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Paper Citation Record · LEDGER

Sharp Stability of Global Compactness on the Heisenberg Group

As of 10 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2506.11404.

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

pith.paper-citation-record.v1
2506.11404 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:28:19.413143Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

22 of 22 outbound references displayed

  • verified exact1
  • verified fuzzy14
  • unresolved7
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 21e12c95-e886-48c6-9bcc-9b3e95bba13d · outbound

This paper cites Aubin, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire,J.

Sharp Stability of Global Compactness on the Heisenberg Group Aubin, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire,J

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:23.650326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:17.780936Z digest=sha256:a46bc591988d691521481a2670658afb9f33a0ab08c66fea2a820eb7a76b2145

Observation 53dbb8a8-6d94-47bf-8fef-9c98de65d6ec · outbound

This paper cites Bahri, J.

Sharp Stability of Global Compactness on the Heisenberg Group Bahri, J

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:23.502150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:17.841834Z digest=sha256:3895380de8c09191a70e3dde8cf08dabf39ec8fd83e336e7e1348ff58a54de8a

Observation 4f11334f-4517-49e3-b334-63107b8c6e7c · outbound

This paper cites Bianchi, H.

Sharp Stability of Global Compactness on the Heisenberg Group Bianchi, H

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:23.351807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:17.887386Z digest=sha256:945824007de7ec29b2dc384b21219ad23f4ec536da452876230f1f690ab42a6e

Observation dfc6173b-dbe1-4638-a804-0ca3ab35833b · outbound

This paper cites Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method.

Sharp Stability of Global Compactness on the Heisenberg Group Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:28:19.632501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:17.977603Z digest=sha256:09684f4531c6afd79108a35ce8a5a5272f6900f4919be8ef70142b1136f95f8f

Observation 95fb01cc-3aa9-42f3-8871-77778307a7b9 · outbound

This paper cites Ciraolo, A.

Sharp Stability of Global Compactness on the Heisenberg Group Ciraolo, A

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:23.192404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.025715Z digest=sha256:072c2f6733c8509234c7ebbb1a4d7110982392e8caea1027474a1df931b789d8

Observation 41b6cffe-24e0-4394-9201-eb90df1fad2b · outbound

This paper cites Citti, F.

Sharp Stability of Global Compactness on the Heisenberg Group Citti, F

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:22.923291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.110809Z digest=sha256:aff0962ce131273056f4fbecb60fd0ae918d2170df1684d4cacb3e27e75a3db2

Observation 320914d5-83f2-425b-bd4c-f9dccf7daf88 · outbound

This paper cites Cygan, Subadditivity of homogeneous norms on certain nilpotent Lie groups,Proc.

Sharp Stability of Global Compactness on the Heisenberg Group Cygan, Subadditivity of homogeneous norms on certain nilpotent Lie groups,Proc

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:22.692056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.178905Z digest=sha256:7bd155295ebc1cf0e7d650f11923964c0a31249877df98a3eeb6536bc77ef195

Observation 1ebb24fd-5e57-4952-bd22-7e193fbc9dda · outbound

This paper cites an unresolved cited work.

Sharp Stability of Global Compactness on the Heisenberg Group Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:28:22.466124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.234613Z digest=sha256:566a4dd8e5730d1ff235e1a3a156a89f41e92fd7ebd2b7042a47b2d5c5381ae2

Observation 25a27916-f7a1-4899-8f3e-ecc45da6266e · outbound

This paper cites Figalli, F.

Sharp Stability of Global Compactness on the Heisenberg Group Figalli, F

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:22.225708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.303697Z digest=sha256:5dc496d57e258e1dcb353cda4f6cb638ca985581f37d352de79d249a75f53319

Observation b335e966-b4ab-4158-bdfa-080f054f3847 · outbound

This paper cites Figalli, R.

Sharp Stability of Global Compactness on the Heisenberg Group Figalli, R

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:22.026054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.374585Z digest=sha256:a332e8296b7bc19eb1aecade4e7a32497b81b7a08b2098d7fd3d064dfbeb6000

Observation 953eeccc-358d-4a88-bfea-6d068334d74d · outbound

This paper cites J.,171(2022), no.

Sharp Stability of Global Compactness on the Heisenberg Group J.,171(2022), no

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:21.827169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.449713Z digest=sha256:7e07f23427169de7dc19d3cfc77c03aec091057a66826d2b2423d57197a79b75

Observation 07f18fab-3b54-4de2-a3c7-fe0132d4f9ad · outbound

This paper cites an unresolved cited work.

