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Shows novel energy laws in periodic remainder orbits, suggesting new mathematical insights.
A finite character-sum treatment of the periodic side of long division. The paper develops signedboundary flux for periodic remainder orbits, proves a conductor-energy decomposition for oddcharacter moments, establishes a full-orbit prime-power energy law, gives an index-two mod 8orbit-energy formula, and reduces higher-index subgroup orbit boundaries to explicit Jacobi-typecharacter sums.
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Alexander S. Petty (2026) studied this question.
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