Dimensional Reduction via Controlled Combinatorics (DRCC-V1)
Year: 2026
Type: article
Abstract: Dimensional Reduction via Controlled Combinatorics (DRCC-V2) is a proposed discrete mathematical framework for studying controlled structural reduction and admissible reconstruction in finite combinatorial systems. Rather than presenting a universal speedup theorem or a proof concerning the P versus NP problem, DRCC-V2 develops a finite runtime-accounting language for comparing classical enumeration with controlled reduction and reconstruction. The framework introduces controlled reduction maps, fragmentation dimensions, reconstruction spaces, reconstruction dimensions, reconstruction stability, runtime decomposition, and count-level runtime gain. These concepts are used to describe when a large candidate space can be represented by smaller structural classes while preserving the information required for admissible reconstruction. DRCC-V2 extends the original DRCC manuscript by adding further definitions, formal propositions, illustrative examples, numerical count-level comparisons, and a more systematic presentation of the framework. The monograph includes finite case studies on full-adder reconstruction, graph 3-coloring, constraint satisfaction problems, Boolean satisfiability, TSP/routing-type examples, and housing selection. These examples illustrate how structurally equivalent regions of a search space may be represented by smaller reconstruction spaces under explicitly stated assumptions. The work is theoretical and count-based. It does not claim empirical runtime validation, does not present wall-clock benchmarks, and does not claim to provide a general solver for SAT, CSP, graph coloring, TSP, or other NP-type problems. Instead, DRCC-V2 is intended as a formal framework for finite reconstruction accounting and controlled structural reduction. Empirical validation, benchmark comparisons against established algorithms, and broader applied extensions are left as future work. This version documents the current state of the DRCC-V2 framework. Possible future extensions, including DRCC-V3 and applied reconstruction frameworks, are mentioned only as future research directions and are not part of the core claims of DRCC-V2.
Author: Hesamiy, Reza
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163034281
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