One Wave Function, One World: Finite-Information Regional Algebras and the Macroscopic World from Holographic Constraint

The primary technical statement of the QIQT-H program: a single-world, exactly-unitary foundations-of-quantum-mechanics framework whose complete per-run ontology is the pair (Phi, lambda) -- Phi the entire dynamical content of reality, evolving by one exactly-unitary law (no collapse, no branches-as-substances, no external observer, no fundamental probability), and lambda a single non-dynamical fact per run: which of Phi's macroscopic realizations is the actual one. The one physical input is a finite-information (Bekenstein-Bousso) bound read literally: a bounded spacetime region R can instantiate only Q_R = A(boundary R) / 4 l_P^2 worth of distinguishable physical records. The framework combines the Chandrasekaran-Penington-Witten Type II crossed-product algebra construction with this holographic constraint. The measurement problem is decomposed rather than solved by a new mechanism: decoherence and einselection furnish stable, effectively Boolean records (robustness, not uniqueness); the surface-area bound makes the set of distinguishable records finite (cardinality, not selection); and lambda supplies which record is actual. It includes the retirement of the Macroscopic Definiteness Conjecture (capacity does not forbid records -- a category error) and reframes the single outcome as lambda's, with a machine-checked covariant Born-reduction (to a single typicality premise, together with a no-go that some premise is unavoidable) and consistency results as the substantive contribution, alongside an honest account of what remains open. The Born rule appears as an across-run frequency, not a per-run probability. An accompanying machine-checked Lean 4 / Mathlib development (DOI 10.5281/zenodo.20837905) and a methods paper (DOI 10.5281/zenodo.20837809) supplement this work.