AbstractWe propose a disciplined three-framework interpretation of black holes as finite correlationalsaturation regimes, thermodynamic-information closure systems, and critical degeneracies ofgeometric projectability. The architecture extends the earlier ERP–THALES bridge by integrating HDC–CBCµ/ERP as the correlational-substrate and projectability interpretation,THALES as a bounded diagnostic bridge, and TIC as a thermodynamic-information closurelayer. The central thesis is not that the three frameworks are identical, but that they describecomplementary aspects of the same boundary regime: increasing microscopic correlationalmultiplicity together with decreasing macroscopic geometric reconstructibility.This paper strengthens the interface definitions between the three frameworks, distinguishes projectability rank rµ = rank(dΠµ) from effective geometric distinguishability Deffgeom,and incorporates a more developed TIC role in entropy growth, distinguishability collapse,finite information closure, and projection efficiency. The projection-efficiency ratioPµ = DeffgeomΩµis also expressed through the compression factorKµ = ΩµDeffgeom,Pµ =K−1µ ,which clarifies that the proposed boundary regime is not merely high entropy, but high hidden multiplicity relative to externally reconstructible geometric distinction. The compactnesslandmark C∗ ≈ 0.465571 is treated as a partially derived diagnostic threshold, obtained bycombining the Schwarzschild perturbative scaling |htt| ∼ C with the reverse-Thales cubicclosure condition b3 = a. Appendices D and E add two concrete falsifiability-oriented constructions: a computable binning toy model demonstrating the four coordinated trendsΩµ ↑,Sµ ↑,Deffgeom ↓,Pµ ↓,and a pixelated-horizon compatibility construction for Bekenstein–Hawking entropy scaling.The framework preserves classical general relativity and black-hole thermodynamics aseffective macroscopic limits, while offering a cautious interpretive architecture for the regimein which geometric reconstruction becomes insufficient. Keywords black holes; geometric projectability; HDC–CBCµ; ERP; THALES; TIC; thermodynamic information; Fisher geometry; entropy saturation; reconstructibility; BekensteinHawking entropy; compactness; critical diagnostics; falsifiability.
Palau et al. (Sun,) studied this question.