summary
plain-language theorem explainer
Recognition Science resolves the strong CP problem by restricting θ_QCD to multiples of π/4 via 8-tick symmetry and selecting exactly zero through J-cost minimization. QCD phenomenologists and particle physicists would cite this summary when comparing discrete symmetry proposals to the axion mechanism. The definition is a direct list literal of four claims with no computation or proof steps.
Claim. Let summary be the list of strings: ``8-tick quantizes θ to 8 values'', ``J-cost minimum at θ = 0'', ``No axion required (but compatible)'', ``Predicts θ = 0 exactly''.
background
The module sets the strong CP problem in QCD as the unexplained smallness of the θ term in the Lagrangian, L_θ = θ (g²/32π²) G_μν G̃^μν, with experimental bound |θ| < 10^{-10}. Recognition Science replaces the continuous θ interval by the discrete constraint from the eight-tick octave: allowed values are multiples of π/4. J-cost is the Recognition Composition Law functional that is minimized at θ = 0 and strictly positive elsewhere. The upstream tick definition supplies the fundamental time quantum whose period-8 repetition enforces the phase quantization.
proof idea
The definition is a literal list construction that enumerates the four summary claims. No lemmas are applied; the body simply returns the fixed list of strings.
why it matters
This definition packages the RS account of the strong CP problem for downstream reference. It rests on the eight-tick octave (T7) to discretize θ and on J-cost minimization to force the zero solution, thereby eliminating the need for new particles while remaining compatible with axions. It touches the open question whether the discrete structure alone suffices or whether an axion field is still required for dynamical relaxation.
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