strongCPNumericalCert
plain-language theorem explainer
The definition constructs the strong CP numerical certificate asserting that the RS-predicted theta_QCD equals zero and satisfies all listed experimental and minimization conditions. A physicist studying the strong CP problem or discrete symmetry resolutions would cite it to link 8-tick phase constraints directly to the observed bound. The construction is a direct structure fill using reflexivity for the zero prediction together with referenced lemmas for the interval, absolute-value, gap, and J-cost claims.
Claim. The strong CP numerical certificate is the structure asserting that the RS-predicted value of $theta_{QCD}$ equals zero, lies strictly inside the experimental interval $(-theta_{max}, theta_{max})$, satisfies $|theta| < theta_{max}$, obeys the gap condition $1 - cos(pi/4) > 0.29$, and that the J-cost function is minimized at $theta = 0$.
background
In the StandardModel.StrongCP module the strong CP problem is the unexplained smallness of the theta term in the QCD Lagrangian, observed to satisfy $|theta| < 10^{-10}$. Recognition Science accounts for this via the eight-tick symmetry: the fundamental time quantum tick equals 1, one octave spans eight ticks, and discrete phase constraints force theta to multiples of pi/4. J-cost minimization then selects the zero value. Upstream results supply the tick definition as the RS time quantum and the Axion structure as the conventional dynamical alternative that this certificate bypasses.
proof idea
The definition is a direct structure instantiation. It sets the predicted field by reflexivity to establish equality with zero, then supplies the inside-experimental bound via the referenced theta_RS_inside_experimental lemma, the absolute-value inequality via abs_theta_RS_lt_bound, the gap via strong_cp_gap, and the universal J-cost minimum via theta_zero_minimizes.
why it matters
This supplies the numerical certificate for the SM-008 claim that eight-tick symmetry solves the strong CP problem without fine-tuning or new particles. It combines the structural prediction from the eight-tick octave (T7) and J-uniqueness (T5) with experimental consistency checks. No downstream theorems yet reference it, leaving open the question of how the certificate integrates into full Standard Model mass ladders or cosmology.
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