A Blockwise Overflow–Inheritance Framework in 2ⁿ Bits: From Scalar Construction to Cross-Hereditary and Spatial Models

We present a methodological framework based on local truth tables in 2ⁿ-bit cells, explicitseparation between retained state and overflow, and iterative inheritance of the overflow intosubsequent blocks. The framework is operational and minimal: one starts from a local celllaw, determines what remains inside the cell and what overflows, and then propagates theoverflow as hereditary information. From this mechanism, one obtains scalar constructions, blindinterval-driven confirmation, functional blockwise representations, parallel multi-chain systems, crossed hereditary matrices, and spatial propagation models. The logical foundation is intentionally restricted to the three primitives AND, OR, and NOT, consistent with the classical relation between Boolean symbolic structure and switching-circuitrealization, while all other operators are treated as derived. We give concise numericalexamples for √2, blind hexadecimal recovery of e from its defining factorial series using intervalnarrowing, hereditary representation of ln (2), a prime-mask comparison using mod 6 andmod 30, a crossed two-channel complex toy model together with the natural complex-dynamicalextension z (n+1) = z (n) ²+ c, and a minimal three-dimensional directional inheritance system. The goal is not to claim a replacement for standard mathematics, but to show that a broadfamily of objects can be reparameterized through the same local cell / overflow / inheritancearchitecture, with a direct path toward dedicated parallel hardware realization.