Selected Riemann-Hypothesis Witness Fibres, Validated Ξ-Certificates, Selection Jump, No-Transfer Barriers, and Maximal A-Priori Uniform Logical Nullity

correspondence at parkeremmerson@icloud.com This paper develops a selected-witness metatheory for the Riemann Hypothesiswhich separates four levels that are often conflated: the raw formula containing\(ζ(·)\), the analytically selected classical RH proposition, the exact\(Ξ\)-certificate calculus, and the global metatheory of proof, disproof,independence, and resolution procedures. At the clause-prior level, the raw strip formula\[:∀ s((0<(s)<1 ζ(s)=0)⇒(s)=12)\]is interpreted in the Dirichlet evaluator \(\), whose only zeta clause isthe Dirichlet-series clause on \((s)>1\). Under strict atomic strong Kleenesemantics,\[{}{}=,\]while the definedness-guarded formula is true by definedness-vacuity. Acrossarbitrary strip-total completions every subset of the critical strip is realizableas a zero-set of the raw \(ζ\)-symbol. Hence the raw formula has noclause-prior bivalent sign and no completion-invariant bivalent sign. Analytic continuation is therefore treated as a selector and formation operation:it forms the selected classical proposition\[: ,\]where \(\) is the unique analytically coherent evaluator agreeing with theDirichlet series on \((s)>1\). The selected RH package constructed here has exact positive and negative witnessfibres. The negative fibre is finite-certificate based:\[ ∃ w\,(w),\]where \((w)\) is a decidable finite exact-count certificate predicate foran off-critical zero of the Riemann \(Ξ\)-function. The positive fibre isall-stage:\[ ∀ n\,∃ c\,(n,c),\]where \((n,c)\) is a decidable half-plane zero-free certificatefor the \(n\)-th stage window in the RH-relevant \(Ξ\)-plane. A finitecomputation-history checker gives a literal \(Π_1\) arithmetic representative\[:∀ w\,∀ u\,(w,u),\]with\[ N.\] The proof-status calibration of this representative is sharp on the negativeside. If \(\), then every \(T⊇\) proves\[.\]Consequently\[T⇒,_T()⇒.\]If \(T\) is \(Σ_1\)-sound, then\[T.\] The validated-numerics backend is included theorem-level and constructively. Thecompleted \(ξ\)-function is defined as the entire removable extension of\[12s(s-1)π-s/2Γ(s/2)ζ(s),\]and the backend gives uniform rational enclosures for \(Ξ⁽ʲ⁾\),\(0≤ j≤3\), on compact subsets of the RH-relevant region. The correctedenclosure theorem is a shrinking-domain theorem: on compact guards, an enclosureradius for \(Ξ⁽ʲ⁾(D)\), \(j≤2\), is bounded by a compact derivative boundfor \(Ξ⁽ʲ⁺¹⁾\) times \((D)\), plus a precision term. The appendices giveexplicit rational interval algorithms, Euler--Maclaurin and gamma-polygamma tailbounds, theta-kernel truncation bounds, and validated quadrature estimates. The winding certificate is formulated as a parameterized tube-homotopycertificate. A rational polygonal loop \(P\) is supplied together with a boundarypartition and zero-avoiding rational image disks \(E_i\) such that both\(Ξ(γ([t_i,tᵢ₊₁]))\) and \(P([t_i,tᵢ₊₁])\) lie in \(E_i\). Thestraight-line homotopy inside the convex disks \(E_i⊂ C^×\)gives rigorous winding soundness. The paper proves global metatheorems: Selection Jump for occupied stagewise-localsuccess classes, computable triage failure, reflection collapse, Tarski anddiagonal barriers, finite-prefix nonclosure, finite-interface nonclosure, andlegacy support-filter laundering. The no-transfer theorem is sharpened to a maximal a-priori selected-logicaluniform-nullity theorem. The Dirichlet-clause formula has no bivalent resolvent,\[_{}()=;\]no bivalent sign is invariant across strip completions,\[_{ C_{}}()=;\]and, for every consistent recursively axiomatizable\(T⊇\), after analytic selection and exact witness packaging, themaximal selected-logical invariant uniform fixed-instance resolvent remainsempty,\[_T^{}(;)=.\]Here \(\) denotes the full selected-logical invariant closure of exactselected packages, not merely a list of theorem schemes proved up to a stage. Thesuperscript \(\) emphasizes that this is a uniform consequence relation overall exact selected packages: it is not the set of all actual metamathematicalfacts about the particular sentence \(\). Thus, after all a-prioriselected-logical invariant consequences are included, the intersection with theuniformly forced fixed-instance label set\[\{True,False,Prov_T,Ref_T,Unprov_T,Unref_T,Ind_T\}\]is empty. This is an unconditional no-forcing theorem for the maximal invariantselected-logical closure, not a statement of failed proof search.