Initial Meta-Rationality: Strong Transcendental Deduction in the KT Family

Transcendental arguments become constitutive only when rational organization converges to a least admissible form from which every successful realization receives its structure. The meta-rational family is the clearest application domain for that claim. Polynomial presentation supplies a grammar of candidate package-worlds and the obligations they generate, but grammar alone is not deduction. The constitutive upgrade is initiality. Once the structured admissibility doctrine attached to a semantically adequate polynomial presentation has an initial object, transcendental force becomes universal-property force: there is a least admissible realization, and every other admissible realization uniquely receives its structure from it. The real burden of strong transcendental deduction is therefore an initiality claim. The issue is not merely whether a rational package can stabilize, but whether there is a least admissible package-world from which all successful package-worlds receive their structure. Public-interface extraction, generic position-filling obligations, free repair, and re-entry yield a weak reconstruction of that family; in the finitary fragment, the present work shows both how initiality can be inherited from an ontological or evidential base and how free repair plus reflectivity can realize it at the package level. In one especially natural semantic reading, that inheritance runs through a reflective internal model presentation in an evidential topos; conversely, when package-level initiality is secured, it determines a least flattened ontological shadow in the restricted image of the doctrine. A public-repair obstruction theorem then shows how least package-worldhood can fail when admissible public completions branch, and a maximal-characterization theorem isolates the exact finitary boundary between the two. The resulting philosophical upshot is that rationality becomes constitutive only when its public burden collapses to a single governable visible condition; once the public frontier remains irreducibly plural, the doctrine yields admissible regimes rather than a least rational world.