Integral Source Completion and a Finite Local–Global Decision Principle for Stationary CCR Polynomial Jets
Year: 2026
Type: preprint
Abstract: The paper complements our stationary CCR triple-zero impossibility research by developing an effective decision theory for integral source completion rather than another finite-range nonexistence result. For fixed odd order and prime transport parameter, it proves that the final three source variables have a unique explicit rational choice forcing the bottom three polynomial coefficients to vanish. It then gives exact integrality conditions for that choice and shows that the upper half of the earlier sources enters the completion map affinely, producing a concrete integer-lattice membership test. Coefficientwise denominator control converts existence of a fully integral completion into a finite collection of local congruence questions, with a local–global equivalence for each fixed parameter pair. Under the stated Bernoulli-admissibility hypothesis, only auxiliary primes no larger than the order can obstruct completion. Exact order-77 denominator exponents illustrate the resulting finite decision precision without settling existence at that order. Its main novelty is the explicit three-source completion and finite local–global decision mechanism for this CCR family, not a general Hasse principle or an all-order triple-zero classification.
Author: Bütün, Alp Eren
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223694466