BU54 | Layered Technical-Path Probing under B_U BU27 / BU20 x BU50, Structured Pruning, Multi-Step Zeroing, Residual Relocation, Minimal-Structure Capture, and SIGReg as a High-Fidelity Information-Projection Shadow

This paper develops BU54 as a layered technical-path probing framework under Single-Universe Boundary Consistency, B_U. Its central claim is that BU27 provides the audit framework for cross-scale fine restructuring, while BU50 provides the discipline for capturing the minimal admissible structure inside each cleared window. Technical directionality is therefore not obtained by blind search or one-step endpoint design, but by repeated clearing, residual relocation, coherence coupling, and minimal-structure capture across strata. BU54 formalizes BU27 as the clearing and structured-pruning layer. It audits local disturbances by testing whether residuals can be zeroed, relocated, orthogonalized, coherently retained, and settled. BU50 then acts as the stake-planting layer: after a cleared background is obtained, it searches for the first lawful nonzero standing S_{\min,L_n}. Each S_{\min} becomes the carrier or stepping stone for the next technical stratum. The paper further defines the engineering interface of BU27 × BU50. Light, electricity, force, heat, magnetism, chemical potential, boundary conditions, and feedback control are classified as projection-level tuning means. Their role is to adjust field states, object boundaries, and residual distributions until coherence, coupling, stable retention, and settlement become possible. As a case layer, BU54 reclassifies SIGReg as a high-fidelity shadow of clearing discipline in the information-projection stratum. SIGReg may approximate zero-mean clearing, isotropic de-coupling, sliced audit, and anti-collapse regularization, thereby stabilizing latent manifolds for planning and materials-modeling tasks. However, it remains a projection model with residuals, gaps, and out-of-distribution risk; it cannot replace ontic audit or grant reality-standing. BU54 concludes that technical progress should proceed through layered clearing, structured pruning, and minimal admissible structure capture.