This record contains the corrected reproducibility archive associated with the theoretical–synthetic study Hydrothermal Memory Kernels for Volcanic Gas and Isotope Signals: Volterra–Spectral Structure and Boundary-Aware Synthetic Comparison. The archive includes Supplementary Codes S1–S8, 51 CSV numerical outputs, 17 vector-PDF figures, Supplementary Note S3 in PDF and LaTeX source form, 36 unit, regression, and cross-artifact tests, an independent pair-level rolling-origin validator, a full validator for all 2,500 archived continuous fits, environment metadata, pinned top-level requirements, Docker and Conda reconstruction recipes, accessible figure descriptions, and SHA-256 manifests. This corrected version replaces the asymmetric rolling-origin tie handling contained in the earlier record. Every paired next-block comparison is assigned to exactly one of three outcomes: Caputo strict win, numerical boundary tie, or tail-tempered strict win. Non-worse rates add ties symmetrically, and uncertainty is computed by resampling simulated records as clusters. The corrected baseline T=30T=30T=30 counts are 209/354/77 under Caputo truth and 159/189/292 under tail-tempered truth. The release also adds origin-specific rolling summaries; a paired common-record AR(1) comparison with 5,000 records per truth–window condition; a full audit of all 2,500 archived continuous fits, including every restart-spread outlier; blocked-prediction distribution summaries with interquartile and 5th–95th percentile ranges, bootstrap intervals for the median, and probabilities below, at, and above unity; and semantic tests covering Sonine integrability, continuous-dependence assumptions, normalization invariance, boundary nesting, figure-caption fidelity, and cross-artifact consistency. The Monte Carlo null calibration remains pointwise and design-specific; it is not a uniform-size test over the composite Caputo family. AICc and BIC are secondary operational rankings. The benchmark compares normalized temporal-response shapes under declared forcing, observation, error, and candidate-domain assumptions. It does not identify physical kernel amplitudes, latent forcing histories, source-to-observation gains, or individual geological compartments. No field-monitoring data or site calibration are included. All data in the archive are synthetic and are generated by the supplied code.