Proof Notes for the General Theory of Cognitive Structuring

Abstract

This document provides the proof and derivation routes associated with the stable result inventory of the Version 2.0 General Theory of Cognitive Structuring (GTCS). For each registered result, it records the relevant assumptions, proof or derivation method, imported proof dependencies where present, witnesses or countermodels, boundary cases, verification hooks, and transfer restrictions that determine how the result may be reused. The current proof layer covers all 45 stable results and separately records the boundary and non-promotion constraints required to prevent false strengthening. The owner audit leaves no unresolved owner proof obligations, so the document is organized around the proof or derivation basis that supports the current closed status rather than around a queue of future proof-development tasks. Proof Notes do not create new result identifiers, rewrite result statements, or assign stronger theorem status. A verified boundary remains a boundary unless it is independently registered as a stable result, and formal proof completion does not by itself establish empirical validation. The document is therefore a proof-route companion to the result inventory rather than an independent source of theory content.