Part 1: Foundational Spectral Traces
This part establishes the spectral framework for understanding the Riemann Hypothesis through real analysis and operator theory. Building on the collapse patterns discovered in Book I, we now seek concrete spectral realizations where zeros emerge as eigenvalues of self-adjoint operators.
Chapter Overview
Chapters 1-8
The transition from natural numbers to real frequency bands reveals new spectral structures through ψ(x)-trace analysis. Key developments include:
- Collapse emergence in the infinitesimal [0.0, 0.1]
- Rational trace pairs and prime embeddings
- Fibonacci spiral resonance in ℝ
- Golden midline φ as collapse pivot
- Zero symmetry field detection at σ = 1/2
Key Themes
- From Discrete to Continuous: ℕ → ℝ transition
- Spectral Theory: Eigenvalues, eigenfunctions, spectra
- Operator Realizations: Concrete constructions
- Trace Formulas: Spectral-arithmetic connections
"In the realm of real numbers, the discrete zeros of zeta reveal themselves as the spectrum of an operator yet to be discovered - the music of the primes waiting for its instrument."