Hierarchical ``Halting''--``View-Relative Completeness'' Unified Theory\\ (Formal Construction Under EBOC--WSIG--RBIT Framework)

Under the frameworks of Windowed Scattering--Information Geometry (WSIG/CCS), Eternal-Static-Block Computation (EBOC), and Resource-Bounded Incompleteness Theory (RBIT), we establish view- and resource-dependent hierarchical ``halting'' criteria and provide equivalence theorems consistent with sampling--frame thresholds, Poisson--Euler--Maclaurin (EM) error theory, and ``trinity'' scale (phase derivative--relative state density--group delay). We unify the sign and branch conventions of the trinity equality chain, clarify the interchangeable use of \Phi_f=\arg\det S's absolutely continuous branch and Birman--Kreĭn (BK) gauge; characterize ``readout/pointer'' and Ky--Fan minimum at operator level; tighten equivalence conditions of ``sampling-period closed-loop'' and ``readout halting'' under strict bandlimiting and tight frame regularity premises; and restate RBIT assertions in Gödel--Chaitin type and extension chain incompleteness.