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Paper Citation Record · LEDGER

Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 10 inbound Pith citation observations for arXiv:2012.04728.

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

pith.paper-citation-record.v1
2012.04728 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 10 of 10 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 10 of 10 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T06:06:57.442994Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T04:27:36.920358Z

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 65df48c7-5d0f-4e6a-a05b-84f11d2b151a · inbound

TeleSparse: Practical Privacy-Preserving Verification of Deep Neural Networks cites this paper.

TeleSparse: Practical Privacy-Preserving Verification of Deep Neural Networks Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-16T06:06:57.442994Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T06:06:57.442994Z digest=sha256:5b5ba44fd63fe42ba58b01fae5ee75a82fb822a1b0c91e0ca5f0b5f0f7ce8339

Observation 93e00a5b-96c1-4402-a5f7-04cb1c2cb686 · inbound

Toward Manifest Relationality in Transformers via Symmetry Reduction cites this paper.

Toward Manifest Relationality in Transformers via Symmetry Reduction Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-02T21:52:35.416538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T21:52:35.416538Z digest=sha256:3f7389b2fde4e2e30b7b704ed205b925b9895e83ba493779347f192d97504aef

Observation 17ce661d-991a-49f7-bbf9-e0aeb971c053 · inbound

A Theory of Saddle Escape in Deep Nonlinear Networks cites this paper.

A Theory of Saddle Escape in Deep Nonlinear Networks Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 27

Resolution
verified exact
arxiv_id, observed 2026-05-11T16:51:05.717524Z

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.

source=pdf_text observed=2026-05-09T14:54:47.763122Z digest=sha256:feb6d1866c0c6eea0ea150319e3a06c998e06a8270cad5aff4175c67c18c0e5f

Observation b12013a8-6950-4565-aaeb-ee34d7e703c7 · inbound

A Theory of Saddle Escape in Deep Nonlinear Networks cites this paper.

A Theory of Saddle Escape in Deep Nonlinear Networks Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 27

Resolution
verified exact
arxiv_id, observed 2026-05-11T02:25:54.510205Z

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.

source=pdf_text observed=2026-05-11T02:22:38.751375Z digest=sha256:0cdb42d383ae0ac82ad0e8125a924c759198874ac4509d056d5f0c1a6cf6c57b

Observation 4c8d2ccd-53fa-4f53-8129-ac2a3b3831a8 · inbound

A Theory of Saddle Escape in Deep Nonlinear Networks cites this paper.

A Theory of Saddle Escape in Deep Nonlinear Networks Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 27

Resolution
verified exact
arxiv_id, observed 2026-07-01T00:45:12.007531Z

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.

source=pdf_text observed=2026-07-01T00:37:16.364388Z digest=sha256:512d5161089faa4d867b08d0af09474966af06cc28b4e1eaf964e4c190539d01

Observation 806b4588-7239-43d2-b5b3-0b18ee09f4e8 · inbound

Learning reveals invisible structure in low-rank RNNs cites this paper.

Learning reveals invisible structure in low-rank RNNs Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 50

Resolution
metadata mismatch
arxiv_id, observed 2026-05-09T06:15:39.625604Z

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.

source=pdf_text observed=2026-05-08T18:38:44.820013Z digest=sha256:581d73e0788ab83811ab709892a3e4e5c6e2c3622259f297a4b3ca7d93f9a6e3

Observation 15937e6f-3936-4566-bfb7-14e57a82d55f · inbound

SOLAR: A Self-Optimizing Open-Ended Autonomous Agent for Lifelong Learning and Continual Adaptation cites this paper.

SOLAR: A Self-Optimizing Open-Ended Autonomous Agent for Lifelong Learning and Continual Adaptation Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 44

Resolution
verified exact
arxiv_id, observed 2026-05-21T11:24:08.626851Z

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.

source=pdf_text observed=2026-05-21T11:21:30.867480Z digest=sha256:655409edb1a2214027fb282503fa48c57ac49295912b35d6d18a51ce4288f00a

Observation d312d5a4-ceb6-4458-91dd-0aed16155d1c · inbound

Dead Directions: Geometric Singular Learning cites this paper.

Dead Directions: Geometric Singular Learning Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 23

Resolution
verified exact
arxiv_id, observed 2026-07-02T11:36:55.214326Z

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.

source=arxiv_source observed=2026-06-28T03:20:09.365073Z digest=sha256:c43d651351f49b78aef781884e1a686efeed4577b6b7d2501dccb5dd83be171b

Observation fe9ba437-3ea4-4217-9cdb-3cee0a70641f · inbound

Second-Order Path Kernel Interpolation Formulas in Machine Learning cites this paper.

Second-Order Path Kernel Interpolation Formulas in Machine Learning Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 21

Resolution
metadata mismatch
arxiv_id, observed 2026-07-02T16:47:10.358792Z

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.

source=arxiv_source observed=2026-06-27T22:20:15.074286Z digest=sha256:15d12a2fb357bf32929eb8d85348048212fff95a1623b130af30ce2238adf100

Observation 984c6536-f890-4d2c-8a13-2f5012ab0002 · inbound

Conservation Laws from Data Symmetry in Neural Networks cites this paper.

Conservation Laws from Data Symmetry in Neural Networks Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics

Reference 22

Resolution
metadata mismatch
arxiv_id, observed 2026-07-03T04:27:36.921807Z

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.

source=arxiv_source observed=2026-06-27T13:53:48.656780Z digest=sha256:f5e158ed042cdd7a67cb8424e4d2f214605f7f5d573385f1b59d0211f9c5fea1