3.4 Towards a Spectrum of Printed Structure
The key insight of this framework is that the initial field modes encode the structure seeds of the universe---not as random noise but as deterministic outcomes of resonant constraint conditions. This implies:
Each structure---voids, filaments, clusters---corresponds to a node or anti-node in standing wave patterns.
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The Cosmic Microwave Background anisotropies are interpreted as modal resonances over , not merely statistical fluctuations.
The spectrum of the universe can be reconstructed from a harmonic expansion dictated by the resonant geometry of spacetime.
4. Derivation of Cosmic Structure from Eigenmodes
4.1 Mapping Eigenmodes to the Large-Scale Cosmic Web
In the Resonant Genesis Hypothesis, the emergence of large-scale structures such as galaxy clusters, filaments, and voids is not the result of stochastic density perturbations followed by hierarchical mergers, but instead arises from deterministic resonant eigenmodes of spacetime itself.
The scalar field modes identified in the previous section define a spatial energy density profile:
\delta\rho(x) \propto |\Phi(x)|^2 = \left|\sum_n A_n \psi_n(x)\right|^2
Regions of constructive interference in this wave superposition correspond to overdense regions---the seeds of galaxies and clusters---whereas nodes or destructive interference zones evolve into voids.
