Paper Citation Record · LEDGER

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem

As of 19 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2412.12851.

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

pith.paper-citation-record.v1
2412.12851 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T13:50:36.136332Z

measured 41 of 41 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

41 of 41 outbound references displayed

verified exact3
verified fuzzy24
unresolved14
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d859f288-46b4-4458-981f-c0ae61ca1ce2 · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.934281Z

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 4979a561-4365-4272-bf3c-904a6a767e5d · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.919977Z

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 355cf559-e33c-4bb2-99fb-85948169f624 · outbound

This paper cites Andrews, Monotone quantities and unique limits for ev olving convex hypersurfaces, Internat.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Andrews, Monotone quantities and unique limits for ev olving convex hypersurfaces, Internat

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.904502Z

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 07822292-fa73-4bad-a26d-a6a5e85ee51c · outbound

This paper cites Andrews, Classiﬁcation of limiting shapes for isotro pic curve ﬂows, J.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Andrews, Classiﬁcation of limiting shapes for isotro pic curve ﬂows, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.889552Z

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 9e18a061-8963-4a35-b5c0-99f2a7fe4c51 · outbound

This paper cites Andrews, B.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Andrews, B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.874683Z

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 3ea9419d-8244-4e9b-b4fe-d55f517f58da · outbound

This paper cites Bianchi, K.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Bianchi, K

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.859316Z

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 8b2bec63-ecd6-40b4-829a-7a43273344f5 · outbound

This paper cites Bonnesen and W.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Bonnesen and W

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.843890Z

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 2955bf5f-95ab-405b-8019-0ebf5acfe825 · outbound

This paper cites B¨ or¨ oczky, E.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem B¨ or¨ oczky, E

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.829278Z

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 e9df228a-d0b1-4519-88ab-59e7751ab89e · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.814011Z

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 120ad136-3a12-48e5-9be1-3bde9521cf5b · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.799336Z

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 b5dfa2f7-8474-4fe7-afdd-5c1207c953bb · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.784499Z

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 933c4fb4-4733-457a-a5cb-0d443a90498d · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.768352Z

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 fef60a86-fd94-4fbd-9477-bc838dcb75e3 · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.751040Z

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 890d67ce-b4d7-4028-8421-48cf3de8f517 · outbound

This paper cites Fenchel and B.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Fenchel and B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.735234Z

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 4fd39f77-c78c-4553-b94b-94892f0b89f1 · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.720667Z

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 2f3e41a6-6fb7-4cc1-97ea-79c3385f10c5 · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.705708Z

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 ac82ea87-0852-487f-b44a-ce15aa4f4eb0 · outbound

This paper cites Haberl, E.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Haberl, E

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.691156Z

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 3ec9b4fa-3476-404a-8eed-c207c310df92 · outbound

This paper cites Hu, The generalized Gaussian log-Minkowski problem , Proc.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Hu, The generalized Gaussian log-Minkowski problem , Proc

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.676749Z

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 33e36848-02ab-4baa-b163-15f486c22abd · outbound

This paper cites Hu and M.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Hu and M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.661829Z

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 1ada5da4-e138-4a29-8270-01d25a0aa014 · outbound

This paper cites Huang, E.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Huang, E

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.646641Z

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 f8c88f3a-110e-438e-8dd1-96d4f54fd215 · outbound

This paper cites Huang, D.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Huang, D

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.632024Z

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 d0c0ebdd-7152-4983-bc7f-0ba37c9b4c37 · outbound

This paper cites Uniqueness of solutions to a class of non-homogeneous curvature problems.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Uniqueness of solutions to a class of non-homogeneous curvature problems

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T13:50:36.026186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91c39dff-26ef-46e3-acef-ff35080153a4 · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.616680Z

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 7659b566-fb8a-4417-9cc6-921968636724 · outbound

This paper cites Jerison, Prescribing harmonic measure on convex dom ains, Invent.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Jerison, Prescribing harmonic measure on convex dom ains, Invent

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.601706Z

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 a846d48d-81a1-424d-88ac-e42b33e0218f · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.586956Z

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 b21fad5d-8f7d-4e32-80ef-3bab5f0d429b · outbound

This paper cites Sharp Poincar\'e-type inequality for the Gaussian measure on the boundary of convex sets.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Sharp Poincar\'e-type inequality for the Gaussian measure on the boundary of convex sets

