Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds | Paper Citation Record

Observation 24cb045d-4e38-4ccc-955d-c9c1e524a703 · outbound

This paper cites Riemannian Lp center of mass: existence, uniqueness, and convexity.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Riemannian Lp center of mass: existence, uniqueness, and convexity

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation adcb2845-212a-4101-bc9c-3f7b35e6b32b · outbound

This paper cites Ambrose and I.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Ambrose and I

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f9093b0-eaa0-4e0a-8e37-ed3bbf82bbfd · outbound

This paper cites Birkh¨auser, 2008.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Birkh¨auser, 2008

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46dc3ec3-60e3-41f1-abce-dcf70c6856e3 · outbound

This paper cites Machine learning line bundle connections.Physics Letters B, 827:136972, 2022.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Machine learning line bundle connections.Physics Letters B, 827:136972, 2022

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 847602e6-89e7-4966-a94d-112f77bc4316 · outbound

This paper cites Birkh ¨auser, 2006.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Birkh ¨auser, 2006

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5df51bf-d6eb-4f4d-919c-c86d5e2d564e · outbound

This paper cites A Geometric Unification of Generative AI with Manifold-Probabilistic Projection Models, 2025.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds A Geometric Unification of Generative AI with Manifold-Probabilistic Projection Models, 2025

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a38dea15-0b1e-441d-aae2-97d777d0b66c · outbound

This paper cites Springer, 2003.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Springer, 2003

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32b7fb1a-3f42-4bca-8998-7e2d7e585c31 · outbound

This paper cites Bhattacharya and A.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Bhattacharya and A

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36dddea0-65e6-4481-999d-29d15c862471 · outbound

This paper cites Large sample theory of intrinsic and extrinsic sample means on manifolds—I.The Annals of Statistics, 31(1):1–29, 2003.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Large sample theory of intrinsic and extrinsic sample means on manifolds—I.The Annals of Statistics, 31(1):1–29, 2003

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53b39a5a-5a22-48c5-bc15-2a98b3a14099 · outbound

This paper cites Large sample theory of intrinsic and ex- trinsic sample means on manifolds—II.The Annals of Statistics, 33(3):1225–1259,.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Large sample theory of intrinsic and ex- trinsic sample means on manifolds—II.The Annals of Statistics, 33(3):1225–1259,

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3019281-1766-4cce-bc84-f3950b51291a · outbound

This paper cites URL https://doi.org/10.1214/ 009053605000000093.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds URL https://doi.org/10.1214/ 009053605000000093

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d7b9937-cc33-41ed-8cf5-44ac5cc42f70 · outbound

This paper cites Cambridge University Press, 2018.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Cambridge University Press, 2018

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24426377-d7eb-4081-be13-41df47d5f43f · outbound

This paper cites Sliced-Wasserstein Distances and Flows on Cartan–Hadamard Manifolds.Journal of Machine Learning Research, 26:1–76, 2025.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Sliced-Wasserstein Distances and Flows on Cartan–Hadamard Manifolds.Journal of Machine Learning Research, 26:1–76, 2025

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c657537a-a64c-48b7-baac-cfa47041c90e · outbound

This paper cites Oxford University Press, Oxford, 2013.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Oxford University Press, Oxford, 2013

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3cd3874-f822-4acc-b894-4ac86c5f7649 · outbound

This paper cites Bridson and Andr´e H¨afliger.Metric Spaces of Non-Positive Curvature, volume 319 ofGrundlehren der Mathematischen Wissenschaften.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Bridson and Andr´e H¨afliger.Metric Spaces of Non-Positive Curvature, volume 319 ofGrundlehren der Mathematischen Wissenschaften

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a26c0dab-9c6b-4af4-b1b8-99847a62f611 · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82b828e3-b5c2-409a-ba45-6e01f1f9823e · outbound

This paper cites Caffarelli.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Caffarelli

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b89104ae-523d-4a5f-8112-f6c94921f299 · outbound

This paper cites Cohen, Mario Geiger, Jonas Koehler, and Max Welling.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Cohen, Mario Geiger, Jonas Koehler, and Max Welling

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba1e593f-bf0c-4e67-96bd-b927cf70e15e · outbound

This paper cites do Carmo.Riemannian Geometry.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds do Carmo.Riemannian Geometry

