Specular Bit Architecture (SBA) for DNA Cloning Fidelity and Epigenetic Drift: A Formal Mathematical Framework

This paper presents the Specular Bit Architecture (SBA) as a formal model for DNA cloning fidelity, repair-load accumulation, and epigenetic drift under repeated copying. SBA encodes signed local state with mirrored carriers, uses Fibonacci positional weights for exact local rewrites, and defines deterministic sanitization and reconstruction with bounded propagation. In the DNA-facing interpretation, local mismatches generated by serial cloning or PCR-like copying are treated as noncanonical conflict states: if repair remains locally coherent, the disturbance is normalized within a certified radius; if repair-load accumulates across rounds, the residual defect becomes a model-layer template for heritable drift. The formal core retained here provides: (1) a signed-digit model with Zeckendorf-style uniqueness per channel; (2) exact rewrite rules derived from Fibonacci identities; (3) synchronous read-compute-write semantics with deterministic local arbitration (Protocol C); (4) a direct canonical unranking map for the unique shifted-Zeckendorf support associated with an integer label; and (5) bounded-propagation guarantees with rule-specific empirical certificates from exhaustive local enumeration. The DNA mapping is made explicit through mirrored channels that can be read either as nucleotide-class carriers or as sense/antisense strand views, with reverse-complement orientation robustness formalized by Corollary 7.4. A hypothesis-level paired-strand layout analogy is retained for double-stranded DNA, without elevating it to theorem status. A companion proofbench provides reproducible DNA-facing artifacts, including chunking replays on declared DNA fragments, mutation-severity and repair-load trajectories, and a reviewer-facing serial-cloning benchmark linked to the Wakayama mouse experiment. These artifacts support pre-registered model comparison between SBA/Fibonacci-weighted repair-load proxies and competing threshold families, including Mersenne-based candidates, but they do not establish a universal cloning-failure theorem, a universal Hayflick limit, or species-independent generation bounds. All biology-facing interpretations remain modeling- or hypothesis-level until independently calibrated and experimentally falsified. Index Terms: Specular Bit Architecture, DNA cloning, epigenetic drift, repair-load accumulation, bounded propagation, reverse-complement decoding, Fibonacci positional coding, Zeckendorf representation