Paper Citation Record · LEDGER

Fractional $Q$-curvature on the sphere and optimal partitions

As of 21 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 1 inbound Pith citation observation for arXiv:2504.16882.

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

pith.paper-citation-record.v1
2504.16882 v1

Coverage vector

measured 50 of 50 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:04:02.051117Z

measured 51 of 51 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:34:41.546490Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T12:34:41.905368Z

Reference resolution

50 of 50 outbound references displayed

verified exact3
verified fuzzy26
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b77c2f99-d1a8-452b-b327-7b6ff259f8e8 · outbound

This paper cites On the maximum principle for higher-order fractional Laplacians.

Fractional $Q$-curvature on the sphere and optimal partitions On the maximum principle for higher-order fractional Laplacians

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:04:02.109965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a931f70a-f2a0-468d-845b-e07a9f61306b · outbound

This paper cites Abreu, E.

Fractional $Q$-curvature on the sphere and optimal partitions Abreu, E

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.496712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 089ea584-2a56-44b4-a3a7-04cb43c5a90b · outbound

This paper cites Angeles and A.

Fractional $Q$-curvature on the sphere and optimal partitions Angeles and A

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:01.921005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff93f9be-e309-4cb9-bc83-c57408b22ccb · outbound

This paper cites Bucur, Some observations on the Green function for the ball in the fractional Laplace framework, Communications on Pure and Applied Analysis, 15 (2016), pp.

Fractional $Q$-curvature on the sphere and optimal partitions Bucur, Some observations on the Green function for the ball in the fractional Laplace framework, Communications on Pure and Applied Analysis, 15 (2016), pp

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.480621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a2850232-2711-4160-a18a-9860f9a89bb8 · outbound

This paper cites Caffarelli and L.

Fractional $Q$-curvature on the sphere and optimal partitions Caffarelli and L

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.471750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e26cc705-b093-4451-b348-99cd5e33e705 · outbound

This paper cites Caselli, E.

Fractional $Q$-curvature on the sphere and optimal partitions Caselli, E

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.463143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a1394635-249f-4dcf-9fb1-206a62c5fbab · outbound

This paper cites Local bifurcation diagrams and degenerate solutions of Yamabe-type equations.

Fractional $Q$-curvature on the sphere and optimal partitions Local bifurcation diagrams and degenerate solutions of Yamabe-type equations

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:04:02.096589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fcf74d6a-098d-4b06-8eb5-6465c538ca91 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.454324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation be4fead4-1a9e-43a6-bd9b-6eefd953a99d · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.445602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 58ec74b2-c0ed-40e4-b482-fdca657c27f8 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:01.941924Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 055da5f6-c187-4151-86f3-4c9c823aa0a5 · outbound

This paper cites Clapp, J.

Fractional $Q$-curvature on the sphere and optimal partitions Clapp, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.431974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f7298752-48df-445a-b3a1-3fd4ef9cf22d · outbound

This paper cites Clapp, J.

Fractional $Q$-curvature on the sphere and optimal partitions Clapp, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.423386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 164eaec1-3d25-402f-9640-58d002294ef4 · outbound

This paper cites Clapp and A.

Fractional $Q$-curvature on the sphere and optimal partitions Clapp and A

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.413882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f1d7c844-1d7e-47f1-9569-7010dc0d0acd · outbound

This paper cites Clapp, A.

Fractional $Q$-curvature on the sphere and optimal partitions Clapp, A

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.403979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f2deee35-c4e8-41ac-b94f-24bcd874150f · outbound

This paper cites Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schr\"odinger system.

Fractional $Q$-curvature on the sphere and optimal partitions Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schr\"odinger system

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:04:02.083441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b09e66fa-5e14-4e93-b3f3-8fcf85e0cb55 · outbound

This paper cites Clapp, A.

Fractional $Q$-curvature on the sphere and optimal partitions Clapp, A

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:01.958000Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04fdbb8c-597b-4fd5-9a60-d38b04cf096e · outbound

This paper cites Clapp and A.

Fractional $Q$-curvature on the sphere and optimal partitions Clapp and A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.390067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f5c79a7e-a60a-4822-8ec8-d18b61e459e1 · outbound

This paper cites Conti, S.

Fractional $Q$-curvature on the sphere and optimal partitions Conti, S

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.381458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c1f62893-c2e2-47b0-aefa-df3402f2a398 · outbound

This paper cites del Mar Gonz ´alez, Recent Progress on the Fractional Laplacian in Conformal Geometry , De Gruyter Open Poland, Warsaw, Poland, 2017, pp.

Fractional $Q$-curvature on the sphere and optimal partitions del Mar Gonz ´alez, Recent Progress on the Fractional Laplacian in Conformal Geometry , De Gruyter Open Poland, Warsaw, Poland, 2017, pp

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:01.965652Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4babdce-397e-4dc7-bb28-45325fbcdb63 · outbound

This paper cites Ding, On a conformally invariant elliptic equation on Rn, Commun.

Fractional $Q$-curvature on the sphere and optimal partitions Ding, On a conformally invariant elliptic equation on Rn, Commun

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.367068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 639cb624-a966-41cc-ac26-bd686fb8948e · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.357937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 150fe9ab-b808-4cef-b363-9d9af685ae8c · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.349523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0bb338da-c12d-453f-8901-2c6af1af454d · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.340804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9308e79c-6d4b-43d6-911a-99dae8524f68 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.331648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e781d71f-012e-4a76-a5f5-75b3d7bd51eb · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.322302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6afe5337-5ee1-4f1d-bf7a-d36b0d507732 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:01.986235Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db5f7736-ce78-4a48-80a2-f5a655d0b7be · outbound

This paper cites Grisvard, Elliptic problems in nonsmooth domains , SIAM, 2011.

