IndisputableMonolith.Cosmology.StructureFormationFromBIT
Module StructureFormationFromBIT defines the phi-powered scaling for CMB acoustic peak wavenumbers as k_n = k_0 φ^n. Cosmologists modeling early structure formation on the 8-tick lattice cite these definitions to set peak positions. The module consists of targeted definitions for positions, ratios, and a certification object with no complex proofs required.
claimThe wavenumber at the n-th CMB acoustic peak satisfies $k_n = k_0 φ^n$.
background
The module imports IndisputableMonolith.Constants, which defines the fundamental RS time quantum τ₀ = 1 tick. It introduces the phi-scaled wavenumber k_n = k_0 φ^n for acoustic peaks together with sibling definitions for k_peak, k_peak_pos, adjacent ratios, and scale-invariant ratios. The local setting applies the eight-tick octave to structure formation, extending the phi-ladder from the forcing chain.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds IndisputableMonolith.Cosmology.CMBAcousticPeakRatios, which 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.
scope and limits
- Does not derive the base wavenumber k_0 from the forcing chain.
- Does not compute explicit numerical ratios for the peaks.
- Does not perform comparison against Planck data.
- Does not extend to non-scale-invariant corrections.