Paper Citation Record · LEDGER

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

As of 18 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 2 inbound Pith citation observations for arXiv:2606.29679.

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

pith.paper-citation-record.v1
2606.29679 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-30T07:00:55.733065Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:38:00.216333Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T15:38:00.418219Z

Reference resolution

35 of 35 outbound references displayed

verified exact11
verified fuzzy0
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 73a4465a-1e04-48fa-be20-d8ed510974dd · outbound

This paper cites M´ ezard, G.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions M´ ezard, G

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ca2fe46-1071-493f-a413-9f8d343a8baa · outbound

This paper cites Euclidean random matrices and their applications in physics.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Euclidean random matrices and their applications in physics

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.139937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 40de372a-cb02-4376-8006-d2eba40c8516 · outbound

This paper cites Spectral properties of distance matrices.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Spectral properties of distance matrices

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.142735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9570414b-8bde-4133-8f67-c83589642105 · outbound

This paper cites Distance matrices and isometric embeddings.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Distance matrices and isometric embeddings

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.140116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7fb8294f-f6dd-4386-911e-ada27fa82844 · outbound

This paper cites Halperin.I-BBS: Inference of Latent Sub-Manifolds in Representation Spaces Using Ran- dom Distance Matrices.2026.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Halperin.I-BBS: Inference of Latent Sub-Manifolds in Representation Spaces Using Ran- dom Distance Matrices.2026

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11446ba0-b987-491f-b5c9-6d0d14493248 · outbound

This paper cites Frustrated Dynamics of Distance Matrices.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Frustrated Dynamics of Distance Matrices

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.137520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5a38684f-194e-4068-bc8d-c95b36bbb414 · outbound

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

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.137241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7a29bce3-0928-40c8-a408-53b851ccf63a · outbound

This paper cites Halperin.Grokking as Bagel Formation in Activation Space: Spectral Evidence for a Phase Transition.2026.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Halperin.Grokking as Bagel Formation in Activation Space: Spectral Evidence for a Phase Transition.2026

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 471405ea-22a6-4f71-9442-86c988529b7a · outbound

This paper cites M´ ezard, G.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions M´ ezard, G

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2fb600c-8a74-4f54-ad3d-415ddd2ec2b0 · outbound

This paper cites Kriegeskorte, M.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Kriegeskorte, M

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17eba081-1aa7-4cec-963d-5d6c40b63d7f · outbound

This paper cites Kornblith, M.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Kornblith, M

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36500704-0fb5-466c-919b-2da44e2a02d8 · outbound

This paper cites Papyan, X.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Papyan, X

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37401f5b-4dbb-4d7d-9682-78b6797f95e2 · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48d813a3-6c02-47c3-bdbd-a1311a21e81a · outbound

This paper cites Zhuet al..A geometric analysis of neural collapse with unconstrained features.In NeurIPS(2021).

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Zhuet al..A geometric analysis of neural collapse with unconstrained features.In NeurIPS(2021)

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3116f57b-52a4-4608-b4f7-00eb271d2279 · outbound

This paper cites Neural collapse with unconstrained features.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Neural collapse with unconstrained features

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:04:21.165618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 73963601-389e-41c0-bd96-3984b3128573 · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09f69bec-a9b4-4baa-b068-198a382d985c · outbound

This paper cites Rangamani, M.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Rangamani, M

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c86bab4-575d-4c20-80ab-7a30e26b8247 · outbound

This paper cites Facco, M.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Facco, M

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 077aebab-650d-45b1-92b2-345841ba31a5 · outbound

This paper cites Ansuini, A.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Ansuini, A

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b5d6369-aa1e-438a-aca7-202e1ae49124 · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b37d3adf-19eb-4ab7-927a-084e07d43a4c · outbound

This paper cites The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:04:21.162501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dc2a70c2-404b-4e8f-aeff-83c3dbf2b95f · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Progress measures for grokking via mechanistic interpretability

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.152446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f554f771-6369-41d7-8d50-005a04cbff2d · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.160722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 52dd86dc-9092-4d92-abb1-783263c6163c · outbound

This paper cites Cohen, M.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Cohen, M

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23da7781-5f70-415e-954a-429776062418 · outbound

This paper cites Esteves, C.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Esteves, C

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e0cc164-65d4-4808-9e04-f04dabdfa859 · outbound

This paper cites Halperin.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Halperin

Reference 26

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T07:04:21.159942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3e6d00cc-c380-4a82-a448-7c98d517ae39 · outbound

This paper cites Frustrated Fields: Statistical Field Theory for Frustrated Brownian Particles on 2D Manifolds.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Frustrated Fields: Statistical Field Theory for Frustrated Brownian Particles on 2D Manifolds

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-06-30T07:04:21.151674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8c18a67e-674d-45c9-b8e9-a1155a524dde · outbound

This paper cites Davis and W.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Davis and W

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76d81114-eeaf-49a2-83fe-773f40178596 · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 402c8136-afca-48fc-abfc-f274b48d6154 · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab1b0575-3eed-431d-92cc-56cdb835e17c · outbound

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

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Grokking as the Transition from Lazy to Rich Training Dynamics

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:04:21.149023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6b31c4bb-1391-4f34-9a5c-27e5a3672afc · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 487fd630-0132-4e7a-ba5f-1f84a24aa43b · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b90a21d-5ef8-4cc8-8039-7ad915b8c891 · outbound

This paper cites Alstott, E.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Alstott, E

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8faf35a8-4999-4bef-899a-b9e1396feffc · outbound

This paper cites an unresolved cited work.

Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-30T07:00:55.733065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation c62059e2-b0e5-4af8-9b8e-609965e4e95b · inbound

Observable Matrix Dynamics of Stocks cites this paper.

Observable Matrix Dynamics of Stocks Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:38:00.422603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 853f5c24-3b0e-413b-8de5-f7aa32a75198 · inbound

Are Three Matrices All You Need To Beat the Market? Observable Matrix Dynamics for Portfolio Optimization cites this paper.

Are Three Matrices All You Need To Beat the Market? Observable Matrix Dynamics for Portfolio Optimization Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T07:41:01.016663Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.