Matthew Riley

Arbitrarily Delayed Spectral Memory in Noncongruent Closed Waveguides

We construct smooth families of closed thin waveguides that remain globally noncongruent while becoming spectrally indistinguishable over independently prescribed observational scales. For any finite wave horizon, the relative cosine wave trace can be made to vanish exactly throu...

Magnitude-Curl Reconstruction in the Plane: Classical completeness, critical weak selection, and observability

Reconstructing a planar vector field from its pointwise magnitude, scalar curl, and partial boundary direction data leads to a nonlinear characteristic inverse problem with distinct classical and weak regimes. This work develops a geometric framework that separates structural obs...

Magnitude-Curl Reconstruction in the Plane: Classical completeness, critical weak selection, and observability

Reconstructing a planar vector field from its pointwise magnitude, scalar curl, and partial boundary direction data leads to a nonlinear characteristic inverse problem with distinct classical and weak regimes. This work develops a geometric framework that separates structural obs...

Dihedral Programming of Topological Charge in Curved Quantum Waveguides

We construct a scalar curved quantum-waveguide hierarchy in which dihedral symmetry programs both the leading geometric release order of a protected two-level degeneracy and its topological charge. For a family with D2q symmetry, representation theory forbids off-diagonal geometr...

Symmetry-Protected Cancellation and Geometric Release of Floquet Sector Splitting in a Framed Lemniscate

We study a closed framed space curve with centreline r(a) = (sin 2a, cos a, sin a) and a periodically driven transverse tube Hamiltonian. The curve exhibits a clean spinorial 4π frame lift, but the corresponding central holonomy does not by itself select a unique two-dimensional...