Reset Dynamics, Paper 14: Observable Correspondence, Identifiability, and Experimental Signatures
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2026
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| author | pan, feiyue |
| author_facet | pan, feiyue |
| contents | <p>This is Paper 14 in the Reset Dynamics series.</p> <p>**Title:** Observable Correspondence, Identifiability, and Experimental Signatures</p> <p>**Abstract:**<br>We complete the Reset Dynamics framework by establishing a rigorous bridge between abstract cohomological structure and experimentally identifiable observables. Beyond observable correspondence, we prove a Topological Identifiability Theorem: under quantization, loop-dependence, and gauge invariance conditions, observed inconsistencies uniquely correspond to nontrivial cohomology classes in H¹.</p> <p>We further provide rejection criteria excluding non-topological explanations (noise, local defects, statistical fluctuations), ensuring that detected holonomy is not merely phenomenological but structurally necessary. A decision flowchart for topological identifiability is provided. We identify the uniform winding number distribution at criticality as the signature of topological tunneling and symmetry restoration.</p> <p>Key contributions:<br>- Observable mapping for mismatch variables, holonomy, winding number<br>- Topological Identifiability Theorem (quantization + loop-dependence + gauge invariance ⇒ H¹ ≠ 0)<br>- Decision flowchart for experimental identification<br>- Rejection criteria for non-topological explanations<br>- Scaling signatures for phase transition (⟨g²⟩ ∼ |R-1|⁻¹) and nonlinear repair (⟨g²⟩ ∼ √D)<br>- Topological tunneling and symmetry restoration at criticality<br>- Complete falsifiability conditions<br>- Detailed numerical experiment protocol and statistical analysis methods</p> <p>**Reset Dynamics Series Overview:**<br>- Paper 1-13: as above<br>- Paper 14 (this work): Observable Correspondence, Identifiability, and Experimental Signatures</p> <p>**Related Zenodo records:**<br>- Paper 1: https://zenodo.org/records/19373151<br>- Paper 2: https://zenodo.org/records/19609968<br>- Paper 3: https://zenodo.org/records/19861236<br>- Paper 4: https://zenodo.org/records/19923360<br>- Paper 5: https://zenodo.org/records/19978542<br>- Paper 6: https://zenodo.org/records/19979476<br>- Paper 7: https://zenodo.org/records/19979922<br>- Paper 8: https://zenodo.org/records/20024507<br>- Paper 9: https://zenodo.org/records/20024960<br>- Paper10: https://zenodo.org/records/20025265<br>- Paper11: https://zenodo.org/records/20036480<br>- Paper12: https://zenodo.org/records/20036915<br>- Paper13: https://zenodo.org/records/20037205 </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20037402 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Reset Dynamics, Paper 14: Observable Correspondence, Identifiability, and Experimental Signatures pan, feiyue observable correspondence topological identifiability cohomological obstruction winding number experimental signatures phase transition scaling topological tunneling symmetry restoration falsifiability, Reset Dynamics <p>This is Paper 14 in the Reset Dynamics series.</p> <p>**Title:** Observable Correspondence, Identifiability, and Experimental Signatures</p> <p>**Abstract:**<br>We complete the Reset Dynamics framework by establishing a rigorous bridge between abstract cohomological structure and experimentally identifiable observables. Beyond observable correspondence, we prove a Topological Identifiability Theorem: under quantization, loop-dependence, and gauge invariance conditions, observed inconsistencies uniquely correspond to nontrivial cohomology classes in H¹.</p> <p>We further provide rejection criteria excluding non-topological explanations (noise, local defects, statistical fluctuations), ensuring that detected holonomy is not merely phenomenological but structurally necessary. A decision flowchart for topological identifiability is provided. We identify the uniform winding number distribution at criticality as the signature of topological tunneling and symmetry restoration.</p> <p>Key contributions:<br>- Observable mapping for mismatch variables, holonomy, winding number<br>- Topological Identifiability Theorem (quantization + loop-dependence + gauge invariance ⇒ H¹ ≠ 0)<br>- Decision flowchart for experimental identification<br>- Rejection criteria for non-topological explanations<br>- Scaling signatures for phase transition (⟨g²⟩ ∼ |R-1|⁻¹) and nonlinear repair (⟨g²⟩ ∼ √D)<br>- Topological tunneling and symmetry restoration at criticality<br>- Complete falsifiability conditions<br>- Detailed numerical experiment protocol and statistical analysis methods</p> <p>**Reset Dynamics Series Overview:**<br>- Paper 1-13: as above<br>- Paper 14 (this work): Observable Correspondence, Identifiability, and Experimental Signatures</p> <p>**Related Zenodo records:**<br>- Paper 1: https://zenodo.org/records/19373151<br>- Paper 2: https://zenodo.org/records/19609968<br>- Paper 3: https://zenodo.org/records/19861236<br>- Paper 4: https://zenodo.org/records/19923360<br>- Paper 5: https://zenodo.org/records/19978542<br>- Paper 6: https://zenodo.org/records/19979476<br>- Paper 7: https://zenodo.org/records/19979922<br>- Paper 8: https://zenodo.org/records/20024507<br>- Paper 9: https://zenodo.org/records/20024960<br>- Paper10: https://zenodo.org/records/20025265<br>- Paper11: https://zenodo.org/records/20036480<br>- Paper12: https://zenodo.org/records/20036915<br>- Paper13: https://zenodo.org/records/20037205 </p> |
| title | Reset Dynamics, Paper 14: Observable Correspondence, Identifiability, and Experimental Signatures |
| topic | observable correspondence topological identifiability cohomological obstruction winding number experimental signatures phase transition scaling topological tunneling symmetry restoration falsifiability, Reset Dynamics |
| url | https://doi.org/10.5281/zenodo.20037402 |