Notes on Periodic Phase Alignment in Modular Accumulators

Key Points

• To establish a general matching condition for periodic phase alignment in modular accumulators.
• Developed a short-period congruence for alignment identification.
• Analyzed the conditions for periodic phase alignments.
• Proposed a framework to identify alignment windows without exhaustive searches.
• Identified specific conditions that enable efficient alignment detection.
• Demonstrated that the matching condition simplifies the search process.
• Showed the relationship between periodic phase alignments and modular accumulation.