Paper Citation Record · LEDGER

A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

As of 21 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 15 inbound Pith citation observations for arXiv:2303.11873.

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

pith.paper-citation-record.v1
2303.11873 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 15 of 15 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 15 of 15 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:18:38.579151Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-10T08:56:58.962761Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation f04ee7fc-58c7-4cd4-bdaa-8e1fbfc2c282 · inbound

Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model cites this paper.

Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T12:18:38.579151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 639f2b71-ed70-49b3-8694-57858d1aaa97 · inbound

Tracing the Path to Grokking: Embeddings, Dropout, and Network Activation cites this paper.

Tracing the Path to Grokking: Embeddings, Dropout, and Network Activation A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T17:10:12.037121Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 969da97b-1d4c-4f77-894e-143a2bbd50c6 · inbound

Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking cites this paper.

Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:14:22.051391Z

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.

Observation 2c6ec1c0-6288-435e-ab6d-eb2f84d4ad74 · inbound

Low-Dimensional and Transversely Curved Optimization Dynamics in Grokking cites this paper.

Low-Dimensional and Transversely Curved Optimization Dynamics in Grokking A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-15T21:36:40.809602Z

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.

Observation ff741f6c-eab0-4bef-b078-acf17faf60de · inbound

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

The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-15T20:40:18.303165Z

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.

Observation 97be2fbc-0723-466a-b3d0-9a1617d0112c · inbound

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

Spectral Entropy Collapse as a Phase Transition in Delayed Generalisation: An Interventional and Predictive Framework for Grokkin A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 1

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T11:11:06.425309Z

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.

Observation ea657177-0aaf-4ba1-ba85-852dac34df03 · inbound

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

Reference 1

Resolution: metadata mismatch; arxiv_id, observed 2026-05-13T06:52:25.803131Z

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.

Observation 12e3afb9-43c8-47c0-9115-8702bc06ae69 · inbound

Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization cites this paper.

Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-11T21:26:13.338165Z

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.

Observation 056a3853-8b9c-4f4f-98e5-4b7c2f4c7db4 · inbound

Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds cites this paper.

Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:56:21.716337Z

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.

Observation 5d415a73-c1d3-48e4-9008-ca13308c6cda · inbound

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

Circuit Synchronization Precedes Generalization: A Causal Precursor to Grokking A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-03T14:08:22.535683Z

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.

Observation 6ccf6603-9419-4883-ab3e-3b127e0517d1 · inbound

Select and Improve: Understanding the Mechanics of Post-Training for Reasoning cites this paper.

Select and Improve: Understanding the Mechanics of Post-Training for Reasoning A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T14:08:21.748681Z

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.

Observation 5493204c-c6a8-4603-8802-7bb08db541d2 · inbound

SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning cites this paper.

SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 74

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:59:45.056001Z

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.

Observation 105daa8b-8656-42cf-8ba8-60e76f45c963 · inbound

SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning cites this paper.

SingGuard: A Policy-Adaptive Multimodal LLM Guardrail with Dynamic Reasoning A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 74

Resolution: verified exact; arxiv_id, observed 2026-07-01T18:55:59.720326Z

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.

Observation bb0bcca0-536e-4258-b4fa-8ac898993632 · inbound

Radial Suppression Accelerates Algorithmic Generalization: A Geometric Analysis of Delayed Generalization cites this paper.

Radial Suppression Accelerates Algorithmic Generalization: A Geometric Analysis of Delayed Generalization A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-07-01T09:45:39.734147Z

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.

Observation 9d0465fb-7c89-4c7f-90a6-f71b700c58b6 · inbound

Grokking and epoch-wise double descent in quantum neural networks cites this paper.

Grokking and epoch-wise double descent in quantum neural networks A Tale of Two Circuits: Grokking as Competition of Sparse and Dense Subnetworks

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-07-10T08:56:58.968694Z

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.