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Paper Citation Record · LEDGER

Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

As of 17 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2307.04204.

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

pith.paper-citation-record.v1
2307.04204 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 3 of 3 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:24:29.602731Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T18:02:14.885399Z

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 684fedf5-f126-4bf2-bd0e-cc9d81604991 · inbound

From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes cites this paper.

From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

Reference 32

Resolution
verified exact
local_arxiv, observed 2026-08-11T18:02:14.895923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=arxiv_source observed=2026-08-11T18:02:14.746290Z digest=sha256:4a8431a5aebbc9d5a160d78ec614a1cf2091c65b26bd931a36a8d4b0de6c26ce

Observation 1da785be-c691-497f-9296-d5c018ac5a35 · inbound

A Physics-Inspired Optimizer: Velocity Regularized Adam cites this paper.

A Physics-Inspired Optimizer: Velocity Regularized Adam Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

Reference 2012

Resolution
unresolved
no resolver link, observed 2026-08-15T20:24:29.602731Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T20:24:29.602731Z digest=sha256:1f49af0bc509751d4104b3484ba1d04c7322cafe64cfde0f0fd8785322dbf2a8

Observation b11462d3-4e60-4bef-954a-4270fe775326 · inbound

On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials cites this paper.

On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory

Reference 29

Resolution
unresolved
no resolver link, observed 2026-08-02T23:10:24.068312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-02T23:10:24.068312Z digest=sha256:07d3d30952135d404319defd9b1f300e3c957beed079972a82123fd29d7bd246