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Paper Citation Record · LEDGER

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics

As of 21 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2607.06639.

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

pith.paper-citation-record.v1
2607.06639 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

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

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

25 of 25 outbound references displayed

  • verified exact23
  • verified fuzzy1
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f34daa9a-3cd0-4894-84fc-e41e2956bae3 · outbound

This paper cites Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 1

Resolution
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local_arxiv, observed 2026-07-11T00:47:42.770337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation bc9ceb39-c026-4b8f-92cf-3069e44e3bf9 · outbound

This paper cites Omnigrok: Grokking Beyond Algorithmic Data.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Omnigrok: Grokking Beyond Algorithmic Data

Reference 2

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local_arxiv, observed 2026-07-11T00:47:42.713247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:5da5a759b3ed006c86b3d164774e35644bf5b4f87e1e459a7100948f75445cbe

Observation f85b0b3c-16f2-42a0-bacd-34e239949148 · outbound

This paper cites Explaining grokking through circuit efficiency.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Explaining grokking through circuit efficiency

Reference 3

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local_arxiv, observed 2026-07-11T00:47:42.192993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:5e25b41504cb8a2837561b1e98a9b2284c9dd203b8bf7299e3bd15fd6d8a3fd8

Observation 1a17297f-11fd-4945-a901-392dee7095cc · outbound

This paper cites Grokking as the Transition from Lazy to Rich Training Dynamics.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Grokking as the Transition from Lazy to Rich Training Dynamics

Reference 4

Resolution
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local_arxiv, observed 2026-07-11T00:47:42.223238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:ab4f215159cfa5fdd9bed1eacd0378329d18c1b56c2663c2e2f987f89a37212c

Observation dcdb55d2-9d6d-4fcd-8632-d75cfd8f6f3e · outbound

This paper cites Nanda, L.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Nanda, L

Reference 5

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verified fuzzy
raw_fallback, observed 2026-07-11T00:47:43.989871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:17c5e8a7e3ce27219c57e7866a9f5b7f03fce3d3bf4f4cc8fd0ecf8bc5ed2bdf

Observation ec834ab3-76ea-4e03-a1d4-056ad0216a62 · outbound

This paper cites The Complexity Dynamics of Grokking.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics The Complexity Dynamics of Grokking

Reference 6

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local_arxiv, observed 2026-07-11T00:47:42.289616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:83396a2fbbe57a5eea668eeecbcf5794e5e6e01fe7099c127fe2c17b2222bf7d

Observation bbf05bf1-6d8f-4568-bbcb-f87cbccd8dc3 · outbound

This paper cites Topological Signatures of Grokking.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Topological Signatures of Grokking

Reference 7

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local_arxiv, observed 2026-07-11T00:47:42.258162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:38cc0423d8904c2780de6a49458634b315e0300423904773b737f9f94406d968

Observation d6e5d374-dba0-4869-aef3-a5c1dd39f622 · outbound

This paper cites Approaching Deep Learning through the Spectral Dynamics of Weights.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Approaching Deep Learning through the Spectral Dynamics of Weights

Reference 8

Resolution
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local_arxiv, observed 2026-07-11T00:47:42.408786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:2a3dabdb38659318fcb25e347eb6125de6b50d73d0610470251238f047edd238

Observation 19c113ba-196b-4a86-8859-7cab247f68bd · outbound

This paper cites Mechanistic Insights into Grokking from the Embedding Layer.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Mechanistic Insights into Grokking from the Embedding Layer

Reference 9

Resolution
verified exact
local_arxiv, observed 2026-07-11T00:47:42.552783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:4407b938d0d341387f54dcdb7a9655ffb5c007c352c77eab81214aba41fca5a6

Observation 60762179-2465-4da9-9a02-9c745ef9b7be · outbound

This paper cites Measuring Sharpness in Grokking.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Measuring Sharpness in Grokking

Reference 10

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local_arxiv, observed 2026-07-11T00:47:42.126309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:3b94a5ae455ccfa90dd4b243268d96dd2fcff6a66f11cfd6d2fa1fa6a7aa8bbd

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

This paper cites Distributional Spectral Diagnostics for Localizing Grokking Transitions.

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

Reference 11

Resolution
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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 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:8b37f0d8c5f18707f2059e94ec42bef2b69920cc89350cbbd40ed76f2859a532

Observation afe5a82c-ec6f-4503-838c-c31ce6aa29b8 · outbound

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

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics

Reference 12

Resolution
verified exact
local_arxiv, observed 2026-07-11T00:47:42.525067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:d1559d8229c7fb7ac42c9c08d523b8c749f35ad9e301d4e319837081a353d4a5

Observation 93c528c9-4c51-4013-89a6-5a6ddbc98ab2 · outbound

This paper cites Early-Warning Signals of Grokking via Loss-Landscape Geometry.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Early-Warning Signals of Grokking via Loss-Landscape Geometry

