The Non-Optionality of Mass–Energy Equivalence from Record Admissibility

Description This paper proves that mass–energy equivalence E = mc^2 is structurally unavoidable once a minimal set of pre physical assumptions is accepted. The framework assumes only consistent records, admissible composition of transitions, inertial relabeling symmetry, and the existence of a finite invariant maximal admissible propagation rate. No spacetime geometry, metric, energy, momentum, dynamics, or field theory is assumed at the outset. From these primitives, Lorentzian structure and an invariant interval are derived as rigidity consequences. A scalar persistence ledger is introduced as the additive envelope of a subadditive persistence cost functional, and invariant mass and energy are defined as derivative quantities of this ledger with respect to invariant and frame-dependent parameters. The mass–energy identity E = mc^2 then follows uniquely from the invariant interval and the chain rule. No alternative rest-energy law is compatible with the stated assumptions, establishing the non-optionality of mass–energy equivalence up to trivial unit rescaling. The work makes no new empirical predictions and does not modify established relativistic physics. Its contribution is a primitive reduction and rigidity result: it identifies why mass energy equivalence could not have been otherwise once admissibility, persistence, and finite signal structure are fixed. The paper is fully self-contained and intended as a foundational clarification of the structural inevitability underlying one of physics’ most familiar relations.