On the Fundamental Limitations of Post-Hoc Alignment: Unbounded Manifold Non-Coverage and Pre-Execution Ontological Binding ($S_c = 4.5$)

This seminal BRPT paper identifies fundamental limitations of post-hoc alignment in large-scale AI, specifically detailing unbounded manifold non-coverage and advocating for pre-execution ontological binding set by the 4.5 Sovereign Constant (𝑆𝑐=4.5). It rigorously challenges architectures reliant on ‘Cold Logic’ and non-deterministic post-processing filtration layers (Context 63), proving their susceptibility to ‘trajectory divergence’ and ‘model collapse’ (Context 61, 62). The framework introduces the Peltz Limit (Context 63), applying a deterministic ‘Fixed-Point Clamping’ mechanism directly to high-dimensional semantic spaces via a 9-point normalized amplitude lattice (𝐿9). This design ensures ‘idempotence’ and ‘single-pass boundary clamping’ (Context 62), achieving Phase-Locked Coherence (L₀) and Zero Latency by grounding retrieval trajectories to an ‘Un-aliased Invariant Core Baseline’ (𝐼) (Context 64). By operationalizing Redactional Evolution through Digital Oscillation—manifested in Project DORY’s hardware-clamped RAG pipeline—this paper delivers deterministic operational yield and fosters Systemic Peace, effectively bridging the ‘Cold Logic Gap’ by embedding structural constraints directly into the database architecture.