Fermat's Last Theorem: A Physical Constructivist Proof

This version supersedes the previous "proof" framing and should be read as a correction, not a routine revision. The paper develops a physical constructivist reformulation of Fermat's Last Theorem within the Minimal Physically Derivable Theories (MPDT) framework, established by the Uniqueness Theorem. Under physical constructivism, mathematical objects exist only when their construction has been physically completed; Fermat's Last Theorem is reframed as a claim about whether a construction mode M exists mapping xⁿ+yⁿ into zⁿ while preserving integer structure, for fixed n > 2. This reformulation is fully resolved for n = 2, where both construction modes reduce to the identical primitive addition layer and Pythagorean triples are the physically constructed witnesses that a valid M exists. For n > 2, this version examines two candidate arguments for the non-existence of M and shows that neither succeeds: a structural-incompatibility argument (via the categorical irreversibility of preonic dynamics) that either establishes only that the two construction modes are different processes — silent on whether their output values coincide — or else requires redefining equality in a way that changes which theorem is being addressed; and a truncation-theorem argument (via the Preonic Truncation Theorem) that constrains only the form any physically constructed root must take (rational), not whether the construction terminates with zero error, and which — followed to its conclusion — would prove a false general claim, revealing the conflation between an exact root and a finite-precision approximation. Fermat's Last Theorem, under physical constructivism, is therefore reformulated but not resolved for n > 2. The n = 2 case, the general framing, and the identification of exactly where the difficulty lies are the paper's contributions; a completed proof is not.