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The aim is to develop a unified internal algebra for regime specifications with a focus on dependency systems.

August 5, 2026Open Access

The Indexed Specification Algebra: One Object, Seven Theorems, and a Factorization Engine for Regimes as Dependency Systems

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The aim is to develop a unified internal algebra for regime specifications with a focus on dependency systems.
Developed the internal algebra of declared-regime specifications post Identity-Persistence results.
Constructed a universal gate quotient for determining gate status and utilized finite system results for proofs.
Performed realizability analysis distinguishing various dependency systems and their representations.
Showed that factorization-based recoverability coincides with quotient-level semantic closure.
Established separate structures for minimal keys and interaction effects, providing insight into their distinctions.
Countermodels evidenced that mixed determination does not always yield closure, presenting limitations in quotient-level recoverability.

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Randomized trial explores quotient-level recovery and closure in dependency systems, indicating significant implications for foundational algebra.

Devin Bostick (2026) studied this question.

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Randomized trial explores quotient-level recovery and closure in dependency systems, indicating significant implications for foundational algebra.