2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75429We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show that, classically, such a thesis is, both, unverifiable and irrefutable, and, that it implies the Turing Thesis is false; that Goedel's arithmetical predicate R(x), treated as a Boolean function, is in the complexity class NP, but not in P; and that the Halting problem is effectively solvable, albeit not algorithmically.12 pages; an HTML version is available at http://alixcomsi.com/Is_the_Halting_problem.htmGeneral Mathematics03B10text