Abstract
Boolean Satisfiability (SAT) is a central problem in theoretical computer science and a cornerstone of modern industrial reasoning systems. While state-of-the-art solvers based on Conflict-Driven Clause Learning (CDCL) achieve impressive results on many benchmarks, they remain fundamentally black-box systems and exhibit severe limitations on globally constrained instances. This paper presents a Glass-Box resolution engine that treats SAT resolution as a process of structural closure rather than heuristic search. On a frozen class of non-local SAT instances (global XOR/parity constraints encoded as CNF), this approach robustly closes all instances while producing complete, auditable resolution traces. These results do not claim to solve SAT in general, but establish that a meaningful subclass of NP problems is already better handled by a structural, auditable reasoning paradigm.Key Results
100% closure
All instances closed across all tested sizes (400–1600 variables), both SAT and UNSAT.
Glass-Box artifacts
Every execution produces a verifiable certificate, a complete event trace, and deterministic replay data.
Robust under global constraints
The target class (global XOR-CNF) is specifically chosen to defeat local reasoning strategies.
What This Paper Demonstrates
The paper establishes three properties on the target problem class:Structural resolution
A class of non-local SAT instances can be resolved through representational closure rather than heuristic search.
Process-level auditability
The reasoning process itself is an observable, replayable mathematical object — not just the final answer.
Experimental Summary
| Size (variables) | R3-MRM Closure Rate | CDCL Baseline Closure Rate |
|---|---|---|
| 400 | 100% | 40% (UNSAT only) |
| 800 | 100% | 40% (UNSAT only) |
| 1600 | 100% | 40% (UNSAT only) |
Scope and Non-Claims
The target class (global XOR constraints encoded as CNF) serves as a structural stress test. Results must be understood in relation to this structural specificity, not as a blanket claim over all SAT.Why This Matters
Beyond SAT, this work demonstrates that it is possible to resolve non-trivial NP-class problems while simultaneously producing artifacts suitable for independent audit. This challenges the widespread assumption that high-performance reasoning systems must necessarily be opaque.- For AI systems
- For mathematics
The same discipline of proof — explicit traces, convergence measurement, and verifiable certificates — is intended to transfer to broader Representation Model instantiations, including language and multi-domain reasoning.
Relation to R3-MRM
This paper constitutes the first published validation of the R3-MRM system. It demonstrates that the RM architectural class, instantiated in a mathematical domain and executed on the QDE computational core, produces measurable and independently verifiable results.R3-MRM
The Mathematical Representation Model that executed this validation.
RM Foundation
The foundational paper defining the Representation Model architectural class.
Citation
Mazzoni, S. (2026). Structural Resolution of Non-Local SAT Instances: Glass-Box Closure for a Subclass of NP Problems. RCUBEAI Research.All instances, logs, and public verification traces are available upon request or via a controlled API under the same experimental protocol.