Abstract

We formulate the proposed connection between quantum magic and matter-responsive geometry at a finite, already-prepared quantum carrier interface. The complete output is an isometry $V:C\to R\otimes B$, and residual response means that its complete complementary channel is not constant on the logical code. Exact recovery from $R$ is equivalent to absence of that response.

The proposed unconditional implication from non-Clifford resources to residual response is false. We prove explicit counterexamples: a Clifford copying circuit has a nonconstant complement, whereas non-Clifford logical evolution and even a fixed syndrome containing bipartite non-local magic can coexist with a constant complement and exact logical recovery. We therefore separate magic, residual response, and physical geometric backreaction.

For a specified controlled-rotation family, we construct a non-Clifford responding program and obtain the exact formulas

A general first-order residual-observable witness gives a quantitative sufficient condition for response under a declared deformation. A Pauli-compression criterion separately characterizes constant complements for Clifford encoders.

Destructive Born–Lüders readout consumes measured quantum names and returns a classical interface. Readout-and-drop of an unobserved residual is exactly partial trace and does not further change the radiation channel. The four-Majorana recovery obstruction, finite-channel certificates, access-preserving endpoint continuity, and finite-proxy recurrence are retained with their proper scope. No metric, field-to-memory receiver, admitted analytic quantum coefficient, or gravitational backreaction theorem is constructed.