Recovery Witnesses in the Prime-Power Checkpoint Program: Service-Clock Geometry and an Exact Quantifier Reduction for the Riemann-Hypothesis Tail -- Part 4
Year: 2026
Type: preprint
Abstract: Suzuki's pointwise criterion expresses the Riemann hypothesis as nonnegativity of a real function Ψ. Prime-power checkpoint theory localizes one constrained minimum between consecutive prime powers, proves a directed-arithmetic finite theorem through q = 10¹⁰, and reduces the unresolved tail to active-event reserves 𝒱_q = 𝒞_q − 𝒥_q. This paper sharpens the remaining quantifier. For the workload Y = −Ψ′ and service clock τ = A′(t), the inter-event dynamics has exact unit drift dY/dτ = −1, interrupted by jumps Y⁺ = Y⁻ + Λ(q)/√q. The last active event q of a recovered episode is characterized by the shrinking service window 0 < Y_q < A′(log q_next) − A′(log q). The pure-debit law therefore reduces every recovered episode to one recovery witness. The companion terminal theorem excludes a terminal active episode, while Suzuki's unconditional sign changes force active states arbitrarily far out; together these imply infinitely many finite recovered episodes and recovery witnesses. The rigorous branch ledger gives 33,781 strict recoveries through 10⁸ and 364,792 ≤ D_rec(10¹⁰) ≤ 366,700. A finite √X-scale fit and an RH-conditional random-phase/local-time model are presented only as diagnostics. The remaining analytic target is a recovery-conditioned level–area theorem proving 𝒥_q ≤ 𝒞_q at every witness. No such RH-independent theorem is proved here. The Riemann hypothesis remains open.
Author: Mittermeier, Rainer Andreas
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204263856
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