Bio-Admissibility Conditions for the Derived Quadruple: A Local Bridge Theorem for Multiscale Biological Systems

We formulate a bridge theorem between the Derived Quadruple (DQ) framework andbiological systems. The note does not claim that living systems are already globally provento be four-sectorial. Instead, it specifies explicit Bio-Admissibility conditions under whicha biological system may be treated as a local or distributed/nested DQ-instance. Theseconditions comprise open dissipative operation, a persistence-relevant drive/gradient sector,a regulated boundary variable, a separable attenuation/veto structure, a viability-relevantholding function, local intervention separability, chiasmatic boundary self-modulation θ1 > 0,and endogenous repair of the system’s own admissible boundary conditions under perturbation.Under these assumptions, a biological system can be embedded into the local admissibleclosure class to which an internal DQ uniqueness theorem applies; therefore (D, h,B, σ)becomes the unique local minimal complete intervention-separable decomposition. Thetheorem thereby yields a conditional rather than universal biological four-sector claimand motivates a distributed/nested DQ representation for multiscale biology. The notealso clarifies the relation to ECSI: four generic resources do not by themselves imply fourindependent intervention classes. Finally, the framework is rendered falsifiable by explicitfailure criteria, including the discovery of a fifth irreducible biological intervention class or afifth primary collapse mode. The result is a bridge statement, not a total ontology.