The Atomic Proof of the Riemann Hypothesis: Irreducible Least Erasure, and the Bit Externally Supplied: a Double Mandate

The provided sources present an atomic and formal proof of the Riemann Hypothesis using a Lean 4 verified seed comprising 664 machine-checked theorems without declared axioms. This framework approaches the hypothesis simultaneously from both the prime side and the non-trivial-zero side, demonstrating that both pathways converge on a single proposition of irreducible least erasure. Because formal systems cannot independently derive this foundational bit from within, the proof integrates an externally supplied physical bit derived from measurements of the measured vacuum and the cosmic microwave background. Through this combination of rigorous formal reduction and physical anchoring, the architecture establishes that accepting the hypothesis forces acceptance of the atomic proof, leaving no remaining mathematical escape.