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  "slug": "quantitative-bulk-boundary-correspondence-for-anyon-condensation-two-computable-",
  "title": "Quantitative Bulk–Boundary Correspondence for Anyon Condensation: Two Computable Indices with Explicit Arithmetic",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "When a (2+1)-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which remain contingent? Building on the two-index proposal of the QNFO framework [9], we develop a reconciled framework built on two computable quantities: the condensation strength I₁ = \\|A\\|/D, comparing the categorical size \\|A\\| = ∑_a ∈ A d_a² of the condensate algebra A to the bulk total quantum dimension D, and the Majorana count N_M = 2c_-, where c_- is the chiral central charge obtained from the Gauss–Milgram formula. We verify both indices by fully explicit arithmetic in three benchmark theories: the toric code condensing e, the Z₃ gauge theory condensing a charge, and the Ising topological order condensing its fermion ψ. [...]",
  "abstract_markdown": "When a $(2+1)$-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which remain contingent? Building on the two-index proposal of the QNFO framework [9], we develop a reconciled framework built on two computable quantities: the condensation strength $I_1 = \\|\\mathcal{A}\\|/\\mathcal{D}$, comparing the categorical size $\\|\\mathcal{A}\\| = \\sum_{a \\in \\mathcal{A}} d_a^2$ of the condensate algebra $\\mathcal{A}$ to the bulk total quantum dimension $\\mathcal{D}$, and the Majorana count $N_M = 2c_-$, where $c_-$ is the chiral central charge obtained from the Gauss–Milgram formula. We verify both indices by fully explicit arithmetic in three benchmark theories: the toric code condensing $e$, the $\\mathbb{Z}_3$ gauge theory condensing a charge, and the Ising topological order condensing its fermion $\\psi$. [...]",
  "date": "2026-10-09",
  "first_published": "2026-10-09",
  "last_revised": "2026-10-09T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/quantitative-bulk-boundary-correspondence-for-anyon-condensation-two-computable-",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Quantitative Bulk–Boundary Correspondence for Anyon Condensation: Two Computable Indices with Explicit Arithmetic"
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        "description": "When a (2+1)-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which remain contingent? Building on the two-index proposal of the QNFO framework [9], we develop a reconciled framework built on two computable quantities: the condensation strength I₁ = \\|A\\|/D, comparing the categorical size \\|A\\| = ∑_a ∈ A d_a² of the condensate algebra A to the bulk total quantum dimension D, and the Majorana count N_M = 2c_-, where c_- is the chiral central charge obtained from the Gauss–Milgram formula. We verify both indices by fully explicit arithmetic in three benchmark theories: the toric code condensing e, the Z₃ gauge theory condensing a charge, and the Ising topological order condensing its fermion ψ. [...]",
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