Specular Bit Architecture (SBA) in the DNA-Storage Setting: A Formal Framework for Local Rewriting, Deterministic Normalization, and Bounded Propagation

This paper presents the Specular Bit Architecture (SBA) as a formal informational layer for DNA data storage. SBA encodes signed information with specular carriers, uses Fibonacci positional weights for exact local rewrites, and defines deterministic sanitization and reconstruction under synchronous local arbitration. The framework provides a signed-digit model with Zeckendorf-style uniqueness, exact rewrite rules, asynchronous read-compute-write semantics with Protocol C arbitration, and a direct canonical unranking map for recovering shifted-Zeckendorf supports without simulating intermediate rounds. It also provides exact width-5 combinatorial counts and exhaustive local enumeration for rule-specific bounded-propagation certificates, together with DNA-facing modeling metrics for copy-endurance loss, repair-load overhead, rewrite stress, and failure-horizon proxies. Under the stated assumptions, SBA yields strict locality, deterministic normalization, and bounded error propagation, with a reproducible workflow for DNA block encoding, round-trip decoding, and repair-load auditing. The manuscript keeps formal results separate from calibrated deployment metrics—parameters such as $m_0$, $c$, and $c_I$ remain substrate-dependent and require independent calibration before laboratory interpretation. A companion proofbench provides reproducible artifacts for independent audit of the reported certificates and DNA-storage calibration workflows. Index Terms: Specular Bit Architecture, DNA data storage, signed-digit arithmetic, bounded propagation, exact discrete reachability, Fibonacci positional coding, Zeckendorf representation, local rewriting