Paper Citation Record · LEDGER

Corner Gradient Descent

As of 19 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 2 inbound Pith citation observations for arXiv:2504.12519.

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

pith.paper-citation-record.v1
2504.12519 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:39:56.698756Z

measured 23 of 23 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:12:15.464614Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-04T23:03:53.722408Z

Reference resolution

21 of 21 outbound references displayed

verified exact0
verified fuzzy12
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 62d581f1-0f4b-4702-8c98-1a1b3f26c5dc · outbound

This paper cites At t→∞ , ifVt = O(1) (respectively,Vt = o(1)), then alsoLt =O(1) (respectively,Lt =o(1)).

Corner Gradient Descent At t→∞ , ifVt = O(1) (respectively,Vt = o(1)), then alsoLt =O(1) (respectively,Lt =o(1))

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.973553Z

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 e2b92a2d-6417-4518-b578-c7d748cbe09b · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.961263Z

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 7cc47a48-0676-4a53-8368-98c931748552 · outbound

This paper cites Suppose also that UΣ < 1 andUt = O(t−ξU ) with some ξU > max(ξV, 1).

Corner Gradient Descent Suppose also that UΣ < 1 andUt = O(t−ξU ) with some ξU > max(ξV, 1)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.948648Z

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 276f5eb7-c8e7-40ec-8738-2addb15686d4 · outbound

This paper cites infinite-memory.

Corner Gradient Descent infinite-memory

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.938422Z

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 25f82c5e-bc7a-418a-8cd0-0529c773712d · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.928022Z

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 38072280-2c7d-4426-9422-207c104a1082 · outbound

This paper cites Neural Networks as Kernel Learners: The Silent Alignment Effect.

Corner Gradient Descent Neural Networks as Kernel Learners: The Silent Alignment Effect

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-16T12:39:56.623518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d83a534c-62e1-4418-9a9d-ceb09f6236a6 · outbound

This paper cites In this case condition (65) is equivalent to−1≤ q0 q1 , i.e.

Corner Gradient Descent In this case condition (65) is equivalent to−1≤ q0 q1 , i.e

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.917518Z

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 eff65e21-d656-4ccf-8d13-4d4c42049b66 · outbound

This paper cites The option q0 q1 <−1 is inconsistent with condition (65), leaving only the option q0 q1 >−β.

Corner Gradient Descent The option q0 q1 <−1 is inconsistent with condition (65), leaving only the option q0 q1 >−β

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.906388Z

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 03805fc8-297b-48a8-8b7c-3858fd594c50 · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.895776Z

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 02c10d52-39a5-46e8-9e71-7398931f0ab2 · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.885148Z

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 6cc1ec79-7736-48a6-a725-d3232163ec0c · outbound

This paper cites (94) We can find limr↘0u(r) as follows.

Corner Gradient Descent (94) We can find limr↘0u(r) as follows

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.874358Z

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 2415b9a0-29f8-46ae-9dc3-51683961be3d · outbound

This paper cites (104) Performing again the change of variablesrz =z′, we have FU(r) =v(r)r−θ−1, (105) where v(r) = cΨθ 2πi Z iR ez′ z′θ−1dz′ (cΨ(z′/r)θ + 1)2.

Corner Gradient Descent (104) Performing again the change of variablesrz =z′, we have FU(r) =v(r)r−θ−1, (105) where v(r) = cΨθ 2πi Z iR ez′ z′θ−1dz′ (cΨ(z′/r)θ + 1)2

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.861175Z

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 cac22282-321e-42d5-829f-5ea5afb345df · outbound

This paper cites , uniformly in all λ ∈ (0,λ max].

Corner Gradient Descent , uniformly in all λ ∈ (0,λ max]

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.849092Z

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 5c2b63a0-6cbb-487f-9865-9a456b4057e6 · outbound

This paper cites (145) We will show that this integral isO( 1 λ).

Corner Gradient Descent (145) We will show that this integral isO( 1 λ)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.834848Z

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 da9044e4-8028-4596-85e9-7f88b6724884 · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.819887Z

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 bde66d63-bcea-4e30-80ac-089b68af8a79 · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.808134Z

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 60bb6793-71b8-4ee9-8af7-a2e6123ea345 · outbound

This paper cites (170) Taking the limitr→ +∞ and deforming the contour to the negative semi-axis as in Lemma 1, lim r→+∞ v(r) = cΨ 2πi Z γ′ z′θ−1ez′ dz′ = cΨ Γ(1−θ).

Corner Gradient Descent (170) Taking the limitr→ +∞ and deforming the contour to the negative semi-axis as in Lemma 1, lim r→+∞ v(r) = cΨ 2πi Z γ′ z′θ−1ez′ dz′ = cΨ Γ(1−θ)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.794364Z

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 17e76158-0d5b-43fc-9521-46e786c9039b · outbound

This paper cites an unresolved cited work.

Corner Gradient Descent Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:39:56.780910Z

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 dab3b693-82d8-4a22-9a2e-6833cde016af · outbound

This paper cites and λ ∈ (0,λ max], with some r,λ - independent constantC.

Corner Gradient Descent and λ ∈ (0,λ max], with some r,λ - independent constantC

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.770056Z

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 673cba4e-e276-479e-a7aa-71d39331442e · outbound

This paper cites of (196) vanishes and the second converges thanks toθ> 1.

Corner Gradient Descent of (196) vanishes and the second converges thanks toθ> 1

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:39:56.757689Z

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 55134020-6bd9-4488-883d-1951954437b1 · outbound

This paper cites Learning Curves for SGD on Structured Features.

Corner Gradient Descent Learning Curves for SGD on Structured Features

Reference 1970

Resolution: unresolved; no resolver link, observed 2026-08-16T12:39:56.630377Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 80680c2b-e2c0-4cca-b2a9-3d41ed95218c · inbound

Dimension-adapted Momentum Outscales SGD cites this paper.

Dimension-adapted Momentum Outscales SGD Corner Gradient Descent

Reference 106

Resolution: unresolved; no resolver link, observed 2026-08-07T15:12:15.464614Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation beb6652a-3fc2-4445-bd65-99edc33bc50f · inbound

Learning from one graph: transductive learning guarantees via the geometry of small random worlds cites this paper.

Learning from one graph: transductive learning guarantees via the geometry of small random worlds Corner Gradient Descent

Reference 64

Resolution: verified exact; local_arxiv, observed 2026-08-04T23:03:53.796280Z

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.