Reality as a Constraint-Invariant Structure — Version 2: The Theoretical-Empirical Bridge

Reality as a Constraint-Invariant Structure develops a theoretical–empirical framework for studying whether a structural component can persist across heterogeneous observational representations of the same underlying system. The theoretical starting point is an ontic–epistemic separation between an inaccessible full system state S and observer-dependent representations Π_i(S). The invariant domain is formally defined as R = ⋂_{Π ∈ P} Π(S), where P denotes the admissible class of observational representations. Because neither the complete system state S nor the full admissible representation class P is empirically accessible, the study does not claim direct recovery of R. Instead, Version 2 introduces a falsifiable finite-family operationalization, R_candidate(P_m), connecting the theoretical definition to empirical testing. The empirical program evaluates eight admissible representations across three operator classes using multi-asset financial data. Representation-specific matched-null ensembles are generated using phase randomization and Iterative Amplitude Adjusted Fourier Transform (IAAFT) surrogates. A locked two-stage R-extraction protocol applies spectral consensus testing, max-Z family-wise error rate (FWER) calibration, and uniform persistence testing. For B_R = 1000 matched-null realizations, two spectral ranks survive both stages of the protocol. The resulting candidate subspace has dimension dim(R_candidate) = 2, with spectral and persistence FWER p-values reaching the Monte Carlo resolution limit 1/(B_R + 1) = 1/1001 ≈ 0.000999. The result provides empirical support for a non-empty, two-dimensional representation-invariant candidate within the tested finite family. It does not establish R_candidate = R, objective reality, or direct access to an ontological substrate. Rather, it establishes a falsifiable bridge between the theoretical concept of constraint-invariant structure and an empirically extractable finite-family candidate. The paper includes the complete research trajectory, operational protocol, matched-null architecture, empirical results, interpretation boundaries, source-code components, terminal execution records, coordinate-extraction framework, public-facing explanatory layer, and a methodological self-assessment. This work forms part of the open Structural Depth research program developed through Market Alchemy Research.