{
  "abstract": "The earlier preprint in this series defined a pair-valued fusion operator: a value V that is a\n\nsoftmax-weighted mean, and a score W that is a scaled log-sum-exp. That work established\n\nclosure, commutativity and associativity at a fixed coefficient, geometric and score\n\nbounds, derivatives, entropy identities, and first-order perturbation bounds. This paper\n\nresumes from that endpoint and contributes four guarded extensions, each with a written\n\nproof and independent numerical evidence:\n\nDuplicate-record consistency. A theorem showing that the full pair (V,W) can be\n\nreproduced from deduplicated storage, in either of two opposite directions (w ± β−1ln\n\nk), together with a bound on the error induced when multiplicities are estimated\n\nincorrectly. The mathematics is simple; the contribution is the pair of executable rules\n\nplus an a-priori damage bound, which turns a known hazard into a controlled\n\nprocedure.\n\nSharp sensitivity. The Hilbert distance between weight vectors never exceeds |β|·(max\n\nδ − min δ). This yields a globally valid total-variation bound, TV ≤ tanh(|β|·range(δ)/4),\n\nvalid without a small-perturbation assumption and proved sharp by an explicit twopoint\n\nfamily. A vector-valued counterpart and a cross-entropy ceiling follow.\n\nCertificates, and an honest negative result. Truncating the score tail can be made\n\nauditable: dropping mass τ bounds the value error by D·τ and makes the score gap\n\nexactly computable. The experiments confirm the certificate in every case — and show\n\nthat certificates do not imply savings. With uniform scores, a 2 % tail budget keeps\n\n98 % of records.\n\nConstrained calibration. Minimum-variance weights are optimal only on the simplex,\n\nand the unconstrained solution can be negative: an explicit analytic counterexample\n\ngives weights (1.25, −0.25) with objective 0.875 against 1.000 on the simplex. This\n\npaper gives an exact face-enumeration oracle for small problems, an equivalence\n\ncondition for the widely used inverse-MSE rule, and a calibration study of 2,400\n\nreplications that reports where weighting wins and where uniform averaging wins.\n\nEvery theoretical statement is proved or explicitly attributed to prior work. Every\n\nreported number is regenerated by seeded code, reproduces byte-for-byte across reruns,\n\nand is checked by an independent verifier of 27 checks that does not import the package\n\nunder test. Thirty-six unit tests accompany the reference implementation. The paper\n\nstates plainly what is prior art (softmax, log-sum-exp, the Hilbert–total-variation\n\ninequality and its constant, forecast-combination weighting) and makes no priority, speed\n\nor efficacy claim.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Al-Mu'taz Billah Salah Aldawdeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ccdzwy8syaqtj.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23678745",
  "fulltext_url": null,
  "id": "ccdzwy8syaqtj",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23678745",
  "language": "eng",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23678745/files/OTAZ_II_Math_AI_Extensions_EN.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ccdzwy8syaqtj.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:20:38Z",
      "native_id": "23678745",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23678745"
    }
  ],
  "subjects": [],
  "title": "OTAZ-II: Mathematical and AI Extensions of Exponentially Weighted Fusion — Duplicate-Record Consistency, Hilbert Sensitivity Bounds, Truncation Certificates and Constrained Calibration",
  "title_text": "OTAZ-II: Mathematical and AI Extensions of Exponentially Weighted Fusion — Duplicate-Record Consistency, Hilbert Sensitivity Bounds, Truncation Certificates and Constrained Calibration",
  "type": "preprint",
  "updated_at": "2026-11-09T12:20:38Z",
  "url": "https://research.draconitic.com/paper/ccdzwy8syaqtj",
  "venue": "Zenodo",
  "versions": []
}