Minimum Economy of Relational Information: Minimal canonical architecture, closure protocol, and execution mandate

This work presents the canonical version frozen for execution of the Minimum Economy of Relational Information, an exploratory program designed to investigate whether difference, comparison, closure, identity, dimension, and dynamics can be constructed from the minimum necessary relational structure. The proposal strictly distinguishes four levels: ontological, canonical, formal, and physical. No translation between these levels is treated as automatic. Each step must state the problem it addresses, the discriminating difference it introduces, the additional structure it requires, its epistemic cost, its remaining residue, and the result that could refute it. The architecture separates the first unoriented difference from the first oriented comparison. A structure of order is first obtained from the closure operator. Linear representation is introduced afterward through a system of discriminants. The generative operator and the projector onto its active space belong to a subsequent algebraic layer. Metrics, norms, adjoints, and physical magnitudes are incorporated only after their normalization and representational freedom have been explicitly declared. The document distinguishes the space on which the generative operator acts from the channel made visible by a particular interface. This separation prevents the active projector from being identified with the channel projector and allows the distinction between visible and conserved content to depend explicitly on the relation between systems. The proposal also establishes a state machine consisting of RESOLVED, OPEN, SUPERPOSED, TRANSFERRED, and COLLAPSED. Every construction must be assigned one of these states together with its dependencies and falsifiers. A locking protocol is also introduced to prevent physical correspondences from being formulated through parameters, profiles, or scales selected after the target observable is known. The branches concerning two-state systems, quantization through monodromy, stratified dynamics, the proton, chemistry, and gravity are presented as conditional and falsifiable research programs. No experimental validation of these correspondences is claimed. The main contribution is not the presentation of a completed new physical theory, but the construction of a minimal and auditable architecture capable of distinguishing which results have been derived, which steps require independent decisions, and under which conditions a construction must be abandoned or transferred to a different formulation. This version closes the stage of general architectural reorganization and is frozen for execution. Subsequent results must consist of formal proofs, computational implementations, or previously locked predictions rather than further interpretative extensions of the architecture.