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  "id": "oai:papers.qnfo.org:invented-representations-discovered-constraints-a-quantitative-case-for-weak-str",
  "slug": "invented-representations-discovered-constraints-a-quantitative-case-for-weak-str",
  "title": "Invented Representations, Discovered Constraints: A Quantitative Case for Weak Structural Realism in Mathematics",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Whether mathematics is invented or discovered remains a live dispute with practical consequences for how research, education, and patent law treat mathematical objects. We assume the 2020 PhilPapers survey reports the field split, with nominalism at 41.85 percent and Platonism at 38.38 percent of the distribution and a fifth of respondents rejecting both labels (Section 3.3), yet both camps argue from the same celebrated cases while no principled criterion separates what practitioners invent from what they discover. We propose such a criterion, a representation/constraint split with an invariance test, and evaluate it against quantitative anchors: the exact sexagesimal arithmetic of Plimpton 322, whose first-row value 1;59,00,15 we reproduce to all four recorded places as (169/120)² = 28561/14400; the extension of the tablet's generating scheme to five rows beyond its fifteen recorded rows, so that the recorded corpus covers 75 percent of a twenty-row extension; a survivorship model of Wigner's applicability puzzle calibrated on documented adoption data for non-Archimedean geometry, where zero of three closest historical analogues achieved mainstream adoption within a decade and current non-adopting activity is bounded near 10² papers per year; and Gödel incompleteness read as metatheory-relative rather than object-level. Every anchor fits the split: representations are culturally variable and partly invented, while the constraint structure they navigate behaves as discovered. We conclude that weak structural realism states the applicability puzzle precisely rather than dissolving it, and we outline the archival search that would falsify the Plimpton anchor.",
  "abstract_markdown": "Whether mathematics is invented or discovered remains a live dispute with practical consequences for how research, education, and patent law treat mathematical objects. We assume the 2020 PhilPapers survey reports the field split, with nominalism at 41.85 percent and Platonism at 38.38 percent of the distribution and a fifth of respondents rejecting both labels (Section 3.3), yet both camps argue from the same celebrated cases while no principled criterion separates what practitioners invent from what they discover. We propose such a criterion, a representation/constraint split with an invariance test, and evaluate it against quantitative anchors: the exact sexagesimal arithmetic of Plimpton 322, whose first-row value $1;59,00,15$ we reproduce to all four recorded places as $(169/120)^2 = 28561/14400$; the extension of the tablet's generating scheme to five rows beyond its fifteen recorded rows, so that the recorded corpus covers 75 percent of a twenty-row extension; a survivorship model of Wigner's applicability puzzle calibrated on documented adoption data for non-Archimedean geometry, where zero of three closest historical analogues achieved mainstream adoption within a decade and current non-adopting activity is bounded near $10^2$ papers per year; and Gödel incompleteness read as metatheory-relative rather than object-level. Every anchor fits the split: representations are culturally variable and partly invented, while the constraint structure they navigate behaves as discovered. We conclude that weak structural realism states the applicability puzzle precisely rather than dissolving it, and we outline the archival search that would falsify the Plimpton anchor.",
  "date": "2026-10-27",
  "first_published": "2026-10-27",
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  "url": "https://papers.qnfo.org/papers/invented-representations-discovered-constraints-a-quantitative-case-for-weak-str",
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    "titles": [
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        "title": "Invented Representations, Discovered Constraints: A Quantitative Case for Weak Structural Realism in Mathematics"
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