An Experimental Binary-Window Pipeline for Detecting Odd Composite Integers

We present an experimental binary-window pipeline for detecting odd composite integers.The method comprises four stages: perfect-square detection, a Mersenne-ones filter, circularbinary windows, and multiplicative deformation by extended binary repunits. The method isnot presented as a primality test, but as a reproducible experimental procedure for detectingcompositeness through binary morphology.The central operation is to search for circular binary windows whose integer values havea nontrivial greatest common divisor with the original number. For difficult survivors, thenumber is multiplied by binary repunits 2^k − 1, producing superpositions of shifted copiesof the original binary word. These deformations often expose hidden nontrivial divisors ascircular windows.The pipeline detected all 4,335,421 odd composite integers up to 10^7. A separate fullvalidation up to 106, covering both odd primes and odd composites, detected all 421,502 oddcomposites and produced zero false positives among 78,497 odd primes.The results suggest that odd composite integers may possess highly detectable binarysignatures through repunits, circular windows, and repunit-induced binary deformation. Thepaper is self-contained: a reference Python 3.10 implementation is included in the appendix.