HDC-CBC/Ic Correlational Index Ic, Historical Admissibility, and Executable Domain of Ct(a)

We present HDC–CBC/Ic, the fifth volume of the Supplementary Structural only a subclass can sustain projectable regimes and, within it, only a part also proves operationally executable. On this basis, we distinguish between: the space of mathematically definable histories of the index, the historically admissible domain, and the executable domain under the minimal validation environment of ΩCt/N. The pipeline is thus reinterpreted not as a fitting engine that grants physical meaning to the index from observational success, but as an operational environment that explores what part of the historically admissible domain can be deployed without breakdown under a criterion of structural consistency plus minimal observational compatibility. In this logic, the so-called operational window of does not constitute the origin of the meaning of the index, but its minimal proof of executability. The work further establishes a stricter methodological protocol for reading runs. The Planck-like, ICCUB-like, and SH0ES-like regions must not be treated as primary physical inputs of the analysis, but as derived observational basins assigned only after the calculation of , the checklist, and the GLOBAL state of the run. In analogous fashion, the references break-(BAO) and break+(WL) are interpreted not as arbitrary labels, but as operational frontiers of the executable domain of the index. The main result of HDC–CBC/Ic is therefore a structural reinterpretation of the Correlational Index: neither eliminable, nor freely adjustable, nor ontologically autonomous, but rather the minimal index of historical admissibility and executable domain of correlational coherence within the HDC–CBC/Ωcₜ framework. In doing so, the volume completes the logical step linking irreducibility, admissibility, historical promotion, and operational falsifiability, thereby making explicit the place of within the general HDC–CBC program.