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-11T13:50:36.350719Z

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 fece8926-e2e8-4842-9c3c-6ae4f35bf57b · outbound

This paper cites Kryvonos and D.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Kryvonos and D

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.571874Z

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 bf21a165-fe64-4606-8b49-f4e6c6fdfbf9 · outbound

This paper cites an unresolved cited work.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-11T13:50:36.557415Z

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 55fa6cc6-2da6-4a5d-b2c4-8c06b6f38f04 · outbound

This paper cites Liu, The Lp-Gaussian Minkowski problem, Calc.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Liu, The Lp-Gaussian Minkowski problem, Calc

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.542382Z

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 6999dc9b-0ea4-4834-9e51-1a490a03ed6d · outbound

This paper cites Liu, On the planar Lp Gaussian Minkowski problem, arxiv: 2405.13725.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Liu, On the planar Lp Gaussian Minkowski problem, arxiv: 2405.13725

Reference 30

Resolution: verified exact; raw_fallback, observed 2026-08-11T13:50:36.327053Z

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 f1f1b69c-e0e4-4c8f-837c-af4cfad97eed · outbound

This paper cites Lutwak, The Brunn-Minkowski-Fir ey theory.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Lutwak, The Brunn-Minkowski-Fir ey theory

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.527691Z

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 5cd1b072-17b3-42a2-adaf-148cfcfd8470 · outbound

This paper cites Lutwak, D.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Lutwak, D

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.512584Z

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 56f58a59-0b15-4781-beb7-6a1029f8dfb5 · outbound

This paper cites Centro-Affine Differential Geometry and the Log-Minkowski Problem.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Centro-Affine Differential Geometry and the Log-Minkowski Problem

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-11T13:50:36.200248Z

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 446e5eee-d7a6-43f1-afb1-c0e913826f71 · outbound

This paper cites Minkowski, Allgemeine Lehrs¨ atze ¨ uber die convexen Polyeder, Nachr.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Minkowski, Allgemeine Lehrs¨ atze ¨ uber die convexen Polyeder, Nachr

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.496468Z

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 c416bc09-cbe3-4776-905f-8a52206501b3 · outbound

This paper cites Minkowski, Volumen und Oberﬂ¨ ache, Math.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Minkowski, Volumen und Oberﬂ¨ ache, Math

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.480541Z

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 e61db73c-f997-4141-bd4f-501f30e30ede · outbound

This paper cites Schneider, Convex bodies: the Brunn-Minkowski theory , second expanded edition, Encyclopedia of Mathematics and its Applications, 151, Cambridge Universi ty Press, Cambridge, 2014.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Schneider, Convex bodies: the Brunn-Minkowski theory , second expanded edition, Encyclopedia of Mathematics and its Applications, 151, Cambridge Universi ty Press, Cambridge, 2014

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.464453Z

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 40464494-d437-4969-80c1-e047028129c6 · outbound

This paper cites Shenfeld and R.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Shenfeld and R

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.448354Z

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 c06930e9-6e4d-44e6-83ea-7125482d83d9 · outbound

This paper cites Flow by Gauss curvature to the $L_p$-Gaussian Minkowski problem.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Flow by Gauss curvature to the $L_p$-Gaussian Minkowski problem

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-11T13:50:36.121329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cef7eaab-dcac-4c62-a89a-4c0406a3c454 · outbound

This paper cites Zhu, The logarithmic Minkowski problem for polytope s, Adv.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Zhu, The logarithmic Minkowski problem for polytope s, Adv

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.431139Z

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 32f3ddb1-2d46-4e4d-9f32-fd1885687a42 · outbound

This paper cites Zhu, The Lp Minkowski problem for polytopes for 0 < p < 1, J.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Zhu, The Lp Minkowski problem for polytopes for 0 < p < 1, J

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.410151Z

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 2587b972-d1b6-437f-a9ba-95476f282fc8 · outbound

This paper cites Zhu, The centro-aﬃne Minkowski problem for polytope s, J.

Uniqueness of solutions to the isotropic $L_{p}$ Gaussian Minkowski problem Zhu, The centro-aﬃne Minkowski problem for polytope s, J

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T13:50:36.390536Z

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

No inbound Pith citation observations are available.