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The note formulates a classical approach to identify self-sustaining branches in the accelerated Collatz map, highlighting its implications for odd orbits.
We study the accelerated odd Collatz map by keeping together three elementary structures: finite products along odd orbits, circular phases given by fractional logarithms, and the residue obstruction modulo 3. The note formulates a classical Eulerian reduction of non-principal obstructions to the existence of a self-sustaining branch preserving a circular mode while remaining compatible with the many-to-one structure of the accelerated map.
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Wangyue (2026) studied this question.
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