Replication of Carry ‑ Structured Block Factorization Structural One ‑ Point Convergence via the Three ‑ World Model

This study replicates the Carry ‑ Structured Block Factorization model proposedby Kakuho (2026) and confirms that its carry ‑ propagation structure in long multiplicationprovides a valid framework for structural integer factorization. Building onthis foundation, we introduce the Yutori ‑ Style Three ‑ World Model—Head, MiddleBand, and Tail—derived from the Yutori Material Engine, and use it to reinforce thetheoretical basis of structural one ‑ point convergence for large integers.The replication demonstrates that the lower three digits (mod 1000) coincide withthe upper bound of the carry and function as a “tail wedge” that completely fixes theterminal alignment. The upper 5 – 8 digits retain dense information about the ratio anddistance between factors, and when the fifth digit is zero, the “head closes,” locking thestructural degrees of freedom. Furthermore, the digit distribution and centroid of themiddle band force intermediate blocks to converge onto a single structural line.Through these three structural constraints, even a 925 ‑ digit (3072 ‑ bit) integercollapses to 116 blocks under 8 ‑ digit block decomposition, enabling factor determinationwithout search. This model represents a structural reconstruction approachdistinct from classical number ‑ theoretic or algebraic methods, showing that the internalstructure of an integer forces its factors to converge to a single solution.