BU112, “Type Inhabitation under B_U,” formulates type inhabitation as a B_U-anchored downstream formal reconstruction. Its object is the class of situations in which a type, proposition, specification, program interface, proof target, constructive object, or formal container claims to be inhabited by a term, witness, proof object, program, value, or admissible construction. The paper places this claim under the B_U chain of boundary consistency, dynamic completeness, admissible path space, structured pruning, residual gating, feedback, and settlement standing. Type inhabitation is therefore treated as a local formal event whose structural force depends on whether the type boundary is declared, the inhabitant enters the admissible domain, the construction path remains valid, the equivalence class is preserved, residual obligations are cleared, and the resulting object becomes compatible with the B_U settlement chain. The central judgment is direct: inhabitation proves local occupancy inside a declared formal container; B_U-compatible standing requires additional structural admission. A type may be syntactically well formed. A term may type-check. A proposition may receive a proof object. A program may satisfy an interface. These events establish local formal inhabitation. They acquire durable standing only when the inhabited object preserves the correct boundary, retains the relevant invariant core, survives admissible transport, exposes hidden proof or construction gaps, and enters a settlement-compatible chain. BU112 therefore separates local inhabitation from retained standing. A term can inhabit a type; the B_U ledger adjudicates whether that inhabitation carries admissible structure beyond the local formal shell. The file develops this handshake through a sequence of definitions: type presentation, declared type boundary, admissible type domain, inhabitant, construction path, inhabitation equivalence, transport of inhabitants, inhabitation gap, verifier, and settlement-compatible inhabitation. These definitions translate the B_U source-axis discipline into a vocabulary familiar to type theory, constructive mathematics, Curry–Howard correspondence, proof assistants, programming language semantics, dependent types, formal verification, and proof-carrying computation. The local formal shell follows a clear chain: type → boundary → admissible domain → inhabitant → construction path → equivalence class → transport stability → gap audit → settlement-compatible standing. The theorem skeletons establish the main structure. The Declared Type Boundary Theorem states that inhabitation becomes structurally meaningful only after the type boundary is fixed. The Admissible Inhabitant Theorem states that a term counts as an inhabitant only inside the declared admissible type domain. The Construction Path Theorem links inhabitation to a valid route of construction rather than mere symbolic placement. The Inhabitation Equivalence Theorem requires equivalent presentations to preserve the same admissible inhabitants. The Transport Stability Theorem requires inhabited status to remain stable under admissible transformations. The Inhabitation Gap Obstruction Theorem identifies hidden assumptions, invalid coercions, boundary drift, and residual construction debt as failure points. The Settlement-Compatible Inhabitation Theorem returns the inhabited object to the B_U ledger through residual clearing, feedback compatibility, and same-world-sheet settlement. The final judgment is that type inhabitation is a powerful local formal tool whose standing depends on B_U. Inhabitation can certify that a formal container has a term, proof, program, or witness. B_U-compatible inhabitation certifies that the inhabited structure can be retained under boundary, admissibility, transport, residual clearing, feedback, and settlement. A type is locally occupied by an inhabitant; the inhabited structure gains durable standing when it enters the same boundary and settles on the same world-sheet.