Companion to 'The Riemann Hypothesis as a Fixed-Point Phenomenon' (doi:10.5281/zenodo.19425929). We introduce the concept of a resolution threshold for self-referential feedback structures: the maximum precision at which the structure can be characterized from within without the characterization collapsing into the structure itself. Below the threshold, lossy characterizations (the prime number theorem, zero density estimates, GUE pair correlation, zeta moments, singular series) are stable and achievable. Above it, the universal conjectures (RH, Goldbach, twin primes) remain open. We enumerate the known below-threshold invariants, pose the completeness question (via the Hamburger moment problem), and ask whether the curvature data forces the universal statements. The finite-field comparison, where RH is a theorem but Goldbach analogs can fail, constrains the role of the infinitude of primes in the forcing question.
Dana Ballinger (Sun,) studied this question.