Strictly Isolated Prime Constellations at Offsets 0, 8, 14, 18, 24, 32 and Their Associated Composite Pairs. A Closed Form Construction With Invariant Decimal Signatures and Universal Repeating Cycle Existence.

We introduce a deterministic construction for generating composite number pairs from strictly isolated prime sextets, configurations of exactly six primes situated at fixed offsets from a base value with no additional prime existing anywhere within the interval We term such configurations strictly isolated prime constellations of order six. The structural constraint forces the six primes to terminate in the digit pattern respectively which is a consequence of the fixed offsets modulo These six primes are arranged into a rectangle whose columns are indexed by the digits , the complete set of possible terminal digits of any prime greater than Column wise addition and subtraction yield a Sums row and a Difference row from which the composite and are defined by their respective totals. We prove that this construction satisfies four universal invariants. First, the closed form identities and hold for every valid cluster. Second, is always divisible by while is always divisible by , both following algebraically from Third, the decimal expansion of always carries a signature and always carries initial signature for all proven via closed form analysis. Fourth, both and always produce non terminating repeating decimal expansions guaranteed by the arithmetic structures of the reduced denominators. These four invariants are established algebraically and confirmed computationally across valid clusters up to billion with zero failures on every claim.