A Stability Theorem Fixing the Critical Exponent at 1/2 in Prime-Indexed Models: A Structural Alternative to the Riemann Hypothesis

This work introduces a structural stability theorem for prime-indexed mathematical models associated with the Riemann zeta function. Rather than addressing the existence or location of zeros of ζ(s), the paper identifies invariant conditions under which the scaling exponent σ is uniquely fixed to 1/2. The central result shows that any coherent framework built from prime multiplicativity, complex phase interference, logarithmic variance growth, and functional symmetry with measure preservation admits no alternative stable exponent. Under these conditions, σ = 1/2 is not a conjectural outcome but a structural necessity. This approach reframes the classical problem surrounding the Riemann Hypothesis. Instead of asking where zeros lie, the analysis explains why the critical line itself emerges universally across spectral, probabilistic, and operator-theoretic models derived from prime-indexed data. The theorem makes no assumptions about zero distributions and does not claim equivalence to the Riemann Hypothesis. The result unifies insights from analytic number theory, random matrix theory, noncommutative geometry, and probabilistic models under a single rigidity principle. The critical exponent is shown to be fixed by compatibility constraints alone, independent of any zero-finding mechanism. This stability perspective suggests that the prominence of the critical line reflects deep arithmetic architecture rather than contingent analytic phenomena.