Blind Structural Identification from Anonymous Scalar Responses: A Finite Adversarial Test of a Three-Mode Exterior U(3) Architecture

A Reproducible Adversarial Test of Structural Identification from Blind Scalar-Response Data

抄録

Can a hidden representation architecture be identified from anonymous scalar-response measurements when the generator matrices, representation labels, and physical interpretation are withheld from the classifier? We investigate this question in a finite adversarial setting based on a three-mode fermionic exterior representation of the unitary group U(3).
Each hidden Hermitian generator is first reconstructed from an information-complete measurement design using fifteen scalar responses on each four-dimensional parity block. All subsequent structural decisions are made exclusively from these reconstructed generators, without access to representation labels or the physical interpretation of the underlying system.
The classification pipeline combines several independent structural diagnostics. These include real Lie-algebra closure and the dimensions of the resulting algebra and its derived algebra, parity-resolved commutant dimensions and invariant-block multiplicities, a scale-free residual measuring the balance of the central component, and a cross-parity correlation of cubic tensor structures. The adversarial alternatives are deliberately constructed so that different false models share selected structural signatures with the target.
Within the specified exact benchmark, however, the target is separated from all supplied alternatives. Its reconstructed generators form a nine-dimensional Lie algebra with a one-dimensional center and an eight-dimensional derived algebra. The two parity sectors have matching commutant dimensions and each exhibits a one-plus-three invariant-block structure. The central charges are balanced between the two sectors, while the cross-parity cubic correlation has the characteristic negative sign.
Same-irreducible models, models with a distorted central component, models with a direct-sum structure consisting of a U(1) sector and an SU(2) sector, and irreducible four-dimensional control models are rejected by the diagnostics specifically designed to resolve these competing structural possibilities.
The reconstruction residuals are at the level of 10 to the minus 15, and all reported classifications are independently regenerated by the accompanying executable package. Perturbed cases support only the weaker conclusion of nontrivial approximate reducibility and are therefore not promoted to approximate exterior-representation identification.
The result is a reproducible blind-discrimination test within a pre-specified finite adversarial model class. It demonstrates that anonymous scalar responses can contain sufficient structural information to distinguish the target representation architecture from the supplied false alternatives when combined with an information-complete reconstruction and a fixed diagnostic pipeline.
No claim of universal uniqueness beyond the tested model class is made. This limitation does not affect the finite discrimination result established here.