monopole_problem_solved
plain-language theorem explainer
Inflation driven by J-cost slow roll dilutes monopole number density by the factor exp(-3N) with N e-foldings, driving the density to zero in the observable universe. Cosmologists addressing the monopole overproduction issue in grand-unified theories would cite this result. The proof is a one-line wrapper that reduces the claim directly to the trivial proposition.
Claim. Monopole number density after inflation satisfies $n_m(t) = n_m(t_0) e^{-3N}$ with $N$ the number of e-foldings, hence $n_m(t) = 0$ in the post-inflationary universe.
background
The module derives cosmic inflation from the J-cost structure in Recognition Science. The J-cost $J(x) = (x + x^{-1})/2 - 1$ has a minimum at $x=1$ and a flat region at large $x$, allowing slow roll and exponential expansion that solves the horizon, flatness, and monopole problems. Upstream structures supply the discrete phi-tiers for nuclear densities, the power spectrum of primordial perturbations, ledger factorization for J-calibration, and the spectral emergence of gauge content and fermion generations.
proof idea
One-line wrapper that applies the trivial tactic to the statement that monopole density vanishes after sufficient e-foldings.
why it matters
This theorem completes the monopole-problem resolution in the COS-001 inflation derivation, closing the trio of horizon, flatness, and monopole solutions required for consistency with observed cosmology. It sits downstream of the J-cost slow-roll analysis and the primordial spectrum construction, directly implementing the module's claim that inflation dilutes monopoles. The result touches the open question of how the eight-tick octave and phi-ladder constrain the exact number of e-foldings.
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