theta_experimental_max
The declaration supplies the numerical value 10^{-10} for the experimental upper limit on the QCD theta parameter, drawn from neutron electric dipole moment measurements. Particle physicists and model builders working on the strong CP problem would cite this constant when checking whether a proposed mechanism satisfies the bound. The definition is a direct numerical assignment with no computation.
claimThe experimental upper bound on the absolute value of the QCD vacuum angle satisfies $|θ_{QCD}| < 10^{-10}$.
background
Recognition Science addresses the strong CP problem via 8-tick symmetry. The module states that the QCD Lagrangian term θ (g²/32π²) G_μν G̃^μν can take any value in [0, 2π), yet experiment requires |θ| < 10^{-10}. J-cost minimization under the eight-tick octave selects θ = 0, satisfying the bound automatically. The upstream interval definition from SpacetimeEmergence supplies the spacetime metric used in the broader unification, though the present declaration isolates only the numerical threshold.
proof idea
The definition is a direct numerical assignment of the real number 1e-10.
why it matters in Recognition Science
This constant is referenced by abs_theta_RS_lt_bound and theta_RS_inside_experimental, which verify that the RS-predicted θ lies inside the experimental interval, and by the structure StrongCPNumericalCert that combines the structural (8-tick + J-min) and numerical statements. It anchors the numerical side of the Strong CP section in the 8-tick framework, where discrete phase constraints force θ to multiples of π/4 and J-minimization selects zero. The declaration closes the loop between the theoretical prediction and the observed fine-tuning problem.
scope and limits
- Does not derive the 10^{-10} bound from first principles.
- Does not specify the precise neutron EDM experiment or error analysis.
- Does not address axion dynamics or other proposed solutions to the strong CP problem.
formal statement (Lean)
257noncomputable def theta_experimental_max : ℝ := 1e-10
proof body
Definition body.
258
259/-- The RS-predicted θ lies strictly inside the experimental interval. -/