{
  "schema_version": 1,
  "problem_number": "AMR-022-5074",
  "title": "Dual Tests and Spatial Obstructions for Positive-Real-Part Majorants",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For a nonnegative measurable function f on the unit circle, we give an attained variational test for almost-everywhere domination by the boundary modulus of a holomorphic function with positive real part. With h = log max(1,f), the logarithm of the least center modulus for a majorant of max(1,f) equals the supremum of integral(hg) - (pi/2) norm(Hg,1) over smooth nonnegative tests g of integral one, where H is the periodic Hilbert transform. Finiteness is the exact existence criterion, the coefficient pi/2 is sharp, and the tests can be restricted to a countable family of rational squared-polynomial moduli. We construct explicit separated spikes in weak L1 with no such majorant, although their symmetric decreasing rearrangement does have one. For N spikes, the weak L1 quasinorm remains at most two while the least clamped center modulus lies between N/8 and N+1. This addresses the almost-everywhere majorant class in Korenblum’s Problem 5.74 in Hayman–Lingham (UnsolvedMath AMR-022-5074) through a dual variational characterization. It is not a finite decision algorithm or a claim of the first historical resolution. The five-page English preprint contains complete proofs; AI-assisted and self-audited, without independent peer review, formal verification, or exhaustive priority certification.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CV",
    "math.FA"
  ],
  "keywords": [
    "AMR-022-5074",
    "positive real part",
    "boundary majorant",
    "Hilbert transform",
    "Herglotz representation",
    "weak L1",
    "convex duality"
  ],
  "manuscript_version_date": "2026-10-26",
  "publication_date": "2026-10-26",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-26",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/amr-022-5074/",
  "pdf_url": "https://eulersolve.org/papers/amr-022-5074/paper.pdf?v=9c568f7ccff7",
  "doi": "10.5281/zenodo.23661163",
  "zenodo_record_url": "https://zenodo.org/records/23661163",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "An attained dual Hilbert-transform test characterizes almost-everywhere positive-real-part modulus majorizability. The coefficient pi/2 is sharp and rational squared-polynomial tests suffice. Explicit separated spikes have bounded weak-L1 quasinorm but no majorant, while their symmetric decreasing rearrangement has one; N spikes require center modulus between N/8 and N+1. Complete proofs of an attained dual variational criterion and explicit spatial weak-L1 obstruction. The optimum concerns majorants of max(1,f); this is not a finite decision algorithm or a claim of the first historical resolution of Hayman-Lingham 5.74. This preprint is AI-assisted, self-audited and unrefereed; no independent or formal verification or certified novelty or absolute-priority claim is made.",
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      "sha256": "9c568f7ccff767d5d2e75c33aba97420f16287a9ea65dc76d7e7b065ab123aa1"
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    "source.zip": {
      "sha256": "387fcba673885c1661648c62fc84b57186b7e38742a4cf71df1953c8146564ed"
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    "verification_report.md": {
      "sha256": "c05816612c79037e74ea517c539f9d4e5f30decaa8638b4ebce6d0a725ea4337"
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  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}