We introduce a formal classification of information loss under gauge reduction into three non-symmetric, mutually independent types: the Jumping Edge J (geometric annihilation), Capture Points C (translational untranslatability), and the Orbital Cycle K (dynamical orbital collapse). The three types are unified by a single Obstruction Functional O from the extended full structure to {0,1}^3, whose 2^3 − 1 = 7 non-zero values correspond to seven distinct modes of observational occlusion. We prove a completeness theorem stating that, relative to the three obstruction predicates, every loss-bearing element triggers one of O_geom, O_arith, O_orb; and we establish that K acts as the dynamical organising principle from which J and C are generated in the canonical model p = 11, g = 2. A concrete arithmetic model on Z/pZ supplies the rigour: a rationality criterion characterises capture points by log_2((x+1)/(p+1)) being an integer, and an exact formula for their number is given by |CP(p)| = (p − 1) − v_2(p + 1), valid for all primes for which 2 is a primitive root. A blurred variant O^ε stratifies the orbit O_p into five layers indexed by the nearest-integer distance δ(x), with exact thresholds for p = 11. The orbital register is identified with a finite reduction of the dyadic solenoid's doubling map. All rigorous results are stated for the canonical model in Sections 1–4; generalisations with explicit scope conditions are in Section 5; physical and interpretive content is confined to Sections 6 and 7. Completeness is relative to the three predicates of the Obstruction Functional, and minimality of p = 11 is internal to the framework's admissibility conditions; both are stated as such.