Theoretical framework reveals prime numbers as arithmetic projections of canonical geometric symmetry states, suggesting primality originates from underlying geometric structures.
Key Points
Introduce a geometry-first theoretical framework called the Prime-Property Generator (PPG) to explain prime numbers as arithmetic projections of canonical geometric states rather than primitive numerical objects.
Constructed a finite geometric state space equipped with local mirror symmetries, finite group actions, hypercube-like orbit structures, and global antipodal geometry.
Applied canonicalization rules and arithmetic projections to map canonical geometric states directly onto conventional prime numbers.
Demonstrated that familiar prime number properties can be systematically derived as arithmetic projections or 'shadows' of an underlying geometric symmetry structure.
Formulated a conceptual correspondence linking open arithmetic problems, such as Goldbach's and twin-prime conjectures, to global geometric relations within the model.