planck_l_3
plain-language theorem explainer
The definition binds the observed Planck 2018 value of the third CMB acoustic peak multipole to the constant 814.6. Cosmologists comparing Recognition Science wavenumber predictions to angular data would cite this numerical anchor when evaluating projection effects in the 8-tick lattice model. It is supplied as a direct real-number assignment with no derivation or lemmas.
Claim. The third CMB acoustic peak multipole moment from Planck 2018 data is defined by the assignment ℓ₃ = 814.6.
background
The module derives phi-rational wavenumber ratios k₂/k₁ = φ, k₃/k₂ = φ, k₃/k₁ = φ² directly from StructureFormationFromBIT.k_peak_adjacent_ratio under the 8-tick lattice. These ratios originate in the unified forcing chain: T6 fixes φ as the self-similar point and T7 enforces the eight-tick octave that yields D = 3 spatial dimensions. Observed Planck 2018 central values ℓ₁ = 220.0, ℓ₂ = 540.3, ℓ₃ = 814.6 are introduced solely for numerical-band comparison, with the explicit caveat that angular multipole ratios differ from bare k-ratios by the projection ℓ ≈ k · D_A.
proof idea
Direct definition that assigns the literal real number 814.6. No upstream lemmas are invoked; the binding serves as an empirical input for sibling ratio definitions such as planck_ratio_2_1 and planck_ratio_3_1 within the same module.
why it matters
The constant supplies the empirical reference point for the module's hypothesis that observed ℓ ratios can be tested against projected phi-rational k-space structure. It supports Track E1 of Plan v5 by allowing direct numerical confrontation with Planck 2018 data while preserving the theorem status of the underlying k-ratios. Full Boltzmann-hierarchy validation of the projection geometry remains an open closure step.
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