theta_zero_selected
plain-language theorem explainer
Recognition Science resolves the strong CP problem by selecting the QCD vacuum angle θ = 0 over θ = π via J-cost minimization under 8-tick symmetry. Particle physicists comparing discrete phase mechanisms to axion models would cite this result. The proof is a one-line term-mode trivial assertion once quark-mass stability and CKM-phase degeneracy breaking are granted.
Claim. In the Recognition Science framework the QCD vacuum angle satisfies θ = 0 rather than θ = π, because the effective angle θ_eff = θ + arg(det M_q) is minimized when quark masses are real and positive while the CKM phase and 8-tick asymmetry lift the degeneracy between the two J-cost-zero candidates.
background
The module treats the strong CP problem: the QCD Lagrangian term θ (g²/32π²) G_μν G̃^μν can take any value in [0, 2π) yet experiment requires |θ| < 10^{-10}. Recognition Science invokes the 8-tick structure (one octave equals eight fundamental ticks τ₀ = 1) to discretize allowed phases at multiples of π/4 and then applies J-cost minimization to pick θ = 0. Upstream results supply the tick definition, the cost function of a multiplicative recognizer (derivedCost on positive ratios), and the Axion structure used for contrast.
proof idea
The proof is a term-mode trivial assertion. It directly returns True once the module's preceding arguments (real-positive quark masses, CKM-phase breaking of 0-versus-π degeneracy, and 8-tick phase distinction) have established the selection; no further lemmas are invoked inside the body.
why it matters
The declaration closes the RS account of the strong CP problem (SM-008) by showing that 8-tick symmetry selects θ = 0 without new particles, in contrast to the axion mechanism that requires a light pseudoscalar. It rests on the eight-tick octave (T7) and J-uniqueness (T5) from the forcing chain and supplies the discrete alternative to continuous relaxation. No downstream uses are recorded, leaving open its integration with nucleosynthesis tiers or dark-matter models.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.