The Riemann Hypothesis — Complete Proof Program

The Riemann Hypothesis — Complete Proof Program: A Certified Framework Reducing RH to Explicit Computable Certificates This deposit presents a node-structured “Complete Proof Program” that reduces the Riemann Hypothesis to a small set of explicitly verifiable conditions within the de Bruijn–Newman deformation framework. The manuscript is organized as a dependency-graph of short nodes, each with a clear problem statement, solution tactic, formal body, and a final verdict. The program isolates one external analytic anchor from classical literature: the existence of a large-time regime where the relevant de Bruijn–Newman deformation has only real zeros. From this anchor, the remaining obstruction is reduced to a slab non-degeneracy condition (NZ1): on a fixed finite time interval, there are no points where the deformation and its first spatial derivative vanish simultaneously on the real line. The document proves that, assuming NZ1 holds on the slab, the “all zeros are real” property propagates from the anchor time down to time zero, which corresponds to the Riemann xi-function on the critical line; this yields the Riemann Hypothesis in the standard equivalence form. A certified computational pipeline is specified modularly (tail splitting, grid refinement, interval evaluation, two-dimensional exclusion boxes, and iterative slab guarding). The pipeline turns NZ1 into a finite set of auditable box exclusions based on validated numerical bounds. All analytic and logical implications internal to the manuscript are proved in-text. The final implication to the Riemann Hypothesis is conditional only on (1) accepting the cited anchor theory and (2) reproducing three explicit computational certificates (D1, E1, L1) that provide: an initial positive gap on the anchor slice in a compact central region, a uniform tail exclusion on the complement, and uniform derivative/Lipschitz bounds enabling safe propagation. The Zenodo record is intended to include the PDF, LaTeX sources, and a reproducibility bundle (code, environment specification, logs, and hashes) for independent verification.