Amplitude modules, fused support, and a coefficient-Bautin bound for polynomial phases

Anonymous unrefereed theorem candidate containing two Atlas-derived amplitude classifications and one externally motivated ordinary coefficient-Bautin theorem candidate. The release has deterministic internal replay but no independent specialist validation, journal peer review, formal verification, settled priority, or claim that three historically posed open problems are solved. Complete Atlas-dependent replay requires the unchanged Cyclicity Support-Fusion Atlas v0.7.0-candidate archive from the related GitHub release; that upstream archive is not redistributed in this Zenodo record and must be verified against SHA-256 3a132530f31c1af3870de7af7a13d41389ffbf051ab2760b3c0110173c268e8a.