-3f6cc4c6d843 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:20.946908Z

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 eb688fa4-c417-463c-bba7-4cc6bcb1afb4 · outbound

This paper cites Dolbeault, M.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Dolbeault, M

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:20.821838Z

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 ce4e9a76-3485-4d15-a619-a343c6e955fd · outbound

This paper cites Duoandikoetxea, Reverse Holder inequalities for spherical harmonics , Proc.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Duoandikoetxea, Reverse Holder inequalities for spherical harmonics , Proc

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:20.677772Z

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 2a4b19b3-a637-402e-acf0-58a9105784e8 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:20.580297Z

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 38557244-48fe-4cd1-924f-4cd6f850bbf9 · outbound

This paper cites Folland and E.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Folland and E

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:20.484468Z

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 31c5df89-3b47-4175-9918-9feb8880e212 · outbound

This paper cites Frank and E.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Frank and E

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:20.372007Z

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 6cd68fa5-93dd-4128-b664-af284fd4558a · outbound

This paper cites Gross, Logarithmic Sobolev inequalities.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Gross, Logarithmic Sobolev inequalities

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:20.283229Z

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 3c636e43-b5bf-4f7d-8d27-ddf59be77f11 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:20.060663Z

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 58c3a0d4-22eb-496e-b195-9f3db92076a1 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:19.902359Z

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 8a8ffba2-b256-4414-82e6-114c1c5ad278 · outbound

This paper cites an unresolved cited work.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:53:19.740780Z

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 c035ec81-8045-46df-a86f-c3f6e4d5d059 · outbound

This paper cites Jerison, J.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Jerison, J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:19.504309Z

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 6d938ab8-ede6-457b-8097-b45c8e7aa59f · outbound

This paper cites Jerison, J.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Jerison, J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:19.359044Z

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 60e21636-ad10-463b-8997-cd5ecd2c12f7 · outbound

This paper cites Liu and A.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Liu and A

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:19.224482Z

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 fad5dd41-475d-4159-8baa-2d67de21e440 · outbound

This paper cites Loiudice, Improved Sobolev inequalities on the Heisenberg group , Nonlinear Anal.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Loiudice, Improved Sobolev inequalities on the Heisenberg group , Nonlinear Anal

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:19.044895Z

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 0d075f8a-c26f-4cdd-8342-f72cec0c5f7d · outbound

This paper cites Lu and J.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Lu and J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:18.855085Z

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 40fb9909-6a86-4255-80bd-8c7930f71a18 · outbound

This paper cites Malchiodi and F.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Malchiodi and F

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:18.663696Z

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 f2cfc357-33db-4336-ada3-66e4fd936d3d · outbound

This paper cites Ye, Global existence and convergence of Yamabe flow , J.

Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants Ye, Global existence and convergence of Yamabe flow , J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:53:18.484767Z

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

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