The Riemann Hypothesis by Exclusion of the Prime-Trace Amplitude Separator

This archive contains The Riemann Hypothesis by Exclusion of the Prime-Trace Amplitude Separator, a full audit-grade manuscript presenting an AASC endpoint-rigidity proof route for the Riemann Hypothesis through explicit-formula scale discrimination. The manuscript frames the Riemann Hypothesis as the positive endpoint ∀ρ (Aζ(ρ)⇒Lcrit(ρ)),\forall \rho \, (A_\zeta(\rho) \Rightarrow L_{\mathrm{crit}}(\rho)),∀ρ(Aζ(ρ)⇒Lcrit(ρ)), where Aζ(ρ)A_\zeta(\rho)Aζ(ρ) denotes nontrivial zeta zerohood and Lcrit(ρ)L_{\mathrm{crit}}(\rho)Lcrit(ρ) denotes critical-line readout. The proof proceeds by analyzing the ordinary off-line branch through the explicit-formula prime-trace amplitude interface. Core Proof Route The manuscript develops a proof strategy based on the following route: fixes the official RH endpoint on the zeta / prime-trace carrier; uses the standard explicit-formula zero-to-prime-trace correspondence; identifies critical-line zeros with neutral critical-normalized amplitude order; identifies off-line zerohood with non-neutral critical-normalized amplitude order; distinguishes descriptive off-line amplitude content from endpoint-standing counterexample force; classifies endpoint-standing non-neutral amplitude as amplitude separator occupation; applies AASC endpoint-use discipline, ATS anchor–tensor–skin locking, UEAP report discipline, and no-independent-discriminator closure; derives a local contradiction for the live off-line countercase; discharges the exact-complement assumption and universally generalizes to the RH endpoint. Methodological Position The manuscript does not introduce or rely on: a new zero-free region; a zero-density estimate; a positivity criterion; a Hilbert–Polya operator; a random-matrix theorem; numerical verification; a redefinition of the zeta carrier. Instead, the proof class is presented as kernel-forced prime-trace amplitude separator exclusion. The central nonclassical dependency is the endpoint-use thesis: official endpoint-defeating counterexample force is treated as theorem-bearing endpoint use. Once this dependency is fixed, the remaining argument is developed as target instantiation, explicit-formula role projection, native-counterforce exhaustion, and local endpoint closure. Audit and Formalization Support The manuscript includes extensive audit infrastructure, including: an endpoint proof spine; theorem ladders and anti-circularity checks; hostile-referee objection matrices; route-locus exhaustion tables; notation and corpus-support ledgers; a Lean4 RH endpoint audit appendix. The Lean4 appendix is presented as proof-spine audit support for the endpoint-role surface, not as a first-principles formalization of analytic number theory. Intended Use This deposit is intended for readers evaluating the AASC endpoint-rigidity proof framework, the explicit-formula amplitude route, and the manuscript’s role-theoretic treatment of counterexample force, endpoint use, and prime-trace amplitude separator exclusion