Corrected Status of the Robin–MVDC Programme: Superseding the Previous Robin–Mertens Proof Branch

This upload replaces the earlier three-part Robin–Mertens proof package with a single corrected status manuscript:

RH_MVDC_corrected_status_2026_en.pdf

The manuscript withdraws the previous final proof claim based on the Robin–Mertens compensation branch. The earlier argument used a lowered abstract B(n)-envelope and treated its deficit β(n)-B(n) as an available proof reserve. The corrected analysis shows that this step is valid only if the lowered product is certified to remain an upper envelope for σ(n)/n. Without that certification, the former compensation argument cannot be used as a proof of Robin’s inequality.

The logarithmic bridge p_k=P(N)<log N for a least hypothetical Robin counterexample N>5040 is retained as an independent auxiliary result. The withdrawn part is the former final Robin step based on the abstract J_1-tail and the claimed Mertens surplus absorption.

The corrected manuscript records the exact Robin ledger and reduces the remaining work to two explicit analytic routes:

1. A signed Chebyshev/MVDC-centre route, based on the endpoint-normalised beta error W(x). This route preserves the cancellation in the beta error, but requires a one-sided analytic theorem for the signed weighted average of t−θ(t).

2. A first-moment reciprocal-prime route, which avoids the Chebyshev oscillation and rewrites the beta block as an S_{−1} certificate. This route requires a sharper local or cumulative estimate for the block sum ∑_{Y<p≤x}1/(p−1).

The numerical audit tables included in the manuscript support the algebraic bookkeeping and the scale of the two targets, but they do not replace the missing analytic theorem.

Therefore this version should be read as a corrected research-status manuscript, not as a completed proof of Robin’s inequality or of the Riemann Hypothesis. It supersedes the earlier drafts in which the swap argument, the J_1-tail interpretation, and the B(n)-envelope compensation step were stated too strongly.