Pre-dynamical Ordering in Protein Folding via Fixed-Kernel Convolution

The paper demonstrates that a single, fixed Ricker (Mexican-hat) wavelet, applied to mean-centered hydrophobicity sequences, produces statistically significant enrichment of long-range residue contacts in a subset of proteins whose folding is dominated by hydrophobic collapse. The method uses no per-protein tuning and is evaluated against a benchmark that includes both collapse-dominated proteins and mechanism-mismatched stress tests (e.g. disulfide-rich and membrane-associated structures). Key findings include: Emergence of a characteristic coherence scale in sequence space Order-of-magnitude enrichment of true long-range contacts in collapse-dominated proteins Clear mechanism specificity: the method succeeds selectively rather than universally The accompanying code package reproduces all figures and statistics reported in the manuscript, including: Kernel convolution and response rectification Contact enrichment and precision-lift metrics Benchmark and stress-test analyses