Coordinate Stabilization in Biological-Information Syntax: Eight-Plus-One Position Assignment, Sequence Sets, and Pre-Translation Eligibility Conditions

This long-form formal architecture paper, close in scope to a technical monograph, introduces an H-relative theory of coordinate stabilization in biological-information syntax. It addresses a methodological problem: how can a formal grammar evaluate a non-standard coordinate hypothesis without assuming its validity, importing biological meaning, or converting formal eligibility into downstream realization? The paper defines Coord_BI(H), an admissibility architecture in which sequence objects, segments, operator-family profiles, coordinate-prepared pairs, coordinate candidates, assignments, stable assignments, and TL0 input status are separated by local gates and declared failure predicates. Its endpoint, TL_Input^H, is a pre-translation input domain: a formal threshold for later analysis, not a claim of biological translation. The eight-plus-one candidate H_8+1 is used as a stress object for the grammar. It is not treated as an established biological schema. Instead, the paper tests whether such a candidate can be typed, evaluated, assigned, rejected, suspended, retyped, stabilized, or admitted to TL0 input under explicit formal conditions. The supplementary coordinate p_sup is governed as a typed test position rather than an informal residual category. The controlled domain D_89(H) provides a finite audit surface for traceability, gate completeness, failure completeness, dependency control, revision paths, coordinate stabilization, and endpoint admissibility. The paper thereby transforms the vulnerability of an unusual coordinate hypothesis into a methodological test of the grammar itself. This work is intended for readers in formal systems, theoretical biology, mathematical biology, information theory, formal language theory, systems theory, and philosophy of science. Its contribution is a formal-methodological layer that prepares biological-information syntax for later translation-layer analysis while preserving the distinction between admissibility, auditability, empirical validity, mechanism, intervention, and external realization.