Hello,
I find the central question of this discussion particularly relevant: can the Hilbert-space formalism and the Born probability rule be derived from a deeper physical structure, rather than taken as fundamental assumptions?
In my independent research programme, Quantum Morphodynamics, I am investigating this question from a discrete geometric and spectral perspective. The PRISM state space contains
[
|\Omega|=64\cdot6\cdot6\cdot6\cdot5=69,120
]
configurations, with graph structure
[
C_{64}\square C_6\square C_6\square C_6\square C_5.
]
The associated graph Laplacian provides a well-defined spectral structure. In parallel, I am exploring connections with Kaluza–Klein geometry, where compact dimensions can encode effective gauge degrees of freedom.
These are related but distinct questions: a discrete spectrum and a geometric interpretation do not, by themselves, derive quantum probabilities or gauge dynamics. The challenge is to establish the mathematical bridge between the underlying structure and the effective physical theory without building the desired result into the assumptions.
I would therefore be interested in a specific point concerning the approach discussed here:
What minimal assumptions about the accessible states, composition of systems, and measurement dynamics are required to derive the Born rule uniquely? Could a discrete geometric-spectral model provide an independent route to those assumptions, or must the probability rule enter at some earlier stage?
I ask this as an open mathematical question, not as a claim that the derivation has already been achieved in my framework.
Best regards,
Fabian Leo Naressi
Independent researcher — Quantum Morphodynamics (PRISM–Krist-All)
