This preprint develops the fourth black-hole module in the TEBAC 9D/9D+ program. Its scope is deliberately restricted to the static admissible branch already organized in BH-I, refined geometrically in BH-II, and equipped with a corrected entropy package in BH-III. Within that precise regime, the manuscript constructs a theorem-bearing enlarged-state-space information-transport package, an admissible coarse-graining class, an intrinsic information-balance functional compatible with the BH-III entropy-variation law, a branch-stable channel-index class, and a conservative linearized ringdown-imprint class. The paper does not claim a full Hawking-radiation theorem, a Page-curve theorem, a generalized second-law theorem, a rotating-branch theorem, or a complete singularity-resolution theorem. Instead, it isolates the exact static-branch transport layer that can be stated noncircularly and exported downstream in a mathematically controlled form. A key feature of this version is the explicit bridge between the theorem-bearing BH-IV package and contemporary observational anchors. The manuscript includes a conservative comparison framework tied to horizon-scale imaging and strong-field gravitational-wave ringdown data, including benchmark discussion around EHT imaging scales and merger-ringdown deviations. The resulting picture is intentionally disciplined: not a claim of observational confirmation, but a concrete and testable comparison class for small transport-induced deviations from the general-relativistic quasinormal-mode spectrum. This version is positioned as an upload-ready intermediate theorem-bearing preprint: strong in scope control, explicit in non-claims, and designed to serve as the information-transport layer between the entropy-side BH-III package and later, more ambitious black-hole modules in the TEBAC 9D/9D+ architecture.
Tosho Lazarov Karadzhov (Thu,) studied this question.
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