Phase-Mediated Attractor Dynamics in High-Throughput Sequencing Fields: Mapping Nonlinear Manifolds, Scaling Slopes, and Basin Depth in Alignment-Rejected Sequencing Ensembles

I reinterpret Phred-scaled sequencing quality scores as trajectories in a dynamical state space.
I introduce a streaming pipeline that isolates the residual, alignment-rejected channel defined strictly 
as sequence records that are unmapped or assigned a mapping quality of zero, yet possess intact, 
non-empty base quality score arrays. Low-dimensional representations of this channel are extracted via 
a window statistical state vector and cosine-based transition filtering. The resulting delta-field is 
analyzed using delay-coordinate embeddings, principal component decomposition, and angular divergence 
metrics across multiple scales. I show that the resulting attractor structure exhibits low-dimensional 
constraints under singular spectrum collapse and stable scaling behavior over tolerance sweeps. Finally, 
a binomial test evaluates the significance of observed structural clustering across independent sequencing runs, 
demonstrating the utility of this discarded data stream as a real-time instrument diagnostic.