Formal Foundations of Architecture Science

Formal Foundations of Architecture Science develops a bounded formal scaffold for studying architectures as scientific objects while explicitly separating definitions, conceptual propositions, research hypotheses, formal results, and empirical claims. The paper introduces a provisional representation of an architecture in terms of entities, relations, states/configurations, transformations, and constraints, and develops a typed framework for examining architecture state spaces, transformations, identity and succession, formation, observation and set-valued reconstruction, reachability, conditional controllability, multi-objective evaluation, uncertainty, and model-relative invariance. The work is positioned explicitly against mature predecessor territories including architecture description, dynamical and transition systems, formal verification, graph and model transformation, observational equivalence, identifiability and reconstructability, compositional methods, optimization, resilience, uncertainty quantification, and control theory. It does not claim these constituent mathematical resources as novel Architecture Science inventions. The residual scientific question is whether architecture-specific relations among formation, identity, succession, architecture-changing transformation, reconstruction, admissibility and constraint inheritance, and cross-domain comparison yield nonredundant formal results or empirical value beyond what is already captured by established fields. This release does not claim a complete mathematical theory of architecture. Architecture Science-specific differentiating claims remain at the level of research hypotheses or lower. No Architecture Science-specific theorem, lemma, impossibility result, demonstrated multi-domain result, candidate architectural law, or mature architectural law is claimed. The release is accompanied by the AS-03 Supporting Constitutional & Scientific Record v0.1, which preserves the manuscript's claim ceilings, closest-work constraints, notation semantics, limitations, counterexamples, adversarial objections, anti-immunization rules, provenance boundaries, and stabilized bibliography. Structured internal human–AI scientific review is disclosed in the manuscript and is not represented as independent external peer review.