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation beb00468-3f35-4164-a0dc-37ae7e47f431 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b50535f5-3270-4f72-bb9c-f54ad5db5f39 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3bc78ca-e100-4915-872c-5daebfb18ef9 · outbound

This paper cites Thomas Fletcher and Sarang Joshi.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Thomas Fletcher and Sarang Joshi

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0e93a09-eef9-43d5-9f28-161585e02ef1 · outbound

This paper cites Universitext.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Universitext

Reference 23

Resolution: malformed identifier; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 465c24fe-8070-47e0-acca-099dd3086f3e · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3dafbb3c-d7af-412e-80e0-507126f9f3cd · outbound

This paper cites A Lower Bound for Estimating Fr\'echet Means.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds A Lower Bound for Estimating Fr\'echet Means

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0984b3b3-a677-41f1-a870-4a2abdfd3597 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c9eebde-54b8-4391-8850-a2d0f9f2fb26 · outbound

This paper cites Springer Series in Statistics.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Springer Series in Statistics

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e483d29d-80d1-4876-b016-6ad4badf0a77 · outbound

This paper cites American Mathematical Society, 2001.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds American Mathematical Society, 2001

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f586874a-0131-4f30-943c-469184ec41ff · outbound

This paper cites A Series of Modern Surveys in Mathematics.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds A Series of Modern Surveys in Mathematics

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1acf07b1-ec9d-4273-9ef2-3c4c02c0bda5 · outbound

This paper cites Lee.Riemannian Manifolds: An Introduction to Curvature, volume 176 of Graduate Texts in Mathematics.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Lee.Riemannian Manifolds: An Introduction to Curvature, volume 176 of Graduate Texts in Mathematics

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b183f447-2ebc-46e5-a61f-db62471faba9 · outbound

This paper cites Mean estimation and regression under heavy-tailed distributions: A survey.Foundations of Computational Mathematics, 19(5):1145–1190, 2019.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Mean estimation and regression under heavy-tailed distributions: A survey.Foundations of Computational Mathematics, 19(5):1145–1190, 2019

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f777e05-6a64-4fce-b52e-ad7b62ae7cfe · outbound

This paper cites A Riemannian framework for tensor computing.International Journal of Computer Vision, 66(1):41–66, 2006.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds A Riemannian framework for tensor computing.International Journal of Computer Vision, 66(1):41–66, 2006

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd71b5ad-9ba1-437d-8981-94e56b288b9a · outbound

This paper cites Optimum bounds for the distributions of martingales in Banach spaces.The Annals of Probability, 22(4):1679–1706, 1994.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Optimum bounds for the distributions of martingales in Banach spaces.The Annals of Probability, 22(4):1679–1706, 1994

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88f2d18f-f7cf-4563-a513-54488f0c9173 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d80ff41b-7843-41b6-b873-3a5bacf0ebf0 · outbound

This paper cites Pullback Bundles and the Geometry of Learning.Entropy, 25(10): 1450, 2023.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Pullback Bundles and the Geometry of Learning.Entropy, 25(10): 1450, 2023

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c54484dc-b9eb-4891-8434-a98ac75130b8 · outbound

This paper cites Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems, 2026.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Wasserstein Parallel Transport for Predicting the Dynamics of Statistical Systems, 2026

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08d5c173-d95f-4e37-aa09-cd5eb08c9c7f · outbound

This paper cites Probability measures on metric spaces of nonpositive curvature.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Probability measures on metric spaces of nonpositive curvature

Reference 37

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9387158f-844c-4500-85eb-4ada7d6c3ad1 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11ce7ba0-ea1d-445f-9505-24f6a392b71a · outbound

This paper cites Tsybakov.Introduction to Nonparametric Estimation.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Tsybakov.Introduction to Nonparametric Estimation

Reference 39

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fe981c0-341b-40a8-a5cf-d0062c69e2e2 · outbound

This paper cites A Wasserstein-Type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis.SIAM Journal on Imaging Sciences, 17(3):1433–1466, 2024.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds A Wasserstein-Type Distance for Gaussian Mixtures on Vector Bundles with Applications to Shape Analysis.SIAM Journal on Imaging Sciences, 17(3):1433–1466, 2024

