Quantum Relay Theory v3 in the b → s sector

This record presents Quantum Relay Theory v3 in the \(b → s\) sector, a structured and falsifiable effective framework built on Olivier Minazzoli’s Entangled Relativity, based on the action \(L_m^2/R\). The document develops a sectorial implementation of the geometric relay mechanism and applies it to rare \(b → s^+^-\) transitions. Within its stated effective formalism, the framework derives a dominantly vectorial correction to the Wilson coefficient \(C_9\), through a chain involving an effective Yukawa coupling \(gσ,=√2/3\,m_/MPl\), a sectorial memory architecture, an \(n\)-branch Wronskian cascade, and a hadronic response kernel closed algebraically as \(Ξ_B=-Wᵢⱼ/(σ_iσ_j)\). This version introduces several closures compared with previous QRT drafts: a Wronskian closure of the hadronic kernel, a one-loop photonic matching structure \(κ_γ=a_γ/(1+q^2/meff^2)\), an absolute normalisation \(a_γ=√2/3/Fₘₑₘ=0.579\), and a memory frequency \(Ω_c=Ω_+\) selected by the mechanism itself. The complete chain from the action to \(R_K\) contains zero free parameters within the stated effective QRT framework and gives the prediction \(R_K0.909\). The document also distinguishes this zero-parameter chain from the frozen phenomenological benchmark \(B2^\*\), which gives \(R_K=0.846\), and from the updated non-linear calculation including BSZ form factors and perturbative charm loops, giving \(R_K0.905\) for the zero-parameter chain and \(R_K0.888\) for \(B2^\*\). The benchmark \(B2^\*\) is presented as a frozen implementation used to test whether the QRT chain produces viable flavour outputs. With full non-linear \(P'_5\) calculation, BSZ form factors and perturbative charm loops, the document reports an improvement in 4/4 \(P'_5\) bins and a reduction of \(χ^2\) from 14.3 to 7.5. The QCD bridge for the hadronic kernel is established at a structural and semi-quantitative level, with compatibility to LCSR estimates within a factor of 3–7. The work explicitly states its epistemic status, limitations and failure criteria. It provides fifteen falsifiable predictions and eight failure criteria. It should be read as a structured, falsifiable and partially derived effective framework, not as a complete microscopic derivation of all flavour anomalies. The main remaining openings are the full GRT-to-EFT matching of \(a_γ\), the QCD normalisation of the hadronic kernel, the derivation of remaining memory parameters, and out-of-flavour tests such as M87* and magnetar signatures.