B08: BRISM Interface Geometry and the Infrared Approximation of the Fine-Structure Constant: A Technical Fact Sheet on π-Structure, Minimal SU(5) Leakage, and α⁻¹ at 10⁻⁹ Accuracy

This technical fact sheet summarizes the structural and geometric foundations of the BRISM (Bulk–Brane Interface Stability Model) framework as they relate to the infrared prediction of the fine‑structure constant. Under the interface constraints of phase neutrality, positivity, σ‑additivity, norm conservation, and two‑sided Naimark–Stinespring embedding, a unique dimensionless additive functional arises: X = 4π³ + π² + π This expression reflects invariant contributions from U(1), S²/SU(2), and volumetric/SU(3) structures. A minimal simple completion of the interface algebra within SU(5) introduces a first‑order, parameter‑free correction: α⁻¹_BRISM = X − 1/(24X) The corrected value matches the CODATA 2022 infrared value of α⁻¹ at the 10⁻⁹ accuracy level. In percentage terms, this amounts to approximately 99.99999960% Accuracy. The coherence scale ε = 1/π², previously identified in BRISM’s dark‑matter phenomenology, appears as a structural constant linking interface geometry to observable coupling behavior across scales. No closed‑form identity is claimed; instead, the result is interpreted as an emergent, stability‑fixed interface quantity within the BRISM projection framework. *** For the current consolidated overview of the BRISM framework, readers are referred to: *** *** BRISM after Ten Months: Status, Claims, Tests, and Future Directions. ****** https://doi.org/10.5281/zenodo.23495535 ****** This article represents the most up-to-date overview of the BRISM research program and serves as the primary review and status paper of the series. ****** Further BRISM articles and preprints can be accessed through the author’s ORCID profile: ****** https://orcid.org/0009-0008-7503-6012 ***