Paper Citation Record · LEDGER

Distributional Spectral Diagnostics for Localizing Grokking Transitions

As of 21 July 2026, this Paper Citation Record lists 17 of 17 outbound references and 2 inbound Pith citation observations for arXiv:2605.08237.

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

pith.paper-citation-record.v1
2605.08237 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-12T01:32:25.729874Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-07-21T06:31:05.380196+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-11T00:46:52.525784Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-11T00:47:42.613064Z

Reference resolution

17 of 17 outbound references displayed

verified exact5
verified fuzzy11
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 82fb55cc-0c0f-448c-b5c7-fa3d018ee4c9 · outbound

This paper cites Data driven modal decompositions: analysis and enhancements.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Data driven modal decompositions: analysis and enhancements

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-06-04T18:11:13.928498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation c52c9ca3-9f2f-4f5c-8d36-803a8a9fcbca · outbound

This paper cites doi: 10.3934/jcd.2014.1.391.

Distributional Spectral Diagnostics for Localizing Grokking Transitions doi: 10.3934/jcd.2014.1.391

Reference 2

Resolution: verified exact; doi, observed 2026-05-12T01:36:14.810069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 88f30354-bce6-4940-8f89-9a82bfac7d55 · outbound

This paper cites active-set complexity.

Distributional Spectral Diagnostics for Localizing Grokking Transitions active-set complexity

Reference 3

Resolution: verified exact; doi, observed 2026-05-12T01:36:14.815372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 4dcbcf81-6a2f-4e2a-ad80-c7d60785d4c1 · outbound

This paper cites Grokking at the Edge of Numerical Stability.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Grokking at the Edge of Numerical Stability

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:56:26.508645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 13063ab6-e14c-4d74-9715-7f35f0e3edba · outbound

This paper cites Mechanism for feature learning in neural networks and backpropagation-free machine learning models.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Mechanism for feature learning in neural networks and backpropagation-free machine learning models

Reference 5

Resolution: metadata mismatch; doi, observed 2026-05-12T01:36:14.819331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 22c9cfda-af3a-4ebd-a1f8-89924dbeac89 · outbound

This paper cites Mean Field Analysis of Neural Networks: A Law of Large Numbers.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Mean Field Analysis of Neural Networks: A Law of Large Numbers

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:56:26.523122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation a449f71a-3e31-43ad-9dcd-ed81f7dbcbe5 · outbound

This paper cites naturally shuffled.

Distributional Spectral Diagnostics for Localizing Grokking Transitions naturally shuffled

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.828213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation e5b30929-1cf0-442d-a0f3-340626c78bf6 · outbound

This paper cites The task maps pairs (a, b)∈ {0.

Distributional Spectral Diagnostics for Localizing Grokking Transitions The task maps pairs (a, b)∈ {0

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.809389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation b6108a4c-9283-4f2b-88a3-ade1113d87d0 · outbound

This paper cites an unresolved cited work.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Unresolved cited work

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.805331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation a71a327a-a177-4800-9c1d-b2dc19e06748 · outbound

This paper cites an unresolved cited work.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Unresolved cited work

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.782333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 2fbd00da-ed37-463e-ae68-5fbe114bd323 · outbound

This paper cites an unresolved cited work.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Unresolved cited work

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.796016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation f19caa83-5697-4347-8262-5e723c947fbb · outbound

This paper cites Lead time is threshold-dependent and is always reported jointly with FPR.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Lead time is threshold-dependent and is always reported jointly with FPR

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.801084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 9568a6c7-ea30-43fc-bb9d-2027addf8cd7 · outbound

This paper cites The result quantifies sensitivity, not causal mechanism; one boundary-case low-RR early-training failure is reported alongside the main pool.

Distributional Spectral Diagnostics for Localizing Grokking Transitions The result quantifies sensitivity, not causal mechanism; one boundary-case low-RR early-training failure is reported alongside the main pool

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.792001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 0ef1ce75-6701-49ce-9b63-729f90fc1ab7 · outbound

This paper cites Norm-derived signals nevertheless remain strong run-level regime indicators on the same pool, and we do not claim RR universally outperforms norm baselines.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Norm-derived signals nevertheless remain strong run-level regime indicators on the same pool, and we do not claim RR universally outperforms norm baselines

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.787289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 76f83762-ae1d-4e7d-bcd1-897000720f10 · outbound

This paper cites an unresolved cited work.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Unresolved cited work

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.813623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation e443c8f0-4f41-4883-bf3d-1a42b7805e30 · outbound

This paper cites an unresolved cited work.

Distributional Spectral Diagnostics for Localizing Grokking Transitions Unresolved cited work

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.818275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation fb7a5fb8-2a91-481c-9e19-4fb21acc5270 · outbound

This paper cites FCN results (Appendix T) are a secondary low-residual regime descriptor use, not a grokking diagnostic claim.

Distributional Spectral Diagnostics for Localizing Grokking Transitions FCN results (Appendix T) are a secondary low-residual regime descriptor use, not a grokking diagnostic claim

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-14T06:44:03.823234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Pith citing papers

Observation d9bc0e3f-99db-4859-a1e5-9b2f3d3061ae · inbound

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics cites this paper.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Distributional Spectral Diagnostics for Localizing Grokking Transitions

Reference 38

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.931073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.

Observation 1ddceb85-b212-41ad-908f-27eeafdb5206 · inbound

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics cites this paper.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Distributional Spectral Diagnostics for Localizing Grokking Transitions

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-07-11T00:47:42.634524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-21T06:31:05.380196+00:00.