This research aims to analyze the distribution of prime numbers in relation to a discrete torus using modular embedding.
Mapped prime numbers using modular embedding Phi_k(n) = (n mod p1, ..., n mod pk).
Investigated prime distribution with the decomposition formula P(prime at s) = mu(s) · S(s) · rho(s).
Empirical validation at N = 10^8.
Identified a non-constant prime preference field with measurable Fourier structure.
Validated conjectures regarding quasi-twin prime signature and prime spectral decomposition.
Envelope curve V(m) was found to approximate C/ln(m).
Resumen
Prime numbers mapped to a discrete torus via modular embedding Phiₖ (n) = (n mod p1,. . . , n mod pk). The prime distribution decomposes as P (prime at s) = mu (s) · S (s) · rho (s), where rho (s) is a non-constant prime preference field with measurable Fourier structure. Three conjectures: quasi-twin prime signature (p = q²-2), prime spectral decomposition, and envelope curve V (m) ~ C/ln (m). Validated empirically at N = 10⁸.
Statistical Probes of the Local Structure of the Prime Numbers: Order-2 Conditional Mutual Information and Detuned Rational Singularities of the Phases {alpha p_n}2026