A Universal Prior Cannot by Itself Select a Preferred Factorization: A Bounded-Alphabet Locality No-Go, with a Route-by-Route Map of the Same Gap in Born-Rule Derivations

A universal (Solomonoff–Levin) prior over computable descriptions cannot, by itself, select a preferred factorization, and therefore cannot supply locality. We prove this in a bounded-alphabet arena: on A^k with fixed a≥2, k≥3, the nearest-neighbour digit shift s is range-one local, while a constant-complexity radix-a carry-increment recoding π(x)=x+1 mod a^k conjugates it into a rule with the all-ones influence matrix — every output digit depends on every input, total influence k² (Theorem 1). Along the cyclic orbit generated by that one cheap increment the influence degree obeys the exact law deg(π_c·s)=k−ν_a(c), and the total-influence profile is an exact alphabet-independent function of ν_a(c) (Theorem 2; Corollary 1, Observation 1; the ν_a(c)=0 branch proved in closed form at the orbit endpoints c=1,N−1 and verified exhaustively over finite ranges otherwise), so a (1−1/a) majority of the orbit has degree k and only an a²⁻ᵏ fraction has degree at most 2: bounded-range locality is exponentially atypical. Because the finite bare-rule prior is quasi-invariant under such cheap recodings while locality varies maximally (Theorem 3), no carry-increment-invariant bare-rule predicate can match bounded-range locality on both witness sides (Corollary 2). The recoding is deliberately elementary, chosen to make the obstruction auditable. The same structural gap — exact additive bookkeeping within a context, none of the cross-context principles working derivations import across contexts — recurs in the Born-rule sector: a route-by-route account locates the principle each derivation imports (noncontextuality, subsystem-decomposition invariance, measurement-neutrality, or epistemic separability) and why a context-relative prior supplies none; this Born account is a map, not a theorem, and the stronger generic-breaking claim is left explicitly as a conjecture. The moral is uniform: locality, factorization, and cross-context Born structure are not class functions of the prior but must be supplied from outside it — a factorization, a reference machine, or a cross-context invariance — which frames the next question: what minimal such supplement a reconstruction must add.