A Constitutive Microtexture Before Spacetime: Pregeometry, Transgeometry, Representation Theorems, and Falsifiability in the Fractal Consistency Law

This deposit contains Paper I of the FCL Microtexture v1.0 series, presenting the formal foundations and certification of a constitutive microtheory developed within the Fractal Consistency Law (FCL) research program. The work addresses a fundamental structural problem in quantum gravity: many candidate approaches begin with mathematical objects that already presuppose part of the geometry they seek to explain, such as manifolds, metrics, causal structures, or Hilbert spaces defined over geometric backgrounds. FCL Microtexture v1.0-F instead adopts an explicitly pregeometric starting point and treats geometric, Hilbert-space, matter, gauge, black-hole, and cosmological structures as typed downstream completions rather than primitive entities. The frozen formal core is organized around five constitutive axioms acting on typed texture objects, refinement morphisms, admissibility domains, physical quotient spaces, and a structural inconsistency functional. The Principle of Minimum Inconsistency (PMI) is formulated as constrained minimization over admissible sectors, while No Fragmentarity is implemented through quotient-compatible descent of physical maps. The paper establishes finite and inductive-limit representation results, a PMI minimizer-state-face theorem preventing unjustified unique-state selection, a faithful reduced-state construction, and a Gelfand-Naimark-Segal route to Hilbert representation without assuming Hilbert-space ontology at the fundamental level. It further introduces an FCL-specific concept of transgeometry for physically persistent relational states not required to possess an ordinary manifold embedding, together with a restricted cohomological parity-record channel and a conditional Cayley-Menger-based trans-embedding diagnostic. Exact, conditional, representational, and no-go results are explicitly separated. A five-observable Texture Observable Suite is defined, together with a versioned certification protocol designed to distinguish formal autonomy from empirical validation. The principal result of Paper I is deliberately limited: FCL Microtexture v1.0-F is established as a formally autonomous constitutive microtheory possessing a nonempty model and representation architecture, typed emergence interfaces, a theorem/no-go registry, and an explicit falsifiability contract. The work does not claim that the physical universe has already been empirically demonstrated to possess the proposed microtexture. Series: FCL Microtexture v1.0Paper: I — Formal Foundations and CertificationCertification identifier: CIT-106Version: 1.0-FResearch area: Fundamental theory / mathematical physics / quantum gravity