A two-certificate trace-energy deduction for simple zeros of the Riemann zeta function

Abstract

This preprint gives the research-draft candidate lower bound `liminf_{T->infinity} N_0^s(T,2T)/N(T,2T) >= 0.6733169771424713... > 0.673316977` for the proportion of simple zeros of the Riemann zeta function on thecritical line. The new step is finite-dimensional: certified seven- andnine-point gap inequalities on the same window are retained simultaneouslyand absorbed by a supporting plane for the trace-energy envelope. The sourcearchive contains the manuscript, exact arithmetic checks, machine-readableresult, proof and review guides, provenance, and pinned small upstream inputs. The local deduction and exact comparison are independently reproducible fromthe archive. The analytic interface and the two exhaustive upstream intervalcertificates are pinned imports; this deposit does not claim to replay theirreported 2,168,370-node and 116,272,426-node interval runs. The result remainsa research-draft candidate pending independent mathematical review. GitHub release: https://github.com/yuhangshi888/zeta-simple-zeros-673316977/releases/tag/v0.1.0 Release commit: `1469eeefe29c48c971ecf98092bc82751dea8bca`