Reference 13

Resolution
verified exact
local_arxiv, observed 2026-07-11T00:47:42.607841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:257711f29919a87e7de419aec586a798f323723b8966eef53474e46f2a957f67

Observation 94dda9d3-13a9-4003-b7f0-ec8814ed7b7a · outbound

This paper cites The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure

Reference 14

Resolution
verified exact
local_arxiv, observed 2026-07-11T00:47:42.159175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:9639ba5e663d34d6c3b0ee7d2ac347bfa470dc61e4dcc3aae006227c56a8d77d

Observation 62f84e2c-47f9-46db-8407-e0b8028a3b71 · outbound

This paper cites Grokking as Dimensional Phase Transition in Neural Networks.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Grokking as Dimensional Phase Transition in Neural Networks

Reference 15

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verified exact
local_arxiv, observed 2026-07-11T00:47:42.350226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:1ba45f6a63376c394684af2563750b5dc23bc529b84fcf2121909abe54b73404

Observation 6e9d7c4c-1ae6-409f-b65c-9e4e20e04a9d · outbound

This paper cites an unresolved cited work.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Unresolved cited work

Reference 16

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arxiv_id, observed 2026-07-11T00:47:42.740739Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:a22a5dc50a524a70b3b3303ed7f8a53c8a88b25557271018c092a58ab446947d

Observation 29a8c750-7205-477e-b453-141d24ed6ab6 · outbound

This paper cites an unresolved cited work.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Unresolved cited work

Reference 17

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raw_fallback, observed 2026-07-11T00:47:43.964062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:60e7271fe915ea8e26a1d08d5a3b789570c50dda454539b4833cfc012b2ab355

Observation 80e70fae-fb70-465f-acbe-778d8f361ee0 · outbound

This paper cites Relating Regularization and Generalization through the Intrinsic Dimension of Activations.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Relating Regularization and Generalization through the Intrinsic Dimension of Activations

Reference 18

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local_arxiv, observed 2026-07-11T00:47:42.468335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:b6661aec524a78ffad66388ea34ef4a01062775bac743ab187ec4367f43409d4

Observation f4bec242-c3a1-4ace-9e1b-5b9d2b72e771 · outbound

This paper cites Circuit Synchronization Precedes Generalization: A Causal Precursor to Grokking.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Circuit Synchronization Precedes Generalization: A Causal Precursor to Grokking

Reference 19

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local_arxiv, observed 2026-07-11T00:47:42.660521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:ba365a9bea04f377f5bc1a36c6b95af3862fb98d295a07095427975ba48a7bd0

Observation 2da7f413-79cf-4136-9c54-afde68a51ca8 · outbound

This paper cites ILDR: Geometric Early Detection of Grokking.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics ILDR: Geometric Early Detection of Grokking

Reference 20

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local_arxiv, observed 2026-07-11T00:47:42.437253Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:3090fe35fe3ec8c534edeb38d3e20a4733acf3ebdad16ac228a18cf6a98afdc0

Observation f566a8fb-abd5-43a7-88e7-2bae26d0ffca · outbound

This paper cites Charles H.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Charles H

Reference 21

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arxiv_id, observed 2026-07-11T00:47:42.497204Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:c9d66f332cf139fedd68a4efd23b94bef4931eccc98e5e8d0068d9370954504d

Observation 3d668a63-eec0-4976-9eb2-8dc52ca42f4f · outbound

This paper cites Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View

Reference 22

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local_arxiv, observed 2026-07-11T00:47:42.684533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:d13669322f8c8205bae4ec12ecb34706976f22d44bcab5965096469007047c3a

Observation 5d7b9c65-70cd-4a83-9692-8900d9932832 · outbound

This paper cites Noise-Driven Escape from Metastable Phases explains Grokking in Deep Neural Networks.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Noise-Driven Escape from Metastable Phases explains Grokking in Deep Neural Networks

Reference 23

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local_arxiv, observed 2026-07-11T00:47:42.320460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:615ca5f99a72caef25160e91e1e53ddc2f623375869016388bc94cc2e26791b2

Observation c23e78be-53ce-4957-85c0-3a8afb60c695 · outbound

This paper cites The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization

Reference 24

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local_arxiv, observed 2026-07-11T00:47:42.379528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:6984c68007e209784da0b347ab1846953c10c82090de02cb9804d42d7f56e8fb

Observation 5edab286-e31f-4f49-82c1-21370e529295 · outbound

This paper cites Spectral Entropy Collapse as a Phase Transition in Delayed Generalisation: An Interventional and Predictive Framework for Grokkin.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Spectral Entropy Collapse as a Phase Transition in Delayed Generalisation: An Interventional and Predictive Framework for Grokkin

Reference 25

Resolution
verified exact
local_arxiv, observed 2026-07-11T00:47:42.580698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-07-11T00:46:52.525784Z digest=sha256:a1c5b7f7baf409aec9e54e4b4d0f0119972495a0cd03e443444f91f56a9b90dd

Pith citing papers

No inbound Pith citation observations are available.