Quantum autopoiesis: A quantum-informational model of recursive identity and knowledge discovery

A formal operational model of quantum autopoiesis is presented that is physically grounded in photon-fermion interactions and in the phase structure of the electromagnetic field. The continuous electromagnetic phase, associated with a U(1) reference symmetry, is treated as an underlying substrate that, under local interaction conditions and finite resolution, yields a finite set of stable phase classes Z_n, interpreted operationally as a symbolic alphabet. Identity persistence is defined by sustained coherence between the electromagnetic field and existing fermionic structure. When coherence is sufficient, the current symbolic state is carried forward; when coherence is locally reduced and admissible transitions exist, discrete phase updates occur. Photon-fermion interactions are thus treated as physically admissible gates acting on elements of Z_n. Formally, persistence is captured by the recursive identity operator I=λs.s, while gate application corresponds to controlled symbolic update I=λs.δs. Within this framework, three questions are addressed. First, identity persistence is characterized as the ability to carry symbols across time under coherence. Second, new knowledge discovery is defined as the successful stabilization of a discrete update in fermionic (symbolic) structure. Third, the accumulation of symbolic logic structure arises from alternating phases of persistence and targeted updates, producing reusable structure without loss of identity. The significance of the model lies in its integration of identity, knowledge discovery, and symbolic computation within a single physically grounded formalism, where computation emerges operationally from composable transitions under physical constraints.