Randomized analysis of closure structures in doubly-even Adinkra topologies, indicating new structural insights.
González Metric Limit Mechanics I (GMLM-I) introduces an informational closure formalism for finite doubly-even Adinkra topologies. The paper defines primitive four-closures, the closure hypergraph, the four-closure rank ratio, and configurational primes as irreducible connected components of primitive closure incidence. Applied to the sixteen-directional doubly-even code classes D16 and E16, the construction shows that both classes share the same size, rank, weight enumerator and number of primitive four-closures, while differing in closure connectivity. In GMLM-I terms, D16 forms a single global configurational prime, whereas E16 decomposes into two configurational primes of size eight. The result demonstrates that the GMLM closure invariant detects structure not captured by ordinary weight enumeration: not only how many admissible codewords exist, but how their supports close. The paper includes a reproducible finite computation in Python verifying the rank and configurational-prime distinction between D16 and E16. GMLM-I is intended as the discrete closure-layer paper preceding GMLM-II, which develops the metric, projection and dynamical layers of the framework.
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Pablo González Ferreiro (2026) studied this question.
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