Symbolic Inflation and Structural Irreducibility in Power-Sum Equations: A Compression-Theoretic Perspective on Fermat's Last Theorem

We analyze power-sum equations such as a^n + b^n = c^n from a symbolic and compression-
theoretic perspective using a formal rewrite grammar Gpow. While not attempting a formal proof
of Fermat’s Last Theorem, we study the symbolic derivation cost of constructing such equalities
and compare it to the minimal descriptive complexity of the parameters involved. We find
that the symbolic entropy of these expressions grows significantly faster than the Kolmogorov
complexity of their inputs. This mismatch — a phenomenon we term symbolic inflation —
offers an information-theoretic intuition for why no compact derivation of a counterexample is
feasible. Our analysis reveals an inherent structural asymmetry and frames irreducibility as a
compression barrier in symbolic logic.