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February 14, 2026Open Access

BRISM and the Born Rule in Continuity with Established Structural Theorems of Quantum Mechanics: U(1) Symmetry, Measure Uniqueness, POVM Dilation and Spectral Stability

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SHSwen Carlo Heinze

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Overview

Reveals how BRISM maintains the Born rule in quantum mechanics, clarifying measurable statistics.

Key Points

  • The aim is to integrate the BRISM model with established quantum mechanics frameworks without changing the existing formalism.
  • Developed four formal bridges embedding BRISM within Hilbert-space quantum mechanics.
  • Analyzed U(1) symmetry and its implications for norm conservation and the Born rule.
  • Examined Gleason–Busch measure uniqueness within POVM structures.
  • Applied Naimark–Stinespring dilation to relate every POVM to projective measurements.
  • Investigated spectral stability of quadratic density mappings under several conditions.
  • Confirmed that the Born rule is a necessary outcome of the BRISM interface rather than an assumption.
  • Proved that all POVM-induced probabilities align with standard probability rules.
  • Demonstrated the mathematical necessity of dilation spaces in relating bulk and measurement statistics.
  • Established that only quadratic mappings remain positive, local, and σ-additive across spectral components.

Cite This Study

Swen Carlo Heinze (2026) studied this question.

synapsesocial.com/papers/699011b32ccff479cfe58916https://doi.org/10.5281/zenodo.18623684
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