Reentrant Canonicality: Initiality, Accessibility and Transcendental Witnesses

A transcendental deduction, in the sense used here, starts from public data and asks for the least hidden or structural support required to reconstruct those data under a specified adequacy standard. We target what we call the universal-property fallacy: the assumption that if a witness is canonical, unique, initial, or universal, the epistemic problem of reconstruction has been solved. The corrective is reentrant canonicality. Reentrancy means that the result of reconstruction must itself become an object of the practice's public norms: exposable, checkable, and available for renewed use. A universal property can make an initial witness cheap to specify once the full reconstruction problem and an effective constructor are public; cost enters when finite agents must select, complete, construct, and certify the relevant route. We formalize this access question through practice-indexed presentation regimes and canonicality route packages; Kolmogorov- and Levin-style costs serve as lower-bound bookkeeping for whether public routes are short, feasible, and surveyable. Our formal centerpiece is a halting-probability stabilization model: a short public obligation generator determines a completed least fixed point, but exact stabilized finite approximants can lack any short charged public route and admit no uniform stabilization certificate. The finite minimal-hidden-support quotient gives the tractable countercase; de Sitter control illustrates certificate complexity in a live landscape-style setting. We conclude that strong initiality may be real while the route that would make it publicly available and transparent remains beyond finite agents.