Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:45:58.257921Z
Paper Citation Record · LEDGER
As of 7 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2506.07504.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:45:58.257921Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T20:21:45.303967Z
A source-named dated measurement, never combined with another source.
Source: cited_works
51 of 51 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e1992c7b-28ef-458e-b0bf-902a31e626c4 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 89107439-0ada-4feb-939f-66f0202a79c4 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8baf70ef-2905-4f28-8b16-dfe353f7b5f9 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Using the partition of unity, one can glue constructions in the local charts to form a global construc- tion on the manifold
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 389b5276-2a9e-4154-9f46-3f710d3db668 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions The proof of Lemma 7 is provided in Appendix E.1
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 200426a8-8d25-4273-bd88-bfa9d0abe5e7 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions 35 A.2 Smooth submanifold family and smooth conditional distributions Firstly we recall the definition of(β Y , βX )-smooth manifold family defined in Definition 4 of the main text
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d641b07e-aae7-4a47-b5c7-0797a88637bd · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 545f720f-4371-4c75-87ab-d2e7093c25a4 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b072e901-28c9-4e38-af80-34ddbb25875e · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 63aa5de2-a233-4f98-aa65-29892cd59bb4 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a83f2e52-ef1c-4d31-8fb1-f9eac1b23dc3 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Then there existsL′ so that{µ ∗ Y|x }x∈MX ∈C βY ,βX ,αY ,αX τ,τ1,L′ (dY , DY ,M X )
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0291a98f-708a-435c-8557-751165a03ae1 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 34456ac7-e6b6-4ddd-ab6d-2455b82a905b · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7f9d9652-f933-42b1-b4f0-057411e7b56c · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions 38 (d) for anyj≥1andx∈R d, {ψ∈ Ψ d j :I ψ ∩B Rd(x,2 −(j−1))̸=∅} ≤C ‡ L
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 717d9667-f1a1-4ccc-9251-ac7870b9ef0f · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b84fb188-f146-4906-b60f-42036e5f9c88 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9b8ca4a9-dd40-479f-a60a-4ee11bb89b97 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation cb7b791e-b201-47ed-b12d-6f0fb3bf419b · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 440c811e-d610-43f5-bd0e-ef67bf09f681 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7ce7f15c-0d06-4eaf-ba9e-70b1c252f8ea · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ca70f7cc-bda5-4328-87d9-89481e950f43 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6b82633e-0ebd-4fa5-a6cb-e122eed72119 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4fdf9c67-a8d7-4494-9806-367bfd8a457a · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9c42f7a7-80d8-4240-9fa3-a3426853c9be · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 40d58c41-7668-4657-8fda-036801a5a5c2 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation db119071-3ac5-4f8f-88a9-6131708d52c7 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Moreover, since for anyk∈[K]\ bK, it holds that 1 n X i∈I1 ρ[k](Xi, Yi)≤ 1 n X i∈I1 1(∥(Xi, Yi)−(x k, yk)∥ ≤ √ 2τ2) = 0
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1c7468e3-9d28-4f3c-84d9-19eab2f301a5 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions For eachω∈ {0,1}mdY 1 ×mdX 2 , define¯ω= 1−ωin the element-wise manner
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation cdfddbd8-deab-4539-88e5-531abc5e2d0b · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Consequently, we have for anyx∈ M X, 1 c4 f(·, x)∈ Hγ 1 (RD Y )(recall that we only considerγ <1)
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a309d367-039e-459f-9003-dba4da66a4f4 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Consider anyγ 1 ∈(0,1]and denoteN(G, d γ1 ∞, ε)as theε-covering number of Gwith respect to thed γ1 ∞ distance, whered γ1 ∞(G1, G2) = sup z∈RdY ,x∈RDX ∥G1(z, x)−G2(z, x)∥γ1
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f983690f-5ecc-4448-b97b-0f0a3d304b92 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4b005d91-4fd3-4e37-97b8-e29e68ec5b9d · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9716a5b1-9534-42ab-86ce-2d1be350951e · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions LetN z c2 −j be ac2 −j-covering set ofB RdY (0, τ1), contained withinB RdY (0, τ1), wherecis a small enough positive constant
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5f6266e1-2ee1-4c4b-9005-1c0e2e19adb4 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation cae4e089-57e2-444e-b250-58bc09e07a49 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions The proof of Lemma 19 is provided in Appendix D.14
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation caad69de-15ec-4dad-b78e-63148304bce8 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Hencesup x∈Rd P ψ∈Ψd j 1(x∈I ψ)≤C ′ L
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a733031d-ee5b-42f1-9fb8-bb047ffccd5c · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 94447610-2f27-4172-9190-df92beda1754 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions 116 For the last statement
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation aabc45be-6132-47c7-9620-ebb2141586fe · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3717858e-0d14-4d4d-a356-255de293c18e · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 214a88ca-0441-49e9-b89f-5f000d0b1a3d · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ee220c95-05dd-4446-a168-9662bd27d042 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1b90515d-1474-4d28-ba1d-db19c56f0023 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2ea0a67a-91fb-446f-99b7-c10a51e7cada · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3348066f-09cd-4382-94cd-d862e7917846 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0cb82a27-3dc7-4121-aab2-98990acd6a0f · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤ p dY L∥z−z 0∥ ≤ p dY L∥z−z 0∥αY −|j1|− αY αX |j2|
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 50524221-e1f6-4159-977c-95061cac46e1 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions • if∥z−z 0∥<1, then |G(ej +j1,j2) [k] (z, x)−G(ej +j1,j2) [k] (z0, x)| ≤L∥z−z0∥βY −|j1|−1− βY βX |j2| ≤L∥z−z 0∥αY −|j1|− αY αX |j2|
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9ad7a178-f59a-461e-9169-1ade79081841 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unresolved cited work
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation aacec020-7d7a-448f-9f08-e8980663ed0e · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Z rn 0 r Wn log 4Tnρ ε2 dε # = C4√n Eµ∗,⊗n
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7a77737c-a993-49b5-bee0-4e863394a0f3 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
Reference 2013
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8e5d2508-6888-4f6b-88d0-b84eaf19986e · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Conditional Generative Adversarial Nets
Reference 2018
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 54a2ed4a-6a03-460d-a877-e6ecf25deb25 · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Minimax Optimal Rates for Regression on Manifolds and Distributions
Reference 2019
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation bcba965b-2753-430c-bd71-34e0aec5429b · outbound
Minimax Optimal Rates for Regression on Manifolds and Distributions Wasserstein Auto-Encoders
Reference 2021
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b545a0df-3538-4765-9e9b-de8138b951a7 · inbound
Semi-Supervised Conditional Diffusion via Label Augmentation Minimax Optimal Rates for Regression on Manifolds and Distributions
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.