ReArt: Relational Generation under Transformable Articulation

Abstract

We study reconstruction when a relation law, the represented subspace, and the observation context may all change. ReArt treats finite carriers as local articulations rather than terminal structures and separates endogenous relation generation, rearticulation, access/domain change, algebraic re-expression, and genuine structural deformation. For metric Lie algebras we use the canonical Lie-growth filtration and alternating layer maps to obtain layer-resolved growth, constrained articulation diagnostics, and exact transport identities. A calibrated first-order observation factors as Y=A(h)-VB; restriction to ker B isolates target information when full cause recovery fails, while a minimum-modulus criterion quantifies first-order separation. Under a positive invariant metric, generated extensions can activate internal visibility without implying algebraic closure or autonomous reduced dynamics. The omitted-relation blocks also control projected Jacobi defects and reduced dynamical memory. We reconstruct the full cross-return kernel from diagonal return and the projected Jacobiator, identify its minimal generated space up to isometry, and relate diagonal return to short-time resolved dynamics. For moving orthogonal articulations the effective coupling is QLP-Q dot(P)P, giving an exact two-time memory equation and a quadratic memory-omission bound. Finite-data certificates cover both known projections and known-rank learned projections under explicit calibration assumptions. An operational extension makes return reconstruction experimentally selective. With coordinate diagonal returns and prescribed cyclic data, mixed diagonal probes are complete exactly when the graph of omitted probes is four-cycle-free. For six represented directions, eight mixed probes are necessary and sufficient within this data class. In a calibrated two-qubit Pauli-response study over 24 local configurations, the sparse protocol predicts held-out ordered-pulse contrasts. After coordinate pruning and coefficient-weighted shot allocation, 966 scalar configurations and about 1.50 million training shots achieve pooled RMSE near 0.01, compared with 1,500 configurations and about 2.42 million shots for the stated direct comparator at matched accuracy; variance-aware all-pair reconstruction remains more shot-efficient. Independent count-only validation supports the fixed-benchmark MSE advantage over that direct comparator. Calibration mismatch produces a nonvanishing error floor, and no hardware, universal algorithmic superiority, or absolute historical priority is claimed. The result is an integrated reconstruction calculus with explicit counterexamples, finite-shot certification, and reproducible mathematical and synthetic tests.