Mathematical registry
Research-caliber questions with known structure and explicit closure criteria.
What is established, what remains open, and what would count as a resolution. The interface realizability question remains under formulation.
GAT VIII constructs physical comparison data on a selected system of admissible covers and refinements. Determine when that construction extends to a larger, precisely specified cover system while preserving its physical data and compatibility relations.
Explore the open problem →A certified continuation need not determine a universal transported object. Find verifiable physical and categorical conditions under which the full comparison distributor is representable, and those representations fit coherently across changes of description.
Explore the open problem →Determine when two specified structured descriptions admit a comparison that satisfies explicitly stated preservation and compatibility requirements. This is a preliminary research question: the domains, allowed interface type, and admissibility conditions still need to be fixed.
Explore the open problem →Finite reconstruction cores, presentation-invariant complexity, nonabelian relative defects, Ward-descent interfaces, and the passage from equation descent to observable descent.
Explore the open problem →Certify injectivity and a rigorously positive least generalized eigenvalue for every normalized passage block required by the confinement reduction.
Explore the open problem →