The Born Rule as the Unique Refinement-Stable Induced Weight on Robust Record Sectors

Quantum Physics [Submitted on 24 Mar 2026] The Born Rule as the Unique Refinement-Stable Induced Weight on Robust Record Sectors Marko Lela This paper proves a conditional structural uniqueness theorem for induced weight on robust record sectors within an admissible Hilbert record layer. Its theorem target and additive carrier differ from those of the standard Born-rule routes: additivity is not placed on the full projector lattice, but on disjoint admissible continuation bundles through an extensive bundle valuation, from which the sector-level additive law is inherited under admissible refinement. Accordingly, the result is not a Gleason-type representation theorem in different language, but a distinct uniqueness theorem about induced sector weight inherited from bundle additivity on admissible continuation structure. Under two explicit structural conditions, internal equivalence of admissible binary refinement profiles and sufficient admissible refinement richness, the quadratic assignment is the only non-negative refinement-stable induced weight on robust record sectors. In the main theorem, refinement richness is secured by admissible binary saturation. A supplementary proposition shows that dense admissible saturation already suffices if continuity of the profile function is added. Under normalization, the result reduces to the standard Born assignment. Comments: Quantum foundations. Distinct conditional uniqueness theorem for induced weight on robust record sectors Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR) Cite as: arXiv:2603.24619 [quant-ph]   (or arXiv:2603.24619v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.24619 Focus to learn more Submission history From: Marko Lela [view email] [v1] Tue, 24 Mar 2026 20:13:44 UTC (28 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: math math-ph math.MP math.PR References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)