Reference 40

Resolution: verified exact; doi, observed 2026-07-14T10:40:25.573205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2b1321d5-280e-481d-a949-f216afccfea9 · outbound

This paper cites Exponential concentration for geometric-median-of-means in non-positive curvature spaces.Bernoulli, 29(4):2927–2960, 2023.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Exponential concentration for geometric-median-of-means in non-positive curvature spaces.Bernoulli, 29(4):2927–2960, 2023

Reference 41

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 630db2bf-6d35-4454-8f75-1a42b988df54 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05e0e6ae-e3a7-44a1-987b-339c37409397 · outbound

This paper cites Assumption A2(Uniform boundedness; cf.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Assumption A2(Uniform boundedness; cf

Reference 43

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70facd8c-378f-4f60-915a-ed68d90907be · outbound

This paper cites , Yn are independent copies of Y and we set ξi :=Y i −E[Y i], then ∥ξi∥Ex0 ≤2B almost surely.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds , Yn are independent copies of Y and we set ξi :=Y i −E[Y i], then ∥ξi∥Ex0 ≤2B almost surely

Reference 44

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ad6b311-47da-4812-9fe4-25fcca687afa · outbound

This paper cites This yields a valid concentration bound, but with an additional multiplicative factor that depends on the net cardinality (hence, dimension-dependent constants).

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds This yields a valid concentration bound, but with an additional multiplicative factor that depends on the net cardinality (hence, dimension-dependent constants)

Reference 45

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5be138f5-8a4c-4bf2-821d-8d0c6ed568aa · outbound

This paper cites Theorem 6 achieves a dimension-free prefactor by invoking the Hilbert-space inequality of Pinelis [31].

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Theorem 6 achieves a dimension-free prefactor by invoking the Hilbert-space inequality of Pinelis [31]

Reference 46

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30cb177a-d4ba-406c-83cf-a72826297fed · outbound

This paper cites Fixx, x 0 ∈U.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Fixx, x 0 ∈U

Reference 47

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4b74c76-7c69-4dce-b95f-584e8cf33039 · outbound

This paper cites This path leads to functional-analytic subtleties (the measurability of sections and operator- valued kernels).

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds This path leads to functional-analytic subtleties (the measurability of sections and operator- valued kernels)

Reference 48

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64c49378-7eaf-4934-a0b3-bd7285e1cb88 · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 49

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68d91d10-57a3-4964-8867-a8d5c0cda138 · outbound

This paper cites For dimension-free optimal constants, one should use the full strength of Pinelis’ inequalities for martingales in Banach spaces as in [31].

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds For dimension-free optimal constants, one should use the full strength of Pinelis’ inequalities for martingales in Banach spaces as in [31]

Reference 50

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0494749e-6fab-4136-b532-66887f904edf · outbound

This paper cites Stochastic regime.Construct s0, s1 ∈ S B differing only in mean by δsto :=B/ √n, e.g., take s1(x) =s 0(x) + (δsto/B)P x0→xw for a fixed unit vector w∈E x0 chosen orthogonal to v.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Stochastic regime.Construct s0, s1 ∈ S B differing only in mean by δsto :=B/ √n, e.g., take s1(x) =s 0(x) + (δsto/B)P x0→xw for a fixed unit vector w∈E x0 chosen orthogonal to v

Reference 51

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acd3a632-e99f-4247-8dc3-d205b728ad4c · outbound

This paper cites Combining.Since the two pairs (s0, s1) are drawn from SB independently of each other, both lower bounds hold simultaneously for the worst-case risk over SB.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Combining.Since the two pairs (s0, s1) are drawn from SB independently of each other, both lower bounds hold simultaneously for the worst-case risk over SB

Reference 52

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c2e5917-8639-47b7-b75d-32760aad130b · outbound

This paper cites an unresolved cited work.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds Unresolved cited work

Reference 53

Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 100fb788-b952-4fa6-b6b3-a5ac6607a39c · outbound

This paper cites holonomy ambiguity.

Sharp Concentration Bounds for Bundle-Valued Statistics on Manifolds holonomy ambiguity

Reference 54

Resolution: malformed identifier; no resolver link, observed 2026-07-14T10:37:11.137176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Coverage vector

Reference resolution

Outbound references

Pith citing papers