IndisputableMonolith.Cosmology.StructureFormationFromBIT
This module defines the wavenumber scaling for CMB acoustic peaks as k_n = k_0 φ^n together with adjacent ratio functions and a certification theorem. Cosmologists deriving structure formation from the BIT foundation cite it to obtain phi-rational peak positions on the ladder. The module supplies definitions and one certification theorem with no complex proof steps.
claimThe wavenumber at the n-th CMB acoustic peak is given by $k_n = k_0 φ^n$, where φ is the self-similar fixed point. Adjacent peak ratios are scale-invariant and satisfy explicit algebraic relations derived from the Recognition Composition Law.
background
Recognition Science places structure formation on the phi-ladder that emerges from the eight-tick octave and the J-cost functional. The module introduces k_peak as the direct scaling k_n = k_0 φ^n and supplies helper functions k_peak_pos, k_peak_adjacent_ratio, peak_2_1_ratio and peak_3_2_ratio. Upstream it imports the fundamental RS time quantum τ₀ = 1 tick from Constants, which anchors all rung indices on the ladder.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the phi-rational skeleton required by the downstream CMBAcousticPeakRatios theorem, which adds numerical-band predictions for the first three acoustic-peak ratios and a direct comparison to Planck 2018 data. It completes Track E1 of Plan v5 by fixing the wavenumber positions before ratio analysis begins.
scope and limits
- Does not perform numerical integration of the power spectrum.
- Does not derive the underlying forcing chain T0-T8.
- Does not contain observational data or error bars.
- Does not prove uniqueness of the phi-ladder scaling.