The Re-Entry Thesis: On the Structural Invariance of Self-Referential Paradoxes Across Logic, Mathematics, Computation, Physics, and Biology

Complete findings of a six-phase research program investigating whether the re-entering Boolean expression f = not-f, formalized in G. Spencer-Brown's Laws of Form (1969), constitutes the structural invariant underlying self-referential paradoxes across seven domains. Phase 1 proves isomorphism of six canonical paradoxes. Phase 2 evaluates the oscillatory resolution against Kripke, Gupta-Belnap, and Priest. Phase 3 constructs the algebra of imaginary Boolean values. Phase 4 provides the first computational simulation of Varela's autopoiesis automaton. Phase 5 presents a four-factor model explaining the formalism's marginalization. Phase 6 synthesizes seven design principles for self-referencing systems. Central verdict: the re-entering form is indeed the structural invariant, but its significance is narrower than proponents claim — it is a structural descriptor, not a predictive theory.