Stabilizer Constraint Theory Working Notes (Vol. 1)

Stabilizer Constraint Theory: Working Notes (Vol. 1) Consolidated working notes extending the discrete algebraic stabilizer-constraint framework of Balogh (2026, IEEE TIT submission IT-26-0613) to continuous and topological settings. The central object throughout is the symmetry-matching constraint Stab(G, F) ∩ E = {e}, which characterises deterministic detection in a finite check-digit setting and, when properly extended, provides a structural lens applicable to several broader contexts. The notes develop, in order: (i) a Haar-measure formulation of the residual vulnerability V on Lie groups, with a continuity result relating measure-theoretic and topological notions of detection; (ii) algebraic and geometric concretisations of the constraint in differential-geometric, operator-algebraic, tensor-algebraic, and topological-cohomological settings; (iii) a unification statement framed as a research programme, with explicit status tags distinguishing what is proven from what is conjectural or programmatic; (iv) a candidate universal form Stab(G(t), F(t)) ∩ E(t) = {e} as the unifying source equation, presented as a programme statement. Status declaration. The discrete results are proven in the referenced manuscripts. The continuous concretisations are at varying levels: some are formally proven (under stated assumptions), others are structural conjectures, and some are programme statements. Each section carries explicit status tags. The notes are released as a time-stamped scholarly record; they are not formal publications and are not intended for citation as established results.