Zero-Inaccessible Balance and the Critical Line

This upload contains a manuscript and an accompanying Lean 4 theorem-package file for the zero-inaccessible balance formulation of the Riemann hypothesis. The central distinction is between formal zero and complete zero. Formal zero exists in mathematics and cognition as a legitimate value, symbol, and equation. Complete zero, understood as realized absolute nothingness, is not admitted as an ontological state. Under this principle, a zero of a nontrivial analytic system is interpreted not as literal absence, but as exact cancellation of nonzero conjugate sectors. For the completed Riemann zeta function, the functional involution s -> 1 - s selects Re (s) =1/2 as the unique real balance axis. The manuscript formulates the Riemann-hypothesis conclusion as a physical-ontological conditional theorem package: if formal zeros of the completed zeta function are realized only as exact balance, and if off-axis sectoral imbalance prevents complete cancellation, then every nontrivial zero lies on the critical line. The accompanying Lean 4 file, riemannᵦeroᵢnaccessiblebalanceᵣh. lean, formalizes this conditional proof architecture without global axiom declarations. The physical-ontological principles are supplied as explicit theorem hypotheses, and the critical-line conclusion is derived from them by theorem composition. This work does not claim an unconditional mathlib proof of the Riemann hypothesis. It isolates the remaining mathematical burden as the off-axis imbalance theorem: the proof that complete sectoral cancellation cannot occur away from Re (s) =1/2 in the completed zeta system.