{
  "id": "oai:papers.qnfo.org:configuration-space-topology",
  "slug": "configuration-space-topology",
  "title": "Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its ±1 Shadow, and a Pre-Registered Derivation Program",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Configuration-space topology (CST) derives exchange statistics from the topology of the space in which identical particles move: the fundamental group pi_1(C_N(M)) is the symmetric group S_N in d >= 3 spatial dimensions (exactly two exchange phases: boson +1, fermion -1) and the braid group B_N in d = 2 (anyons, including the non-abelian braiding used in topological quantum computation). This paper draws the boundary of that framework. It names the five silent scaffolds CST imports from classical geometry -- point-like particles, a fixed background manifold, the deleted hard-core diagonal, externally imposed dimension, adiabatic exchange -- and engages the active counter-literature testing each one (orbifolds, traid groups, graph configuration spaces, extended objects, supersymmetric anyons). It concedes the framework's hard boundary: the spin-statistics connection requires Lorentz symmetry, microcausality, and positive energy, which no topological or logical argument supplies. Against this boundary it reports the status of the QNFO pre-registered derivation program (exchange phase as a logical scalar R = e^{2 pi i s} from the re-entrant mark): T2 now carries construction content -- the +/-1 dichotomy is the ribbon identity evaluated in the d >= 3 sector; T1 is partially constructed; T3 is restated with named boundary conditions. It then states a synthesis conjecture -- the Distinction Calculus lifted into homotopy type theory, with the Grothendieck-Teichmuller group acting on braided monoidal categories, renders boundary-drawing an arithmetic act -- with explicit falsification conditions F1-F3, and differentiates it from the cohesive-HoTT program of Sati and Schreiber. The paper proves no new theorem; its contribution is a verified boundary map of a mature framework and a falsifiable route toward the logical origin of quantum statistics.",
  "abstract_markdown": "Configuration-space topology (CST) derives exchange statistics from the topology of the space in which identical particles move: the fundamental group pi_1(C_N(M)) is the symmetric group S_N in d >= 3 spatial dimensions (exactly two exchange phases: boson +1, fermion -1) and the braid group B_N in d = 2 (anyons, including the non-abelian braiding used in topological quantum computation). This paper draws the boundary of that framework. It names the five silent scaffolds CST imports from classical geometry -- point-like particles, a fixed background manifold, the deleted hard-core diagonal, externally imposed dimension, adiabatic exchange -- and engages the active counter-literature testing each one (orbifolds, traid groups, graph configuration spaces, extended objects, supersymmetric anyons). It concedes the framework's hard boundary: the spin-statistics connection requires Lorentz symmetry, microcausality, and positive energy, which no topological or logical argument supplies. Against this boundary it reports the status of the QNFO pre-registered derivation program (exchange phase as a logical scalar R = e^{2 pi i s} from the re-entrant mark): T2 now carries construction content -- the +/-1 dichotomy is the ribbon identity evaluated in the d >= 3 sector; T1 is partially constructed; T3 is restated with named boundary conditions. It then states a synthesis conjecture -- the Distinction Calculus lifted into homotopy type theory, with the Grothendieck-Teichmuller group acting on braided monoidal categories, renders boundary-drawing an arithmetic act -- with explicit falsification conditions F1-F3, and differentiates it from the cohesive-HoTT program of Sati and Schreiber. The paper proves no new theorem; its contribution is a verified boundary map of a mature framework and a falsifiable route toward the logical origin of quantum statistics.",
  "date": "2026-08-15",
  "first_published": "2026-08-15",
  "last_revised": "2026-08-15T00:00:00Z",
  "modified": "2026-08-15T00:00:00Z",
  "version": "0.3.0",
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  "language": "eng",
  "keywords": [
    "configuration-space topology",
    "exchange statistics",
    "spin-statistics theorem",
    "braid group",
    "laws of form",
    "distinction calculus",
    "Grothendieck-Teichmuller group",
    "homotopy type theory",
    "anyons",
    "pre-registered derivation"
  ],
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    "open-access scholarly work",
    "versioned research publication"
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  "url": "https://papers.qnfo.org/papers/configuration-space-topology",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its ±1 Shadow, and a Pre-Registered Derivation Program"
      }
    ],
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    "publicationYear": "2026",
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    "subjects": [
      {
        "subject": "configuration-space topology"
      },
      {
        "subject": "exchange statistics"
      },
      {
        "subject": "spin-statistics theorem"
      },
      {
        "subject": "braid group"
      },
      {
        "subject": "laws of form"
      },
      {
        "subject": "distinction calculus"
      },
      {
        "subject": "Grothendieck-Teichmuller group"
      },
      {
        "subject": "homotopy type theory"
      },
      {
        "subject": "anyons"
      },
      {
        "subject": "pre-registered derivation"
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        "date": "2026-08-15",
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        "description": "Configuration-space topology (CST) derives exchange statistics from the topology of the space in which identical particles move: the fundamental group pi_1(C_N(M)) is the symmetric group S_N in d >= 3 spatial dimensions (exactly two exchange phases: boson +1, fermion -1) and the braid group B_N in d = 2 (anyons, including the non-abelian braiding used in topological quantum computation). This paper draws the boundary of that framework. It names the five silent scaffolds CST imports from classical geometry -- point-like particles, a fixed background manifold, the deleted hard-core diagonal, externally imposed dimension, adiabatic exchange -- and engages the active counter-literature testing each one (orbifolds, traid groups, graph configuration spaces, extended objects, supersymmetric anyons). It concedes the framework's hard boundary: the spin-statistics connection requires Lorentz symmetry, microcausality, and positive energy, which no topological or logical argument supplies. Against this boundary it reports the status of the QNFO pre-registered derivation program (exchange phase as a logical scalar R = e^{2 pi i s} from the re-entrant mark): T2 now carries construction content -- the +/-1 dichotomy is the ribbon identity evaluated in the d >= 3 sector; T1 is partially constructed; T3 is restated with named boundary conditions. It then states a synthesis conjecture -- the Distinction Calculus lifted into homotopy type theory, with the Grothendieck-Teichmuller group acting on braided monoidal categories, renders boundary-drawing an arithmetic act -- with explicit falsification conditions F1-F3, and differentiates it from the cohesive-HoTT program of Sati and Schreiber. The paper proves no new theorem; its contribution is a verified boundary map of a mature framework and a falsifiable route toward the logical origin of quantum statistics.",
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