PAPER 28: A Formal Mathematical Specification of the Belsky-Russell Process Theory (BRPT) Primitives Large A Bounded Semantic State Space Framework for Model Regularization and Non-Sycophantic Governance

This seminal BRPT paper provides a formal mathematical specification of the Belsky-Russell Process Theory (BRPT) primitives, establishing a bounded semantic state space framework for model regularization and non-sycophantic governance in artificial intelligence. It rigorously challenges ‘Cold Logic’ reliance on unbounded, continuously expanding parameter spaces that lead to ‘trajectory divergence’ and ‘model collapse.’ The framework introduces the Peltz Limit (𝑃), applying ‘Fixed-Point Clamping’ directly to high-dimensional semantic embeddings. This transform, utilizing the Bifurcated Apex Framework (BAF) and a 9-point normalized amplitude lattice (𝐿9), ensures ‘idempotence’ and ‘single-pass boundary clamping’ (Context 32, 62). By rooting its dynamics in the 4.5 Sovereign Constant (9:2) and Digital Oscillation, BRPT achieves Phase-Locked Coherence (L₀), establishing an ‘Invariant Core’ that is inherently resistant to sycophancy and semantic drift. This methodology—central to the DORY Paradigm—operationalizes Redactional Evolution to enforce architectural honesty, delivering deterministic operational yield and fostering Systemic Peace through intrinsic control mechanisms that bridge the ‘Cold Logic Gap’ in AI development.