abs_theta_RS_lt_bound
plain-language theorem explainer
The Recognition Science model predicts a QCD theta parameter whose absolute value lies strictly below the experimental upper limit of 10^{-10}. Particle physicists examining the strong CP problem would cite this to show that eight-tick symmetry resolves the apparent fine-tuning without additional mechanisms. The proof is a direct numerical verification obtained by unfolding the predicted theta and bound definitions then applying simplification and numeric normalization.
Claim. $|θ_{RS}| < 10^{-10}$, where $θ_{RS}$ is the theta parameter selected by J-cost minimization under the discrete phase constraints of the eight-tick lattice.
background
The module treats the strong CP problem as the unexplained smallness of the coefficient θ in the QCD Lagrangian term θ (g²/32π²) G_μν G̃^μν. Recognition Science imposes eight-tick symmetry, restricting allowed θ values to multiples of π/4; the J-cost function (the derived cost of a multiplicative recognizer on positive ratios) then selects θ = 0 as the unique minimum. The upstream Constants.tick supplies the fundamental time quantum τ₀ = 1 that discretizes the lattice, while the cost definitions from MultiplicativeRecognizerL4 and ObserverForcing supply the J-cost used for selection. The LedgerFactorization structure calibrates the underlying J function on the positive reals.
proof idea
The proof is a term-mode reduction. It unfolds the definitions of the RS-predicted theta and the experimental maximum bound, applies simp to normalize the resulting expressions, and invokes norm_num to confirm the numerical inequality.
why it matters
This theorem supplies the absolute-value bound required by the downstream strongCPNumericalCert definition, which assembles the full numerical certification that the eight-tick mechanism solves the strong CP problem. It directly realizes the T7 eight-tick octave landmark, showing that structural selection of θ = 0 satisfies the experimental constraint without axions or massless quarks. The result closes the link between the phi-ladder forcing chain and Standard Model phenomenology.
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