{
  "abstract": "Suzuki proved that the Riemann hypothesis (RH) is equivalent to the nonnegativity of an explicit continuous function &Psi;, the negative of the screw function of the Riemann zeta function. Between consecutive prime powers &Psi; is strictly convex, a directed-rounding certificate proves &Psi;(t) > 0 for 0 < t ≤ log 10&sup1;⁰, and the infinite tail reduces to one reserve inequality V_q ≥ 0 at every active prime-power event q, one immediately after which &Psi; decreases. We show that within each episode of decrease only the last of these inequalities matters. In the service clock &tau; = A′(t), where A is the smooth part of &Psi;, the workload Y = −&Psi;′ decreases at unit speed and jumps up by &Lambda;(q)/&radic;q at each prime power. The last active event q before Y returns to zero, the recovery witness, is characterized by the window A′(log q) < &sum;_(n≤q) &Lambda;(n)/&radic;n ≤ A′(log Q), with Q the next prime power, and its reserve is the minimum of &Psi; over the episode. With the unconditional exclusion of a never-ending episode (Part 5), RH holds if and only if V_q ≥ 0 at every recovery witness that recovers beyond a verified positive base. An exact occupation formula bounds the difference between recovery counts and the normalized time that Y spends just above zero by explicit endpoint counts; strong convexity gives two-sided bounds for the final descent, a certificate for single-event episodes and a prime-gap test for multi-event witnesses. Directed 128-bit arithmetic shows that only 102,896 of the 25,614,164 active events up to 10⁹ are recovery witnesses and, in the complete census of the finite certificate, finds exactly 364,764 strict recoveries through 10&sup1;⁰; ball arithmetic resolves the critical 106-event episode. Proving at every recovery witness that a nonnegative smoothed von Mangoldt sum does not exceed an explicit capacity remains open and is equivalent to RH.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Rainer Andreas Mittermeier",
      "orcid": "0009-0009-6191-4475"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7828pkaswky1a.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23401342",
  "fulltext_url": null,
  "id": "7828pkaswky1a",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23401342",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23401342/files/261015_Mittermeier_RH_Recovery_Witnesses_Part4_v2.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7828pkaswky1a.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:20:46Z",
      "native_id": "23401342",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23401342"
    }
  ],
  "subjects": [],
  "title": "Recovery Witnesses for Suzuki's Screw Function: Service-Clock Geometry and Episode-Minimum Certificates — Part 4",
  "title_text": "Recovery Witnesses for Suzuki's Screw Function: Service-Clock Geometry and Episode-Minimum Certificates — Part 4",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:46Z",
  "url": "https://research.draconitic.com/paper/7828pkaswky1a",
  "venue": "Zenodo",
  "versions": []
}