Finite window diagnostics and noise channels in a kicked Ising chain

Finite-time return measurements can assign the same stability label to different dynamical responses. We document this ambiguity in a periodically kicked Ising chain initialized in a Neel product state, and replace an earlier numerical claim with a reproducible finite-model benchmark. For ten spins, even-period return highlights identity-like pulse settings as well as a period-doubled cycle. Signed odd-period and Fourier diagnostics distinguish these cases. At the perfect-pulse point, diagonal phase perturbations preserve the basis-state cycle exactly. Under fresh Gaussian transverse rotations, the alternating ensemble-mean local correlation has envelope exp(-2σ²n), independently of the diagonal Ising coupling. Independent local channels also give an elementary product expression for the ensemble cycle fidelity; a shared pulse-angle fluctuation has the same local mean but can have a different fidelity. These ensemble identities do not determine nonlinear per-realization scores, whose averaging order must be retained. All simulation results derive from one newly seeded state-vector dataset with raw traces and source hashes; analytic controls are evaluated separately. The resulting shelves and sampled noise crossings describe a specified preparation, channel, diagnostic and observation window. They supply no evidence for a universal discreteness mechanism, interaction protection from these exact-center ensemble observables, or a thermodynamic time-crystal phase.

Corrective release with the corrected manuscript, code, data and figure pipeline. Related Research Square record: https://www.researchsquare.com/article/rs-8790240 . This version replaces the earlier audit bundle with the reviewed reproducibility package. Archived claims are retained for provenance and are not endorsed. This preprint is not peer reviewed.