Paper Citation Record · LEDGER

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity

As of 18 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2608.06719.

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

pith.paper-citation-record.v1
2608.06719 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:06:11.360009Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

29 of 29 outbound references displayed

verified exact1
verified fuzzy22
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e2516b66-eccd-469d-828d-17cd7e06cff7 · outbound

This paper cites Proceedings of the 36th Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 36th Conference on Learning Theory , series =

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:12.070181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bb4f5d93-85dd-41b5-8f23-552c8b761705 · outbound

This paper cites Proceedings of the 35th Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 35th Conference on Learning Theory , series =

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:12.055471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7b5585a4-6109-4b88-8552-6e37b0f4b4d1 · outbound

This paper cites High-Order Oracle Complexity of Smooth and Strongly Convex Optimization.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity High-Order Oracle Complexity of Smooth and Strongly Convex Optimization

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:11.231512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54002cac-124d-4124-9aad-caa75d8d9aba · outbound

This paper cites arXiv preprint arXiv:2601.22126 , year =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity arXiv preprint arXiv:2601.22126 , year =

Reference 4

Resolution: verified exact; raw_fallback, observed 2026-08-10T22:06:11.632129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3177153a-9df2-4fff-ab33-bd01733ae69c · outbound

This paper cites 2016 , doi =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity 2016 , doi =

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:12.040364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a977c5fa-8f31-47c7-94c4-06fa0aa8ee61 · outbound

This paper cites Proceedings of the 35th Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 35th Conference on Learning Theory , series =

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:12.023837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 947ef7a0-4cba-4723-bc01-308beceb7c19 · outbound

This paper cites Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:11.253883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ce9d88d-f253-449f-bd4b-b451ba0609dc · outbound

This paper cites 2023 , doi =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity 2023 , doi =

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:11.259258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82841411-7edb-4f2d-8e3f-e386c8485a3f · outbound

This paper cites 2014 , verified =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity 2014 , verified =

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.996382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 395c0f4f-0d0d-4c6b-b41d-6953cfc0d827 · outbound

This paper cites Mathematical Programming , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Mathematical Programming , volume =

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.980540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 03c21b9b-9956-4d98-beab-1e67e5368049 · outbound

This paper cites SIAM Journal on Optimization , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity SIAM Journal on Optimization , volume =

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.966848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 00dc80e4-12cc-47fa-b3c3-d5a8787e824e · outbound

This paper cites Proceedings of the 32nd Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 32nd Conference on Learning Theory , series =

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.950262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7bca4e89-2749-4cc8-acab-8a1323ef21cb · outbound

This paper cites Proceedings of the 32nd Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 32nd Conference on Learning Theory , series =

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.934486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b927021a-f2d3-40bd-8fa0-8f17ec061295 · outbound

This paper cites Proceedings of the 32nd Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 32nd Conference on Learning Theory , series =

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.918775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 46e41636-e376-4ecd-aec2-e2a9275a280e · outbound

This paper cites Advances in Neural Information Processing Systems , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Advances in Neural Information Processing Systems , volume =

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.898161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e55fd017-7f41-434a-b570-ee913cde5486 · outbound

This paper cites Proceedings of the 31st Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 31st Conference on Learning Theory , series =

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.880000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation eb149f70-7078-405a-999a-b58a04fb2f2e · outbound

This paper cites Mathematical Programming , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Mathematical Programming , volume =

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.862934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2ab21cfb-73a5-4c4d-b8c2-e485527993e2 · outbound

This paper cites Advances in Neural Information Processing Systems , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Advances in Neural Information Processing Systems , volume =

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.842752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f469b658-dbc4-4e2f-8b35-b61a3912debd · outbound

This paper cites Mathematical Programming , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Mathematical Programming , volume =

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.825164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1bd41e21-fac6-4810-b38b-896047224e32 · outbound

This paper cites Riemannian Adaptive Regularized Newton Methods with.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Riemannian Adaptive Regularized Newton Methods with

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.805819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a845ba6a-6632-4b87-a7c8-3544a4609c0c · outbound

This paper cites Proceedings of the 29th Annual Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 29th Annual Conference on Learning Theory , series =

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.783583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6b2327c5-bcde-4cf2-9393-27c58d51638f · outbound

This paper cites Proceedings of the 31st Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 31st Conference on Learning Theory , series =

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.763847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 99cc6752-ba59-4d3c-8160-24edd7fba76f · outbound

This paper cites an unresolved cited work.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:06:11.744510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5a29f6cd-96b5-4479-87a4-310174ac6561 · outbound

This paper cites Proceedings of the 33rd International Conference on Algorithmic Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 33rd International Conference on Algorithmic Learning Theory , series =

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.727589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 815eb69c-72fb-494d-8706-99620ba2eb81 · outbound

This paper cites Proceedings of the 39th International Conference on Machine Learning , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 39th International Conference on Machine Learning , series =

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.709612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation afc386bc-f82a-4128-997b-2596aa113408 · outbound

This paper cites Advances in Neural Information Processing Systems , volume =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Advances in Neural Information Processing Systems , volume =

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.687226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a2c6fed2-a202-4939-af8e-e6ef190f8eb3 · outbound

This paper cites Proceedings of the 36th Conference on Learning Theory , series =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Proceedings of the 36th Conference on Learning Theory , series =

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:11.667195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fb825f84-a69d-4943-b5f3-8ae8d2e86162 · outbound

This paper cites Horoballs and the subgradient method.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity Horoballs and the subgradient method

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:11.354956Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62134f52-bdaa-46e6-b1d1-d5d8b6223272 · outbound

This paper cites arXiv preprint arXiv:2412.06730 , year =.

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity arXiv preprint arXiv:2412.06730 , year =

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:11.360009Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.