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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19326265 |
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| _version_ | 1866901079034167296 |
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| author | Brennan, Thomas |
| author_facet | Brennan, Thomas |
| contents | <p>Conjecture UMP-FRM states that a dynamical system satisfies the FRM delayed-feedback conditions D-2.1(a)-(c) if and only if there exists an observation point O in its signal flow graph that is causally independent of the current feedback cycle. The characteristic delay τ simultaneously produces both the quarter-wave resonance (β = 1/2) and the upstream observation window required by the Upstream Measurement Principle (UMP). These are structurally inseparable consequences of nonzero delay in a feedback loop. The conjecture is topological (signal flow graph), not analytical, and holds for continuous-time, discrete-time, event-driven, and variable-delay architectures.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19326265 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The UMP-FRM Structural Identity Conjecture: Upstream Measurement Principle and Fractal Rhythm Model are Structurally Identical Brennan, Thomas UMP-FRM, structural identity, upstream measurement principle, fractal rhythm model, delayed feedback, causal independence, signal flow graph, quarter-wave resonance, beta = 1/2, oscillatory bifurcation, D-2.1, DRP-3, Meta-Kaizen, Fractaltalix <p>Conjecture UMP-FRM states that a dynamical system satisfies the FRM delayed-feedback conditions D-2.1(a)-(c) if and only if there exists an observation point O in its signal flow graph that is causally independent of the current feedback cycle. The characteristic delay τ simultaneously produces both the quarter-wave resonance (β = 1/2) and the upstream observation window required by the Upstream Measurement Principle (UMP). These are structurally inseparable consequences of nonzero delay in a feedback loop. The conjecture is topological (signal flow graph), not analytical, and holds for continuous-time, discrete-time, event-driven, and variable-delay architectures.</p> |
| title | The UMP-FRM Structural Identity Conjecture: Upstream Measurement Principle and Fractal Rhythm Model are Structurally Identical |
| topic | UMP-FRM, structural identity, upstream measurement principle, fractal rhythm model, delayed feedback, causal independence, signal flow graph, quarter-wave resonance, beta = 1/2, oscillatory bifurcation, D-2.1, DRP-3, Meta-Kaizen, Fractaltalix |
| url | https://doi.org/10.5281/zenodo.19326265 |