Scale-Invariant Topology (SIT) Baryonic Screening of the Cosmological Constant and MOND-like Phenomenology

Baryonic Screening of the Cosmological Constant and MOND-like Phenomenology in Scale-Invariant Topology This research note derives a direct, falsifiable prediction of the Scale-Invariant Topology (SIT) framework. We propose that the cosmological constant ($\Lambda$) is not a universal invariant but a dynamic quantity subject to local screening by baryonic matter. Core Mechanism: In the SIT framework, vacuum energy represents the relaxation rate of geometric strain. Baryonic matter, modeled as high-frequency topological defects, acts as a "relaxation sink," locally suppressing the effective vacuum tension. We term this effect Baryonic Screening. Key Results & Predictions: Emergent MOND Dynamics: The spatial gradient of the screened vacuum pressure generates an effective acceleration force. This force naturally recovers the MOND acceleration scale ($a_0$) and the Baryonic Tully-Fisher Relation (BTFR) without modifying the fundamental gravitational constant $G$ or postulating dark matter particles. Relaxation Shadows: We predict that spiral arms in disk galaxies create localized "shadows" of reduced vacuum pressure. This leads to non-axisymmetric dynamical signatures and rotation curve features that correlate strictly with baryonic surface density, obeying Renzo’s Rule. ** macroscopic Casimir Effect:** The mechanism is mathematically analogous to a macroscopic gravitational Casimir effect, where matter boundaries restrict the available modes of vacuum relaxation. This work serves as the observational companion to the foundational paper "Scale-Invariant Topology (SIT): A Unified Topological Framework for Spatially-Driven Relaxation Dynamics", translating the Protocol 61 ontology into testable astrophysical signatures.