IndisputableMonolith.Cosmology.StructureFormationFromBIT
This module defines the scaling of CMB acoustic peak wavenumbers in the Recognition Science framework as k_n = k_0 φ^n. It supports analysis of structure formation from the phi-ladder and eight-tick lattice. Cosmologists comparing to Planck data would cite the peak ratio definitions here. The content is organized as successive definitions leading to a certification object.
claimThe wavenumber at the n-th CMB acoustic peak satisfies $k_n = k_0 · φ^n$, where φ is the self-similar fixed point.
background
Recognition Science derives cosmology from the forcing chain T0 to T8, with the eight-tick octave and D = 3 spatial dimensions as key landmarks. This module focuses on structure formation, introducing the BIT-derived model for acoustic peaks in the CMB. Key definitions include the peak wavenumber and scale-invariant ratios such as the adjacent peak ratios. It imports the fundamental RS time quantum (RS-native). τ₀ = 1 tick from the Constants module, setting the stage for phi-powered scalings in the lattice.
proof idea
This is a definition module, no proofs. The argument proceeds by defining the base peak wavenumber, then positions, followed by adjacent ratios and the scale-invariant property, concluding with the certification object.
why it matters in Recognition Science
This module provides the base definitions that the CMB Acoustic Peak Ratios from the 8-Tick Lattice module builds upon. The downstream module states it deepens StructureFormationFromBIT (Plan v5 Track E1) with explicit numerical-band predictions for the first three CMB acoustic-peak ratios, and a falsifiable comparison to Planck 2018 data. It implements the structure formation component linking the eight-tick octave to observable cosmology.
scope and limits
- Does not specify the numerical value of the base wavenumber k_0.
- Does not include direct comparisons to observational data.
- Does not extend to non-scale-invariant corrections or higher peaks.