Fractional $Q$-curvature on the sphere and optimal partitions Grisvard, Elliptic problems in nonsmooth domains , SIAM, 2011

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:01.989457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc07a9aa-982c-444d-8630-dd53075aa249 · outbound

This paper cites Hebey and M.

Fractional $Q$-curvature on the sphere and optimal partitions Hebey and M

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.301863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0866df9a-aa4e-4882-bfea-4dd32a83a317 · outbound

This paper cites Henry and J.

Fractional $Q$-curvature on the sphere and optimal partitions Henry and J

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.293636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 652e8041-1c26-4976-97ba-8a6ef7ad517b · outbound

This paper cites Hern´andez-Santamar´ıa and A.

Fractional $Q$-curvature on the sphere and optimal partitions Hern´andez-Santamar´ıa and A

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.284943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0b72f3e6-f7d9-4b09-8eee-3f649b7ee5e4 · outbound

This paper cites Hern´andez Santamar´ıa and A.

Fractional $Q$-curvature on the sphere and optimal partitions Hern´andez Santamar´ıa and A

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:02.002454Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7359bc07-14a5-4373-9947-9251982ffa06 · outbound

This paper cites Hora and A.

Fractional $Q$-curvature on the sphere and optimal partitions Hora and A

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.269602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e211a27c-6510-4870-968f-fa52cb3e5050 · outbound

This paper cites Jarohs, A.

Fractional $Q$-curvature on the sphere and optimal partitions Jarohs, A

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-16T11:04:02.007744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd29ec00-b773-4228-b06f-2018bc0b77a1 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.254438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2607b6de-b294-4b2e-8ff3-7c16c9e8ac51 · outbound

This paper cites Lang, Differential and Riemannian manifolds , vol.

Fractional $Q$-curvature on the sphere and optimal partitions Lang, Differential and Riemannian manifolds , vol

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.246760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2b9ad039-fa97-441c-9820-0e0a2d778745 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.238194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fcc47b64-fbf4-44c7-868e-502fe2e6f037 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.229471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1eca46d6-337c-47ef-84be-9830a25045c0 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.220478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cdf1e120-bce2-4560-8bdc-4466c8ca2ae3 · outbound

This paper cites Ritorto, Optimal partition problems for the fractional Laplacian , Annali di Matematica Pura ed Applicata (1923-), 197 (2018), pp.

Fractional $Q$-curvature on the sphere and optimal partitions Ritorto, Optimal partition problems for the fractional Laplacian , Annali di Matematica Pura ed Applicata (1923-), 197 (2018), pp

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.212635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1d3aba6d-6f34-4ec3-88fe-acdb29a94fb7 · outbound

This paper cites Rudin, Functional Analysis, McGraw-Hill, Inc., 1991.

Fractional $Q$-curvature on the sphere and optimal partitions Rudin, Functional Analysis, McGraw-Hill, Inc., 1991

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.204486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fda374eb-93d1-4615-98bb-5cc3a1a6dd34 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.196584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7df68fc9-e214-4511-935a-064ccf592a98 · outbound

This paper cites Struwe, Variational methods, vol.

Fractional $Q$-curvature on the sphere and optimal partitions Struwe, Variational methods, vol

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.188579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 240b6820-fc80-45d5-bd86-62781c766903 · outbound

This paper cites Szego, Orthogonal Polynomials, vol.

Fractional $Q$-curvature on the sphere and optimal partitions Szego, Orthogonal Polynomials, vol

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.180728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 11b4dea9-83f4-4b83-a068-f1c93310d1ea · outbound

This paper cites Tavares, Topics in elliptic problems: from semilinear equations to shape optimization , Communications in Math- ematics, 32 (2024).

Fractional $Q$-curvature on the sphere and optimal partitions Tavares, Topics in elliptic problems: from semilinear equations to shape optimization , Communications in Math- ematics, 32 (2024)

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.172344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 514bb5f9-8650-41a9-8f4d-57a1ae126615 · outbound

This paper cites an unresolved cited work.

Fractional $Q$-curvature on the sphere and optimal partitions Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:04:02.164207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7fce05cf-bdaa-4b93-9907-dab742c649bf · outbound

This paper cites Terracini, G.

Fractional $Q$-curvature on the sphere and optimal partitions Terracini, G

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.155582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1c1c535a-3e05-4fee-ba06-2f24c6a3a712 · outbound

This paper cites Tortone and A.

Fractional $Q$-curvature on the sphere and optimal partitions Tortone and A

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.146448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 38da7d41-4ed8-4a75-8110-3139d3728794 · outbound

This paper cites Willem , Minimax theorems, vol.

Fractional $Q$-curvature on the sphere and optimal partitions Willem , Minimax theorems, vol

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.137006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7268b5d4-b4a3-48a8-99fb-d24083b101b6 · outbound

This paper cites Witten, Anti de Sitter space and holography , Adv.

Fractional $Q$-curvature on the sphere and optimal partitions Witten, Anti de Sitter space and holography , Adv

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.127594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0433a9f9-d4d5-48f8-a19e-fc7a7db3f065 · outbound

This paper cites Zilio, Optimal regularity results related to a partition problem involving the half-Laplacian , New Trends in Shape Optimization, (2015), pp.

Fractional $Q$-curvature on the sphere and optimal partitions Zilio, Optimal regularity results related to a partition problem involving the half-Laplacian , New Trends in Shape Optimization, (2015), pp

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:04:02.119307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation f25f4e8a-eb6a-453b-be57-dd1b034bb163 · inbound

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces cites this paper.

The conformal logarithmic Laplacian on the sphere: Yamabe-type problems and Sobolev spaces Fractional $Q$-curvature on the sphere and optimal partitions

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:34:41.913019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.