Genomic Sequences as Discrete Spacetime Condensates: An End-to-End Generative Physics Framework via Gauge Symmetry Breaking

We investigate an end-to-end generative-physics hypothesis for genomic structure with explicit separation of verified finite models and the proposed microscopic and condensate mechanisms. The constructive foundation is an oriented cellular two-complex with a designated genomic boundary and a normalized four-state sequence/contact model. We prove its cellular incidence identities, exact local $\mathbb{Z}_2$ gauge invariance, and the gauge quotient that reduces the boundary theory to four observable states. Binary contact variables can be marginalized exactly, yielding a pairwise Potts-type law and exposing a sequence-only parameter-identifiability obstruction. Small-system exact enumeration and exploratory Python sampling check these identities; these tests establish computational consistency at the scale of the constructed finite systems; biological benchmarking remains a separate objective. A separate smooth-field discretization has a controlled second-order continuum error, while the uncoupled sequence model obeys an exact block-composition fluctuation law. Both results provide limited mathematical benchmarks; an interacting continuum limit and a physical condensate require further derivation. Nonlinear nucleotide readout also fails, in general, to commute with coarse-graining. Independently of any microscopic group-field derivation, we develop data-informed genomic two-complex analysis through persistent and relative homology, cellular maps, attributed cochains, and optional sheaf or symmetry structures. We specify the face-construction assumptions required for these invariants to be biologically interpretable. Fixed-complex homology is invariant under changes to nucleotide labels; truncating higher-dimensional complexes and changing resolution may alter measured topology. We derive conditional stability and correspondence results, including bounds for uncertain contact scores, multiresolution chain maps, partial alignments, and probability distributions over alternative genome correspondences. Finite stochastic examples illustrate identifiability limitations, intervention-dependent distinctions, topology-changing histories, and Bayesian filtering of latent cellular events. A genome-scale implementation architecture and benchmarks are proposed, not claimed to have been realized. Finally, an information-theoretic analysis shows why observation maps preserve only distinctions retained by their measurement channels and why deterministic topological descriptors preserve the information ceiling set by the full input available to an ideal predictor. The framework’s prospective scientific value therefore lies in demonstrable additional evidence, interpretable constraints, improved inference, or independently validated physical predictions. Derivation of a genomic cellular-history law from a microscopic group-field action, chemically grounded nucleotide formation, a gauge-invariant condensate phase, and a nontrivial geometric continuum remain open research problems.