Finite-Range Dyadic Residual Organization for Exact Reconstruction

A finite-range reconstruction method based on dyadic residual organization is proposed. Theobjective is not to derive new global asymptotic formulas, but to organize exact reconstructionon bounded domains by separating a discrete target object into a structural base layer and aresidual layer observed under dyadic refinement. The method is computational, reversible on theprescribed range, and especially suitable when the base layer arises from an exact identity or anexact recurrence.Two case studies are presented. The first uses a factorial-derived reduced kernel obtained froman exact odd-part decomposition and then observed modulo a fixed dyadic mask. On the testedfinite range, the refinement of branch prototypes is governed by a short alphabet of residualmutations, and exact reconstruction on the bounded range is immediate once branch prototypesand leaf residuals are retained. The second case uses Fibonacci numbers, where separation intoodd core and 2-adic valuation reveals a dyadic correction law relative to golden-ratio growth.In this second case, the paper does not claim a complete generative residual mechanism, butdocuments a second exact-structure phenomenon compatible with the same dyadic viewpoint.The contribution is therefore methodological and bounded-range: a framework for exact finitereconstruction and structural residual organization of discrete objects with compatible dyadicstructure. No claim of universal compression, universal automaton generation, or universalasymptotic replacement is made.