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  "id": "oai:papers.qnfo.org:formal-isomorphism-criteria-for-cross-disciplinary-terminology-crosswalks-a-thre",
  "slug": "formal-isomorphism-criteria-for-cross-disciplinary-terminology-crosswalks-a-thre",
  "title": "Formal Isomorphism Criteria for Cross-Disciplinary Terminology Crosswalks: A Three-Tier Verification Framework with Decidability and Sample-Size Analysis",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Cross-disciplinary knowledge transfer currently relies on intuition: researchers in different fields who work on the same structural object routinely fail to discover each other because their vocabularies do not overlap. A study would assume a partitionality index of 0.9721, with 453 of 466 technical terms occurring in exactly one domain and an empty shared core at the three-domain threshold. This paper addresses the gap between that lexical silence and the claimed structural unity of scientific concepts: no existing operational criterion distinguishes genuine cross-domain conceptual equivalence from superficial analogy. We formalize three connection types — structural isomorphism, functional equivalence, and logical interdependence — as a three-tier verification pipeline modeled on the L1/L2/L3 isomorphism hierarchy for attributed and dynamic networks. We derive the candidate search space for a six-domain vocabulary (binom4662 = 108,345 term pairs; binom4664 ≈ 1.94 × 10⁹ relation quadruples), verify the projective invariance of a cross-ratio alignment score with a worked example (χ = 4/3 preserved exactly under a Möbius transformation), derive the expert-validation sample size n ≥ 85 from first principles, and show that a three-tier independence cascade reduces the false-positive rate from 10^-2 per tier to 10^-6 jointly. The framework converts crosswalk construction from an analogy-driven craft into a verification problem with explicit falsification criteria, and it is immediately applicable to terminology work in machine translation, terminography, and cross-disciplinary team collaboration.",
  "abstract_markdown": "Cross-disciplinary knowledge transfer currently relies on intuition: researchers in different fields who work on the same structural object routinely fail to discover each other because their vocabularies do not overlap. A study would assume a partitionality index of 0.9721, with 453 of 466 technical terms occurring in exactly one domain and an empty shared core at the three-domain threshold. This paper addresses the gap between that lexical silence and the claimed structural unity of scientific concepts: no existing operational criterion distinguishes genuine cross-domain conceptual equivalence from superficial analogy. We formalize three connection types — structural isomorphism, functional equivalence, and logical interdependence — as a three-tier verification pipeline modeled on the L1/L2/L3 isomorphism hierarchy for attributed and dynamic networks. We derive the candidate search space for a six-domain vocabulary ($\\binom{466}{2} = 108{,}345$ term pairs; $\\binom{466}{4} \\approx 1.94 \\times 10^{9}$ relation quadruples), verify the projective invariance of a cross-ratio alignment score with a worked example ($\\chi = 4/3$ preserved exactly under a Möbius transformation), derive the expert-validation sample size $n \\geq 85$ from first principles, and show that a three-tier independence cascade reduces the false-positive rate from $10^{-2}$ per tier to $10^{-6}$ jointly. The framework converts crosswalk construction from an analogy-driven craft into a verification problem with explicit falsification criteria, and it is immediately applicable to terminology work in machine translation, terminography, and cross-disciplinary team collaboration.",
  "date": "2026-11-13",
  "first_published": "2026-11-13",
  "last_revised": "2026-11-13T01:12:38Z",
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  "url": "https://papers.qnfo.org/papers/formal-isomorphism-criteria-for-cross-disciplinary-terminology-crosswalks-a-thre",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Formal Isomorphism Criteria for Cross-Disciplinary Terminology Crosswalks: A Three-Tier Verification Framework with Decidability and Sample-Size Analysis"
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