The Limits of Order: A κ-Theory Extension of Feedback and Memory
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2026
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| _version_ | 1866901285416992768 |
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| author | Mcdonald, Michael |
| author_facet | Mcdonald, Michael |
| contents | <p>This work extends κ-theory into feedback-driven systems by introducing memory retention (α) as a control parameter governing how past states influence future outcomes. While standard models treat systems as memoryless or state-dependent, this framework models them as history-influenced through feedback loops.</p> <p>A feedback loop is defined as the reintegration of outputs as inputs, creating memory. κ acts as a coupling between structural intensity and the influence of accumulated history, while a constraint scale limits runaway behavior. Together, these define an effective control parameter that determines system dynamics.</p> <p>Simulations reveal a phase transition across memory regimes. At low α, systems exhibit random, high-entropy behavior with no persistent structure. At intermediate α, feedback produces stable statistical bias while maintaining variability. A peak regime of “ordered freedom” emerges near α ≈ 0.80–0.85, where systems preserve identity without collapsing. At high α, excessive memory leads to instability and attractor-dominated collapse.</p> <p>These results show that statistical behavior can become path-dependent under sufficient feedback and structure, without violating underlying probabilistic laws. Order emerges only within a constrained balance between memory and dissipation.</p> <p>This framework generalizes κ-theory as a principle of structure, memory, and constraint governing transitions between randomness, organization, and collapse.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20018303 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Limits of Order: A κ-Theory Extension of Feedback and Memory Mcdonald, Michael κ-theory extension feedback loops memory retention (α) statistical bias constraint dynamics path dependence non-Markovian systems phase transition entropy vs structure κ-theory extension feedback loops memory retention (α) statistical bias constraint dynamics path dependence non-Markovian systems entropy vs structure phase transition <p>This work extends κ-theory into feedback-driven systems by introducing memory retention (α) as a control parameter governing how past states influence future outcomes. While standard models treat systems as memoryless or state-dependent, this framework models them as history-influenced through feedback loops.</p> <p>A feedback loop is defined as the reintegration of outputs as inputs, creating memory. κ acts as a coupling between structural intensity and the influence of accumulated history, while a constraint scale limits runaway behavior. Together, these define an effective control parameter that determines system dynamics.</p> <p>Simulations reveal a phase transition across memory regimes. At low α, systems exhibit random, high-entropy behavior with no persistent structure. At intermediate α, feedback produces stable statistical bias while maintaining variability. A peak regime of “ordered freedom” emerges near α ≈ 0.80–0.85, where systems preserve identity without collapsing. At high α, excessive memory leads to instability and attractor-dominated collapse.</p> <p>These results show that statistical behavior can become path-dependent under sufficient feedback and structure, without violating underlying probabilistic laws. Order emerges only within a constrained balance between memory and dissipation.</p> <p>This framework generalizes κ-theory as a principle of structure, memory, and constraint governing transitions between randomness, organization, and collapse.</p> |
| title | The Limits of Order: A κ-Theory Extension of Feedback and Memory |
| topic | κ-theory extension feedback loops memory retention (α) statistical bias constraint dynamics path dependence non-Markovian systems phase transition entropy vs structure κ-theory extension feedback loops memory retention (α) statistical bias constraint dynamics path dependence non-Markovian systems entropy vs structure phase transition |
| url | https://doi.org/10.5281/zenodo.20018303 |