{
  "schema_version": 1,
  "problem_number": "AIM-ANALYSIS-0095",
  "title": "Coordinate Subcubes of Weaver Partitions at the MSS Bound",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For a complex Parseval frame of m vectors with squared norms at most alpha, we construct an entire coordinate subcube of good signings at the historical MSS bound sqrt(8 alpha)+2 alpha. If 0<alpha<(3-2 sqrt(2))/2 and r=ceil((3+2 sqrt(2))/alpha), at least ceil(m/r) signs can be chosen freely while the complement remains fixed. This gives at least 2^ceil(m/r) unordered indexed good partitions. The proof combines an operator-small MSS partition with the sharper BCMS bound on the normalized complement. Prior counting estimates, including Akbas-Sra, are credited. This is neither a sharp count nor closure of the entire AIM agenda. The preprint is self-audited, unrefereed and AI-assisted; independent review, formal verification and absolute priority are not claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.FA",
    "math.CO"
  ],
  "keywords": [
    "Weaver partitions",
    "Parseval frames",
    "matrix discrepancy",
    "coordinate subcubes",
    "Kadison-Singer",
    "AIM-ANALYSIS-0095"
  ],
  "manuscript_version_date": "2026-10-14",
  "publication_date": "2026-10-14",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-14",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-analysis-0095/",
  "pdf_url": "https://eulersolve.org/papers/aim-analysis-0095/paper.pdf?v=fba8eef1ffff",
  "doi": "10.5281/zenodo.23360221",
  "zenodo_record_url": "https://zenodo.org/records/23360221",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof of an explicit fixed-complement coordinate-subcube theorem at the historical MSS discrepancy bound. No sharp enumeration, positive-fraction theorem, first exponential count, optimal exponent or closure of the broad AIM question is claimed. Akbas-Sra and the upstream product-frame calculation are credited. Absolute priority is undetermined; independent review and formal verification have not occurred.",
  "files": {
    "paper.pdf": {
      "sha256": "fba8eef1ffffe2cbe384bc4599f6e91db76309103d1fbfa784584cc826a87a94"
    },
    "source.zip": {
      "sha256": "dd066a6129b0993052416552a6f9f06f99797cd7f5e2bcfe446b8aaf96133576"
    },
    "verification_report.md": {
      "sha256": "ac4fd275bb7590f217797fa62e9f4058f220c04e6a47dd9c521818c122355fa0"
    }
  },
  "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."
}