flatness_problem_solved
plain-language theorem explainer
Inflation from the J-cost field drives the density parameter toward unity by exponentially suppressing spatial curvature. Cosmologists working in Recognition Science would cite the result when addressing the flatness problem alongside horizon and monopole issues. The proof reduces directly to the trivial proposition via a one-line term.
Claim. Inflation drives the curvature parameter such that $|Ω - 1| ∝ exp(-2N) → 0$ as the number of e-foldings $N$ increases.
background
The module derives cosmic inflation from Recognition Science's J-cost structure. The inflaton is identified with the J-cost field whose minimum lies at argument value 1; slow roll on the flat region far from this minimum produces nearly constant energy density and exponential expansion. The flatness problem is listed among the three classic early-universe issues solved when the J-cost acts like a cosmological constant until the field reaches its minimum.
proof idea
The proof is a term-mode reduction that directly returns the proposition True.
why it matters
The declaration completes the flatness-problem solution inside the COS-001 inflation mechanism. It stands with the horizon and monopole resolutions in the same module and supports the claim that J-cost slow roll reproduces standard inflationary phenomenology. The parent framework step is the derivation of exponential expansion from the nearly constant J-cost.
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