(Σ^2_1)^uB STATEMENTS ARE DOWNWARDS ABSOLUTE TO HOD

The paper presents a clear logical progression, building from definitions and known results to lemmas, propositions, and the main theorems. The arguments are structured rigorously, though dense.

Strengths: Uses formal mathematical proofs., Definitions are provided or clearly referenced., Builds upon established theorems and techniques in the field.
Weaknesses: Some proofs are very brief or refer to standard arguments without detailing steps, requiring significant prior knowledge., The complexity of the subject matter makes dense sections challenging to follow for non-experts.

All claims presented as theorems or propositions are supported by mathematical proofs within the text or by explicit reference to prior established results in the literature.

The paper presents novel theorems, particularly Theorem 6.4 and 6.6 regarding downwards absoluteness to HOD, and explores new connections between universally Baire sets via OD trees and scales. It also corrects a specific error in previously published work.

The results are highly significant within the specialized field of set theory, addressing fundamental questions about absoluteness and the structure of HOD under strong axiomatic assumptions. They contribute to the ongoing research program related to inner models and large cardinals.

Strengths: Uses precise mathematical terminology., Definitions are explicitly stated or referenced.
Areas for Improvement: Highly dense and technical writing style requires deep expertise in the specific subfield of set theory., Proofs are often very concise, omitting steps that would be necessary for readers without advanced knowledge.