MA-05–MA-10 | Certified Mathematical Aggregates A Unified Architecture for Compositional Contracts, Distributed Interfaces, and Information Lower Bounds Synthesis of the MA-05–MA-10 research sequence

This paper consolidates six executable research notes, MA-05 through MA-10,into one narrowly scoped architecture for certified mathematical aggregates:components whose public contracts are sufficient for specified forms of safecomposition, information-minimal observation and substitution. We separate fourmathematical layers: centralized admissible-action synthesis, contextual bound-ary minimization, distributed zero-error communication, and transportation ofinformation lower bounds across additional ports. Explicit propositions charac-terize minimum command palettes, separator languages, simultaneous-messagecompatibility, graph/hypergraph conflicts, a structured linear promise, and thejoint communication-budget region of a multi-sender linear-helper system. Corre-lated uncertainty, quantifier order, resource accounting, horizon, and observationtopology are treated as substantive interfaces rather than implementation de-tails. The prior six independent verifier programs have been rerun against theirarchived passports; all completed successfully. None of these checks establishesphysical-model fidelity or priority over existing literature. The main contributionof the present document is a unified, falsifiable engineering-mathematical spec-ification with an explicit novelty audit. The individual propositions rely largelyon established techniques including variable elimination, automata minimiza-tion, zero-error functional compression and linear algebra. No new foundationaltheorem is claimed.