ON THE ASSUMPTION OF STRUCTURAL COHERENCE IN ALGEBRAIC EQUIVALENCE

This paper examines the hidden physical assumption required when exact algebraic equivalence is applied to independently generated physical structures. Using a strict physics-only, logical-necessity framework, it shows that symbolic equivalence does not itself enforce coordination, suppression of divergence, or synchronization between uncoupled generators. Because independent physical processes naturally diverge under iteration and conservation, exact equivalence can only hold if a real, enforcing mechanism—structural coherence via active coupling or back-reaction—is implicitly assumed. The paper isolates that assumption and demonstrates, by removal and invariance tests, that algebra alone does not supply the required enforcement.