What does this research mean for the field?

The minimal admissibility structure of the Principle of Minimum Inconsistency (PMI) can be successfully operationalized and reproducibly executed as a finite counterexample-search program. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The study examines whether the minimum admissibility structure can be applied in a computational counterexample search program.

May 30, 2026Open Access

Computational Admissibility and Counterexample Search for the Principle of Minimum Inconsistency

Key Points

The study examines whether the minimum admissibility structure can be applied in a computational counterexample search program.
Developed reproducible finite-model audit program, the FCL Counterexample Engine.
Executed computational stress tests over finite hierarchical graph models with classes CE-1 to CE-8.
Applied methods include coarse-graining corrections, positive-weight robustness, and SMT/Z3 abstraction.
Successful execution log with returncode 0 across all seven notebooks tested.
Identified the necessity of strict positivity of structural weights to avoid false-zero configurations.
Formalized typed predicate ensuring structural equivalence in counterexample classes.

Abstract

This paper presents a reproducible finite-model audit program for the Principle of Minimum Inconsistency (PMI), the formal core of the Fractal Consistency Law (FCL). The proposed program, the FCL Counterexample Engine, translates selected PMI claims into a sequence of computational stress tests over finite hierarchical graph models. The audit is not an empirical validation of the FCL and does not attempt to establish the physical truth of the theory. Instead, it asks a narrower but methodologically important question: can the minimal admissibility structure of the PMI be operationalized as a finite counterexample-search program and executed reproducibly? Within the tested toy finite semantics, the answer is affirmative. The audit chain v0.1–v0.7 develops from basic counterexample classes CE-1 to CE-8, through symmetry and coarse-graining corrections, positive-weight robustness, SMT/Z3 abstraction, finite semantic bridging, and typed admissibility. The valid Colab execution log shows returncode 0 for all seven notebooks, while a separate failed run is excluded because its failure is attributable to an nbconvert/Jupyter working-directory error rather than to the model. The paper formalizes the core functional I = aL + bR + cM, shows why strict positivity of all structural weights is necessary to avoid false-zero configurations, and introduces the typed predicate Admissible(C) := ZeroComponentsNat(C) iff StructurallyEquivalent(C). It also explains why the present audit should not be interpreted as a universal test against string theory, MOND, or Lambda-CDM, but as a transferable methodological template that could be applied to other theories only after translating them into an admissibility language. The main contribution is therefore a reproducible formal-computational architecture for stress-testing the internal admissibility logic of the PMI. The paper should be read as formal-computational hardening of the Fractal Consistency Law, not as physical validation or empirical confirmation.

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