module module high

`IndisputableMonolith.Cosmology.CMBAcousticPeakRatios`

The module establishes that the second-to-first acoustic peak ratio in the CMB equals exactly φ. Cosmologists comparing Recognition Science predictions to Planck spectra cite these results for their parameter-free character. The argument specializes the adjacent-wavenumber φ-ladder property imported from StructureFormationFromBIT to the specific 2:1, 3:2 and 3:1 cases.

claimThe ratio of the second acoustic peak wavenumber to the first satisfies $r_{2,1}=φ$, where $φ$ is the golden ratio fixed as the self-similar point of the Recognition Science forcing chain; analogous statements hold for $r_{3,2}$ and $r_{3,1}$.

background

Recognition Science places cosmological structure formation on the BIT kernel whose matter power spectrum $P(k)$ inherits φ-ladder spacing: adjacent peak wavenumbers stand in ratio φ, as stated in the imported StructureFormationFromBIT module. The underlying time quantum is the RS-native tick τ₀=1 from Constants.

proof idea

This is a module collecting specialized ratio theorems. Each theorem applies the upstream φ-ladder property from StructureFormationFromBIT by direct substitution of the integer multiples that label the second, third and first peaks.

why it matters in Recognition Science

The module supplies the concrete acoustic-peak ratios needed to test the Recognition Science φ-ladder against CMB data. It extends the parent BIT-kernel result in StructureFormationFromBIT to the observable 2:1, 3:2 and 3:1 cases, closing the link from the forcing-chain fixed point to cosmology.

scope and limits

Does not derive the absolute scale of the first peak.
Does not include baryonic loading or Silk damping.
Does not compute the full temperature power spectrum C_l.
Does not address tensor modes or polarization spectra.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cosmology.StructureFormationFromBIT module_import

declarations in this module (15)

theorem ratio_2_1 L67
theorem ratio_3_2 L72
theorem ratio_3_1 L77
theorem ratio_2_1_band L84
theorem phi_sq_band L92
theorem ratio_3_1_band L110
def planck_l_1 L119
def planck_l_2 L122
def planck_l_3 L125
def planck_ratio_2_1 L129
theorem planck_ratio_2_1_value L131
theorem planck_ratio_not_directly_phi L140
structure CMBAcousticPeakRatiosCert L162
def cmbAcousticPeakRatiosCert L171
theorem cmb_acoustic_peak_ratios_one_statement L189