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A new $\theta$ function primitive is proposed that almost achieves thecombined efficiency of the addition, multiplication and successor growthoperations. This $\theta$ function symbol enables the constructing of an"IQFS(PA+)" axiom system that can corroborate a fragmentary definition of itsown Hilbert consistency, while it will simultaneously verify isomorphiccounterparts of all Peano Arithmetic's $\Pi_1$ theorems. Many propositions andintermediate results are also established. Only one intermediate result, whichmost readers will intuit should be true, does remain formally unproven.

On How the Introducing of a New $\theta$ Function Symbol Into  Arithmetic's Formalism Is Germane to Devising Axiom Systems that Can  Appreciate Fragments of Their Own Hilbert Consistency