PathfinderSNT: An Operator-Constrained Framework for Phase Transitions Between ORF Conservation and De Novo Expansion

We present PathfinderSNT (Sequence Nucleotide Tracker), a constraint-driven genome reorganization framework whose central empirical finding is phase-dependent behaviour: the same operator system operates in a conservation regime on high-density sequences, suppressing spurious open reading frame (ORF) inflation, and exhibits an expansion trend on low-density sequences, actively installing new coding structure. This behaviour emerges automatically from the interaction of two orthogonal mechanisms: the ΠORF disjoint projection invariant, which prevents representation-level metric inflation, and the frozen soft-clamp, a density-adaptive feedback controller that ensures probability-preserving operator consistency at every reorganisation cycle. The framework models genome reorganisation as a seven-operator dynamical system {∧=, ⟲=, ↗=, ⟲r, ∞/, □/, ⋄+} implementing a coupled diagnose–measure–delete–fill pipeline governed by a Markov operator semigroup. We validate on six real genomic sequences spanning bacterial chromosomes, a bacteriophage, a cloning plasmid, and vertebrate mitochondrial DNA: E. coli K-12 MG1655, Prochlorococcus marinus MIT 9313, Mycoplasmoides genitalium M2288, pUC19, Lambda phage, and the complete human mitochondrial genome (NC 012920). Across N = 10 independent seeds (N = 5 for the human mitochondrial genome) and 30 reorganisation cycles, the framework significantly suppresses ORF-count inflation relative to random mutation on all five high-density genomes (Δ = −3.0 to −26.6, pboot = 1.000), including the human mitochondrial genome analysed under the vertebrate mitochondrial genetic code. On the low-density pUC19 plasmid, an expansion trend was observed (Δ = +0.4) that did not reach statistical significance (pboot = 0.195). Critically, 45% of framework-inserted ORFs across all six organisms (33/74) returned significant BLAST hits (E < 0.01) against UniProtKB/Swiss-Prot, including humanin-like peptides and core respiratory-chain subunits in human mitochondrial DNA, indicating that the framework operates de novo—without reference to existing annotations—yet preferentially installs biologically plausible coding structure rather than statistical noise.