Theoretical Propositions

The preceding sections developed the conceptual architecture of Correspondence Theory. The theory now contains an ontology, two formal constructs, and one canonical mechanism. This section presents the proposition architecture that follows from that theory. The purpose is not to test the theory empirically or define measures. It is to state the expected theoretical relationships that future empirical work can investigate.

Correspondence Theory distinguishes predictions, propositions, hypotheses, measurements, and empirical tests. Predictions describe what the theory expects to occur. Propositions express those expectations as formal theoretical statements. Hypotheses operationalize propositions for empirical testing. Measurements define observable indicators, variables, and metrics. Empirical tests evaluate whether hypotheses are supported. This section remains at the proposition level.

Table 4 - Canonical Proposition Summary

The canonical proposition catalog organizes propositions into four categories: structural, dynamic, organizational, and AI-native. Structural propositions concern representations, relationships, and representation networks. Dynamic propositions concern Correspondence Loop behavior. Organizational propositions concern Organizational Correspondence and Cognitive Integrity. AI-native propositions concern organizations in which AI-generated representations increase the speed, volume, or distribution of organizational cognition.

This categorization is not intended to create additional constructs. It is a manuscript and research-program device for organizing expectations derived from the theory. Each category traces back to canonical elements already introduced. Structural propositions trace to the representation-network ontology. Dynamic propositions trace to the Correspondence Loop. Organizational propositions trace to the dependency between Organizational Correspondence and Cognitive Integrity. AI-native propositions trace to the claim that AI increases the rate and volume of representation-network change.

Structural propositions express the theory's expectation that representation-network maintenance matters for Organizational Correspondence. The first proposition states that higher quality representation-network maintenance is positively associated with Organizational Correspondence. The second states that representation-network degradation accumulates when Correspondence Loop activities fail to preserve semantic and causal relationships. The third states that increasing representation complexity without corresponding maintenance capacity reduces Organizational Correspondence.

Dynamic propositions follow from the mechanism. They concern the activity of the Correspondence Loop rather than the constructs themselves. The fourth proposition states that the frequency of local Correspondence Loop mechanism instances increases with the rate of meaningful representation-network change. The fifth states that higher Mechanism Readiness improves recovery from representation-network degradation. The sixth states that successful Correspondence Revision reduces accumulated correspondence degradation within the affected region of the representation network.

Organizational propositions connect the two formal constructs. The seventh proposition states that higher Organizational Correspondence is positively associated with higher Cognitive Integrity. The eighth states that representation-network degradation precedes observable declines in Cognitive Integrity. The ninth states that organizations with similar resources, strategies, and governance may exhibit different levels of Cognitive Integrity because of differences in representation-network maintenance.

AI-native propositions specify expected implications for organizations in which AI systems generate, modify, or act upon organizational representations at increased speed and scale. The tenth proposition states that AI-native organizations require more frequent Correspondence Loop activation than organizations with lower rates of representation-network change. The eleventh states that increasing AI-generated representation volume without corresponding increases in representation-network maintenance increases correspondence degradation risk. The twelfth states that AI systems improve organizational cognition only when representation-network maintenance scales with AI-generated representation change.

These propositions are theoretical statements rather than empirical findings. They should not be read as validated claims. Their value is architectural: they show how the theory can generate testable expectations without redefining its constructs or mechanism. They also provide a disciplined bridge from conceptual theory to future research. Future hypotheses should derive from these propositions rather than creating independent theoretical claims.

The proposition architecture also protects the theory from performance reductionism. Correspondence Theory does not claim that high Organizational Correspondence guarantees organizational success or that low Cognitive Integrity explains every failure. Market conditions, regulation, leadership, resources, competition, politics, and external shocks all matter. The propositions focus on relationships among representation-network maintenance, Organizational Correspondence, Cognitive Integrity, and AI-native representation change.

The propositions also indicate the empirical shape of the research program. Structural propositions point researchers toward evidence concerning representations and relationships. Dynamic propositions point toward traces of mechanism activity, including updates, evaluations, and revisions. Organizational propositions point toward inferred relationships between correspondence conditions and Cognitive Integrity. AI-native propositions point toward contexts in which representation-network change is accelerated by machine-generated artifacts. These are research directions, not measurement specifications.

The publication version summarizes these propositions for scholarly presentation; future empirical work should retain traceability to the underlying proposition catalogue without exposing repository identifiers in journal-facing prose. Doing so preserves cumulative theory development. It allows later papers to derive hypotheses, identify observable traces, construct variables, and design empirical studies while remaining traceable to the conceptual model developed here.