Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-15T22:09:36.352687Z
Paper Citation Record · LEDGER
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition
As of 10 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2602.13759.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
44 of 44 outbound references displayed
- verified exact1
- verified fuzzy16
- unresolved26
- parse uncertain0
- malformed identifier1
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 5cbdf9aa-50f7-4eac-b4b9-31c8fcf14700 · outbound
This paper cites Why Transformers Need Adam: A Hessian Perspective.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Why Transformers Need Adam: A Hessian Perspective
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T22:10:21.398194Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 54f33004-40c7-4b15-a541-35808d2c0ba6 · outbound
This paper cites The entrywise condition follows fromΩ ij = (Ajj −A ii)Aij.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition The entrywise condition follows fromΩ ij = (Ajj −A ii)Aij
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.177112Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 971091e1-7a14-4e33-99d3-1b334b5b7dab · outbound
This paper cites Our flow uses D= diag(A(M)) , which varies with state.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Our flow uses D= diag(A(M)) , which varies with state
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.185879Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 29aaf5a1-e1ea-4936-a561-9865c6eb8018 · outbound
This paper cites computational waste.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition computational waste
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.168345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 76326c44-73fb-428a-9476-1c8771160810 · outbound
This paper cites Euclidean SGD with Riemannian projection.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Euclidean SGD with Riemannian projection
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.155544Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 86760996-c6e1-43ee-9914-dc8d0b8ebd1f · outbound
This paper cites global phase.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition global phase
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.199483Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1f5388a3-80af-4b6e-ae71-ba5d7fc3fb57 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.163815Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0775c9bc-5b92-4ba2-9f92-0fd000bec7fc · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.172298Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1b6ec4c6-e1ed-4f6c-a0f4-c52c90b57b3b · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.180867Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 938dc183-8739-424a-9ff3-5933f0ea591e · outbound
This paper cites 61 Discrete Double-Bracket Flows Table 3.E1: Trajectory differences for Cayley method (n= 20,K= 5000).
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition 61 Discrete Double-Bracket Flows Table 3.E1: Trajectory differences for Cayley method (n= 20,K= 5000)
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.194226Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation fb2492c3-b140-452a-a1e7-86cc12d6aa62 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.189265Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation ea52c6f7-fd4c-4f6e-abb5-4f69e374ce74 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.159852Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 8d28a38d-4d0a-46e8-bb70-a5068862e9f4 · outbound
This paper cites Results.Table 5 presents the mean iterations to convergence.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Results.Table 5 presents the mean iterations to convergence
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.203870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation e41cfc51-0bef-42e2-b6cd-55133363f5af · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.138286Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 36c08a82-df52-426c-a60f-84b0322c2d3b · outbound
This paper cites trace-free noiseE k at each step.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition trace-free noiseE k at each step
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.087264Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation a0d370fe-b954-4a6d-a728-a2380c67af2a · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.150803Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 4441a8be-02ba-4429-8a3b-a2c7bdf8aa1a · outbound
This paper cites Results.Table 6 shows linear regression fits forlim sup √fvsε E.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Results.Table 6 shows linear regression fits forlim sup √fvsε E
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.067831Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 498c551d-1add-4592-9629-dbbd366ef0d1 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.117443Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7d9c6963-9e66-4df7-9f2a-a1e3afac23f3 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.132775Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 300123b9-5386-4b6b-82ea-1f45386b4a12 · outbound
This paper cites Results.Withn= 20and∥C e∥2 ≈0.95, theoreticalη max ≈0.03.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Results.Withn= 20and∥C e∥2 ≈0.95, theoreticalη max ≈0.03
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.146452Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 99a819d7-b6e4-41b1-9de7-ad0b2c40be50 · outbound
This paper cites 66 Discrete Double-Bracket Flows.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition 66 Discrete Double-Bracket Flows
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.050613Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 70ec2901-144c-4b66-b9d5-1ef44c18dbdd · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.055488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 56d8ae96-fa76-412a-90d5-5445e4ec3452 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.120835Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 6348d6bd-8ade-4f8a-8b2a-b43f3f480fea · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.059693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation fa5a0bf3-f56e-4c97-bb4d-bfcc3b360bc0 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.113698Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation dd167599-a65f-428c-ac3f-dac0715fa8e5 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.142741Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation e26e254a-26f5-4f96-be3b-b58567e07c30 · outbound
This paper cites Table 8.E9: Escape probability vs noise level (20 seeds per level).
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Table 8.E9: Escape probability vs noise level (20 seeds per level)
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.138667Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1dc8200e-5d44-4a92-ac46-b42e856d012b · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.027509Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 90d6b773-6a8e-49d1-a5cf-94a1df4249cb · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.108075Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7c56b20e-cee9-40e2-9c78-cc5942f061cf · outbound
This paper cites signal vanishing.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition signal vanishing
Reference 30
- Resolution
- malformed identifier
- raw_fallback, observed 2026-05-15T22:10:22.092844Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation edeb97e9-5522-4df1-8870-a1ee63653bcd · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.128602Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 669eb502-cb3e-46c8-951e-256dc4f3616e · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.117861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation ac48307e-66b3-424e-a2e6-386de52abda7 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.040255Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 51c25352-c173-49b2-8ac9-ab9cb6518e36 · outbound
This paper cites FAIL” if convergence not reached within10 6 iterations. Table 11.Wall-clock time (seconds) across methods. “—.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition FAIL” if convergence not reached within10 6 iterations. Table 11.Wall-clock time (seconds) across methods. “—
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.126274Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f09afb14-7b62-4e19-907f-f6f301f0ca27 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.122783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation c1414e85-4b02-4c29-aa54-1853b1de3680 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.054855Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9784e929-b12a-4be7-8529-1b72e1f21fae · outbound
This paper cites Table 14.Haar initialization:δ(M 0)/gstatistics.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Table 14.Haar initialization:δ(M 0)/gstatistics
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.143115Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 8c24e3b0-2d71-42ba-ae3d-1021cd331c05 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.088484Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2b51e211-b4f2-4840-bfcf-bb9f80fafaef · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.075652Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 14d436e9-fc63-47a6-b3ed-17f1b3bb2f8c · outbound
This paper cites Table 15.Lipschitz constant: empirical vs.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Table 15.Lipschitz constant: empirical vs
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.112964Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 3b753d94-c621-4ff2-a478-cc099d7a75d3 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.147157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 16586215-aa3b-4c5b-8941-56c46d1d3afc · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.103693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation bbd5a85e-67d6-46ec-9bb7-52fbc0eb56e7 · outbound
This paper cites an unresolved cited work.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T22:10:22.101494Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 8f9cf719-40bc-4cf9-a5a9-6abf9a127f95 · outbound
This paper cites better Oja.
Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition better Oja
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T22:10:22.109733Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Pith citing papers
No inbound Pith citation observations are available.