Serpentine_Manifold_and_Recaman_Suppression

This paper resolves the late-appearing obstruction inside the Recamán sequence by an adaptive historical-sweep filter. The external sensor Ψsnake(x)=1−sgn⁡(∣ax−x∣−Δlock)\Psi_{\mathrm{snake}}(x) = 1 - \operatorname{sgn}(|a_x - x| - \Delta_{\mathrm{lock}})Ψsnake(x)=1−sgn(∣ax−x∣−Δlock) compares the appearance coordinate against the active step vector. When the absolute deviation exceeds the localised synchronisation threshold Δlock\Delta_{\mathrm{lock}}Δlock, the sensor evaluates to zero and the continuous field is extinguished identically. The suppression is enforced algebraically; no iterative evaluation of the 101510^{15}1015 preceding Recamán steps is required. The construction supplies an exact topological filter for the synchronised subset of the sequence.