2026-10-14T10:07:59Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33472975 2026-10-14T06:52:22Z category_30121 category_29803 item_type_12 month_year_10_2026

Scale-Invariant Boundary Geometry: A Geometric Ladder from Point to Scale Mitchell Hoppe (24728200) Atomic and molecular physics Mathematical physics not elsewhere classified Theoretical physics outreach <p dir="ltr">This work presents a simplified geometric framework exploring how relationships emerge from basic structures: point, line, square, and triangle. The framework examines connections between dimensional progression, square and triangular geometry, root relationships, the combined boundary term , and the reciprocal scale pair �. The focus is on identifying minimal geometric relationships that may describe repeating patterns across scales. Established mathematics is separated from interpretation and open questions. This document does not claim to replace existing physics, but explores whether simple geometric transition rules can provide a useful cross-scale description.</p> 2026-10-14T06:52:22Z Text Preprint 10.6084/m9.figshare.33472975.v18 https://figshare.com/articles/preprint/Scale-Invariant_Boundary_Geometry_A_Unified_M_0_Lattice_Model/33472975 CC BY 4.0