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Zero-count deviation identity, cubic repulsion and deterministic corridor: a conditional framework for analytic bound tightening

Numerical evidence (298,190 zeros, t <= 200,000, fully verified; large-t sampling to 10^7 verified and 2x10^14 sampled) reveals: (1) an identity S(gamma_n) ~ sum delta_k with correlation r = 0.999958; (2) cubic repulsion P(u<eps) = 0.8 eps^3 with micro-calculus structure 0.8 = 2....

Zero-count deviation identity, cubic repulsion and deterministic corridor: a conditional framework for analytic bound tightening

Numerical evidence (298,190 zeros, t <= 200,000, fully verified; large-t sampling to 10^7 verified and 2x10^14 sampled) reveals: (1) an identity S(gamma_n) ~ sum delta_k with correlation r = 0.999958; (2) cubic repulsion P(u<eps) = 0.8 eps^3 with micro-calculus structure 0.8 = 2....

Zero-Count Deviation Identity: S(T) as Accumulated Gap Fluctuation

Numerical identity: S(γ_n) ≈ Σ_{k<n}(1 − gap_k/ρ(t_k)), ρ(t) = 2π/log(t/2π), verified over 298,190 zeros (t ≤ 200,000) with r = 0.999958. The ρ-choice is uniquely pinned: fixed/halved/ doubled alternatives give r ≈ −0.38/0.94/−0.94. Residual error converges (0.48 → 0.11). This is...

A Reproducible Quantitative Framework for Zeta-Zero Verification (Summary for Researchers)

Concise summary of a reproducible quantitative framework for zeta-zero verification: Criterion 1 (argument-quantitative jump = pi +/- delta_theta iff exactly one zero, with Riemann-Siegel error bound, Gabcke constant); Criterion 2 (lock-circle geometry); five-dimensional omission...

A Reproducible Quantitative Framework for Zeta-Zero Verification (Summary for Researchers)

Concise summary of a reproducible quantitative framework for zeta-zero verification: Criterion 1 (argument-quantitative jump = pi +/- delta_theta iff exactly one zero, with Riemann-Siegel error bound, Gabcke constant); Criterion 2 (lock-circle geometry); five-dimensional omission...

A Reproducible Quantitative Framework for Zeta-Zero Verification (Summary for Researchers)

Concise summary of a reproducible quantitative framework for zeta-zero verification: Criterion 1 (argument-quantitative jump = pi +/- delta_theta iff exactly one zero, with Riemann-Siegel error bound, Gabcke constant); Criterion 2 (lock-circle geometry); five-dimensional omission...

Riemann Hypothesis Under Siege: 298,190 Zeros Locked at sigma = 1/2

Constraint-order numerical verification of the Riemann hypothesis on 298,190 nontrivial zeros of the Riemann zeta function (up to t = 200,000).\n\nCORE RESULTS\n- Zero-free band (sampling): no off-line suspects at sigma = 0.52 (grid sampling, t step 500 across full range; true-su...

Riemann Hypothesis: 298,190 Zeros Verified, Sampled to 200 Trillion — Pure Python, One Command

Numerical verification of the Riemann hypothesis: complete verification of the zero list\n(t <= 200,000, density-matched to the von Mangoldt formula), extended and confirmed at the\nbillion scale (t ~ 10^8) by truncation sampling. Every listed zero carries two independent\nexhaus...