Derivation of the Born Rule and Operational Quantum Formalism in the Accessibility Framework through Boundary Reduction
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Quantum Physics arXiv:2604.27125 (quant-ph) [Submitted on 29 Apr 2026] Title:Derivation of the Born Rule and Operational Quantum Formalism in the Accessibility Framework through Boundary Reduction Authors:Everett Fall, Hironori Kondo View a PDF of the paper titled Derivation of the Born Rule and Operational Quantum Formalism in the Accessibility Framework through Boundary Reduction, by Everett Fall and Hironori Kondo View PDF HTML (experimental) Abstract:We show that the operational quantum formalism -- the Born rule, Lüders state updating, quantum interference, non-Markovian effective dynamics, and Bell inequality violation at the Tsirelson bound \(2\sqrt{2}\) -- arises within Accessibility Theory (AT) from the Aperture construction together with explicit coherence and locality assumptions stated in the paper. AT is a framework built on real graded spectral triples and a single algebraic selection principle. The Principle of Universal Accessibility Balance requires three independent measures of the complexity of a spectral triple -- its algebraic, gauge-theoretic, and geometric content -- to be exactly equal and minimized, uniquely selecting the algebra \(\C \oplus \Hbb \oplus M_3(\C)\) and with it the Standard Model gauge group, particle content, four-dimensional Lorentzian spacetime, three generations, and gravitational dynamics. Restriction to a codimension-one geometric boundary reduces this algebra to its commutative center \(\C \oplus \C \oplus \C\) -- the Aperture -- which defines a permanent information bottleneck for any embedded observer. Coherence conditions on inference through this bottleneck, together with Gleason's theorem on the 48-dimensional internal Hilbert space, uniquely determine the Born rule; the remaining operational features follow from the same observer-level framework under the stated assumptions. At the ontological level the theory is deterministic and state-realist, while the operational quantum formalism appears at the observer level as a consequence of structurally limited access to the underlying algebraic reality. Subjects: Quantum Physics (quant-ph) MSC classes: 81P10, 81T75, 81P15 Cite as: arXiv:2604.27125 [quant-ph] (or arXiv:2604.27125v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.27125 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Everett Fall [view email] [v1] Wed, 29 Apr 2026 19:24:11 UTC (34 KB) Full-text links: Access Paper: View a PDF of the paper titled Derivation of the Born Rule and Operational Quantum Formalism in the Accessibility Framework through Boundary Reduction, by Everett Fall and Hironori KondoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)