Stronger local overlap certificates and distinct zeros of the Riemann zeta function

We derive a lower asymptotic proportion 30945470743359/36955122080000 = 0.8373797460706156... of distinct nontrivial zeta zeros, relative to zeros counted with multiplicity, by applying Knausgard's mixed-multiplicity Gram argument to Lavery's seven-point local theorem with unequal gap pressures. The external local theorem is an explicit dependency; its reported Lean and nanoda checks were not rebuilt locally. A separate complete eight-gap interval computation proves a stronger nine-point local inequality at pressure 1/2500 and gives the independently replayed bound 3997934614153/4775507750000 = 0.8371747724947154... . The block transfer uses an elementary spectral dichotomy, without a sharp trace envelope. Independent rational window enclosures, complete closed-cell input comparisons and extracted-source checks support the computations. The analytic input is the corrected integrated unconditional pair-correlation theorem of Baluyot, Goldston, Suriajaya and Turnage-Butterbaugh. The results are asymptotic; they do not prove the Riemann hypothesis or give an effective height. Code and data: https://github.com/fsantibanezleal/CAOS_RESEARCH . The complete exact-byte EXP-020 runtime archive and scoped mathematical source are supplied with the PDF.