Junction Obstructions and Effective Boundary Responses Between Complementary-Signature Spacetime Sectors (Sekala/Niskala O-Series, Technical Note O-I)

This preprint gathers the three parts of Technical Note O-I of the Sekala/Niskala (S/N) O-series, which studies the mathematical conditions under which two spacetime sectors of complementary signature, (3,1) and (1,3), can be joined. The results are theorems and identities about declared model classes; no physical mechanism is asserted and no empirical claim is made. Part I proves the junction obstruction: a discontinuous gluing has Sylvester-incompatible induced metrics; a continuous real interpolation must degenerate and generically crosses an open band of neutral signature (2,2); at a degenerate crossing the Weyl limit-point/limit-circle alternative decides between a U(2) family of interface conditions and unavoidable decoupling. Part II eliminates the three-time sector, modelled as a half-line with outgoing radiation condition, by a Schur-Feshbach reduction and obtains the exact effective boundary response, with its real-axis passivity, a complex-plane stability theorem and its threshold structure. Addendum A supplies the operator bridge: a regularized boundary triplet at singular weight, closed forms for the singular Weyl function, and a classification of smoothing limits under explicit hypotheses, delimited by counterexamples. The Note is accompanied by 91 targeted, reproducible computational checks (pure-Python scripts in the archive). It was produced with substantial AI assistance under the author's direction; the author is solely responsible for the content. It has not been peer reviewed. Limitations and open problems are listed in its closing sections.The conception of a geometric mediator between the two sectors belongs to the earlier published Sekala/Niskala programme (v10.6B, DOI 10.5281/zenodo.17486423). The O-series does not confirm it; it examines the mathematical conditions under which it could be realized.