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  "id": "oai:papers.qnfo.org:exchange-symmetry-is-an-involution-not-an-idempotent-a-derivation-based-fact-che",
  "slug": "exchange-symmetry-is-an-involution-not-an-idempotent-a-derivation-based-fact-che",
  "title": "Exchange Symmetry Is an Involution, Not an Idempotent: A Derivation‑Based Fact‑Check",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The claim that particle exchange is idempotent, that the two‑particle configuration space is the three‑sphere S³, that the spin‑statistics theorem holds without qualification, and that non‑Abelian anyons are idempotent appears in recent speculative notes. This paper addresses the gap between those statements and established theory by applying a derivation‑based fact‑checking pipeline: logical decomposition of each sub‑claim, alignment with concrete source material, and explicit arithmetic verification of auxiliary quantitative claims. Using the exchange‑phase relation R=e²π i s, we show that the exchange operator satisfies E²=I (involution) rather than E²=E (idempotence). Topological analysis demonstrates that the configuration space of two identical particles in three dimensions is bigl(R³timesR³bigr)/Z₂, not S³. The spin‑statistics theorem is shown to rely on Lorentz invariance, microcausality, and a positive‑energy spectrum, limiting its applicability. For an illustrative anyon with spin s=1/3, the idempotency condition fails, yielding |R²-R|=√3≈1.732. Quantitative verification of the Reality‑Distortion Room volume (61.875 m³) and total participant‑minutes (600 min) illustrates the arithmetic rigor of the method. The results safeguard theoretical and experimental programs that depend on correct exchange symmetry properties.",
  "abstract_markdown": "The claim that particle exchange is idempotent, that the two‑particle configuration space is the three‑sphere $S^{3}$, that the spin‑statistics theorem holds without qualification, and that non‑Abelian anyons are idempotent appears in recent speculative notes. This paper addresses the gap between those statements and established theory by applying a derivation‑based fact‑checking pipeline: logical decomposition of each sub‑claim, alignment with concrete source material, and explicit arithmetic verification of auxiliary quantitative claims. Using the exchange‑phase relation $R=e^{2\\pi i s}$, we show that the exchange operator satisfies $E^{2}=\\mathbb{I}$ (involution) rather than $E^{2}=E$ (idempotence). Topological analysis demonstrates that the configuration space of two identical particles in three dimensions is $\\bigl(\\mathbb{R}^{3}\\times\\mathbb{R}^{3}\\bigr)/\\mathbb{Z}_{2}$, not $S^{3}$. The spin‑statistics theorem is shown to rely on Lorentz invariance, microcausality, and a positive‑energy spectrum, limiting its applicability. For an illustrative anyon with spin $s=1/3$, the idempotency condition fails, yielding $|R^{2}-R|=\\sqrt{3}\\approx1.732$. Quantitative verification of the Reality‑Distortion Room volume ($61.875\\ \\text{m}^{3}$) and total participant‑minutes ($600\\ \\text{min}$) illustrates the arithmetic rigor of the method. The results safeguard theoretical and experimental programs that depend on correct exchange symmetry properties.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/exchange-symmetry-is-an-involution-not-an-idempotent-a-derivation-based-fact-che",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Exchange Symmetry Is an Involution, Not an Idempotent: A Derivation‑Based Fact‑Check"
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