obs_radius_m
The definition supplies the observed comoving radius of the universe in meters as 4.40 × 10^26 from the Planck 2018 ΛCDM fit. Cosmologists comparing Recognition Science scale predictions to data would cite this anchor. The assignment is a direct numerical definition with no computation.
claimThe observed comoving radius of the observable universe is given by $r = 4.40 × 10^{26}$ meters, taken from the Planck 2018 ΛCDM fit that corresponds to 46.5 Gly.
background
The module sets up the SI calibration seam that converts Recognition Science native units (c = ℓ₀ = τ₀ = 1) into meters and seconds for comparison with observations. The Planck length and time act as the external bridge, with their SI values treated as experimental inputs rather than RS predictions. Upstream structures supply the J-cost minimization from PhysicsComplexityStructure, the ledger factorization from DAlembert, and the spectral emergence of gauge content from SpectralEmergence that justify the ratios calibrated by this constant.
proof idea
This is a direct definition that assigns the numerical value 4.40e26. No lemmas or tactics are applied beyond the literal constant from the doc-comment.
why it matters in Recognition Science
This definition anchors the conversion of Recognition Science cosmological predictions into SI units, enabling direct comparison with observations. It fills the reporting seam in the module where ratios such as R_obs / ℓ_P carry the theoretical content. It connects to the forcing chain landmarks T7 eight-tick octave and T8 D = 3 by providing the observable scale against which phi-ladder mass and length predictions are tested.
scope and limits
- Does not derive the numerical value from Recognition Science axioms or the phi-ladder.
- Does not include observational uncertainty or error bars from the Planck fit.
- Does not apply to proper distances, angular diameter distances, or non-comoving radii.
- Does not claim the value is exact or independent of the chosen ΛCDM parameters.
formal statement (Lean)
102def obs_radius_m : ℝ := 4.40e26
proof body
Definition body.
103
104/-- Observed age of the universe (seconds).
105 13.787 ± 0.020 Gyr (Planck 2018). -/