Sharp Stability of Global Compactness on the Heisenberg Group Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:28:21.646599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.523889Z digest=sha256:0c1b3146f96abb430cf20955596717e8620596d0ec961e9fdaecb3cbb04e79d7

Observation e2caeb3e-4376-404a-86b4-eba59c1354c9 · outbound

This paper cites an unresolved cited work.

Sharp Stability of Global Compactness on the Heisenberg Group Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:28:21.468915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.593872Z digest=sha256:9ec5a72dbbfb3d4bd7dfbba49fbca413de1d5853d796a2044c275698b01ea65b

Observation a0ef81a7-15ea-4d07-82d4-2a7a1cfb14df · outbound

This paper cites Fusco, F.

Sharp Stability of Global Compactness on the Heisenberg Group Fusco, F

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:21.141318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.676518Z digest=sha256:1c2b4b04ea52f1eba45b028185f65023fd6e3f68580c9466426c4d04ed0b7cc3

Observation ca3fb946-d19d-4c92-82a3-5a550f51cc6e · outbound

This paper cites an unresolved cited work.

Sharp Stability of Global Compactness on the Heisenberg Group Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:28:20.896451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.767731Z digest=sha256:eed46c62adda970ee5cff9820931592bd7ddbc7b82b42c62b9ee7095ac8437ff

Observation 767ffc1c-3ded-48c3-81a5-b92fec20437e · outbound

This paper cites On the stability of critical points of the Hardy-Littlewood-Sobolev inequality.

Sharp Stability of Global Compactness on the Heisenberg Group On the stability of critical points of the Hardy-Littlewood-Sobolev inequality

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-07T04:28:18.854209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T04:28:18.854209Z digest=sha256:3e0028322ba6d68140254718adb474f7b33a51fce2eb57c57601e3c2dbdb6f7d

Observation 3e945b8e-bfa6-4120-9646-d9f69a0a2f1b · outbound

This paper cites Loiudice, Improved Sobolev inequalities on the Heisenberg group,Nonlinear Anal., 62(2005), no.

Sharp Stability of Global Compactness on the Heisenberg Group Loiudice, Improved Sobolev inequalities on the Heisenberg group,Nonlinear Anal., 62(2005), no

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:20.700692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:18.921722Z digest=sha256:2ecbfc746b7a8504ff877a5515ccddaf63b34c3fa34d2f5621f444f8ce2de20d

Observation 9c25d074-dd44-451d-b829-318acf62d981 · outbound

This paper cites an unresolved cited work.

Sharp Stability of Global Compactness on the Heisenberg Group Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:28:20.548120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:19.015618Z digest=sha256:63efaa82cd44d3fb192b68f01e44b409073cf0fd80ecb8f6266e82f9d3cbc35b

Observation 41970caa-2750-4ce4-97b8-701cb1d1c097 · outbound

This paper cites Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities,Math.

Sharp Stability of Global Compactness on the Heisenberg Group Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities,Math

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:20.368562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:19.113458Z digest=sha256:d4aab716d5cc54051ec5309a12bbb0cd6d1f4beea66baa2d9388fb5a59e8332e

Observation d71e2a5e-083a-44da-b6eb-5a577919f2f1 · outbound

This paper cites Talenti, Best constant in Sobolev inequality,Ann.

Sharp Stability of Global Compactness on the Heisenberg Group Talenti, Best constant in Sobolev inequality,Ann

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:20.207283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:19.230845Z digest=sha256:53ed42b686f6e8e6913c892aa6ba8fd6958092d59682a082d0b8ac6b6ad8677f

Observation 367ffcfd-a6cd-4d97-9df1-8b922254a66e · outbound

This paper cites Tintarev, K.

Sharp Stability of Global Compactness on the Heisenberg Group Tintarev, K

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:28:20.037035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:19.300180Z digest=sha256:5ee54b5dd40b845c387372d3d17f8c0f175e2772b871cb26a27f1f0c45d08f7c

Observation 4b4477ad-f95c-415e-9f6b-696d0aedce15 · outbound

This paper cites an unresolved cited work.

Sharp Stability of Global Compactness on the Heisenberg Group Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:28:19.857518Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:28:19.413143Z digest=sha256:348accd505f3702e2f519d6d6476a073fcce2864ca57ee0f380d6aaeacb2508a

Pith citing papers

No inbound Pith citation observations are available.