This document provides author-side proof notes for the General Theory of Cognitive Structuring. Its purpose is to record, in a compact and operationally useful form, how the main formal results of the series are expected to be checked, what their minimal proof logic is, what typical risks of misreading or false strengthening arise, and what later proof-compendium work may still be needed. The note is not yet a full proof compendium. It functions as an intermediate canonical layer between the collected proposition/theorem layer, the proof-status register, and any future proof compendium. For each main result family, it records what should be checked, the expected result, the minimal proof idea, the main dependencies, typical assumptions, common proof risks, and what remains missing for later full proof extraction. This document is intended to preserve author-side control over the emerging canonical proof layer of the theory.