planck_fine_tuning
plain-language theorem explainer
The constant encodes the bound of 10^{-63} on the deviation from flatness at the Planck epoch. Cosmologists examining the flatness problem cite this figure to illustrate the initial condition precision demanded by standard Big Bang evolution. The definition arises from scaling the observed |Ω-1| < 0.001 today backward by the factor (a_now / a_Planck)^2 ≈ 10^{60}.
Claim. The deviation from spatial flatness at the Planck time must satisfy $|Ω_{Planck} - 1| < 10^{-63}$ for the density parameter to remain within 0.001 of unity at the present epoch.
background
The flatness problem in cosmology stems from the instability of the Ω = 1 fixed point, where curvature deviations amplify as |Ω - 1| ∝ a²(t). In this module, Recognition Science resolves the issue by showing that ledger balance and J-cost minimization select critical density exactly. The imported PhiForcing module supplies the self-similar fixed point φ that constrains early-universe geometry. The doc-comment calculates the required tuning from the scale factor ratio a_Planck / a_now ≈ 10^{-30}, yielding a squared amplification of 10^{60} and thus the 10^{-63} bound for Planck-era flatness.
proof idea
This is a direct definition that assigns the real constant 10^{-63} to represent the Planck-era bound on |Ω - 1|. No lemmas or tactics are applied; the value follows from the scaling argument stated in the accompanying documentation.
why it matters
The declaration quantifies the fine-tuning challenge that downstream results such as rs_flatness_necessity address within the Recognition Science framework. It fills the COS-005 target by stating the problem that φ-constraints and critical density from J-cost minimization solve. The bound highlights the necessity of ledger structure for locking the universe to flat geometry from the outset.
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