{
  "id": "oai:papers.qnfo.org:is-the-harmonic-oscillator-an-infrared-attractor-in-all-places-a-place-resolved-",
  "slug": "is-the-harmonic-oscillator-an-infrared-attractor-in-all-places-a-place-resolved-",
  "title": "Is the Harmonic Oscillator an Infrared Attractor in All Places? A Place‑Resolved Analysis of the Harmonic Paradigm",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The universal infrared (IR) attractor claim for the quantum harmonic oscillator (HO) has been examined only over the Archimedean absolute value on ℚ. This work asks whether the attractor status survives under the non‑Archimedean p‑adic and adelic norms. We construct a place‑resolved renormalization‑group (RG) framework, define a dimensionless distance α_v from a flowing bosonic system to the HO fixed point for each place v, and adopt a geometric p‑adic spectrum E^(p)_n=E₀ p^-n organized on Bruhat–Tits tree levels. Explicit derivations include (i) verification of the adelic product formula for three rationals, (ii) counting of Bruhat–Tits tree vertices up to depth 5, (iii) comparison of constant Archimedean gaps with geometric p‑adic gaps for p=2,3,5, (iv) exponential RG decay α_v(ℓ)=e^-γ_vℓ with illustrative γ_v=0.1, (v) testing a product‑of‑distances linkage hypothesis, and (vi) a cross‑place gap‑ratio divergence. The principal result is that attraction can occur in every place but with spectrally distinct fixed points; the adelic product formula constrains amplitudes, not spectra, so no strong spectral linkage exists. Consequently, the Harmonic Paradigm’s attractor thesis is not an Archimedean artifact but also not place‑invariant in a strong sense.",
  "abstract_markdown": "The universal infrared (IR) attractor claim for the quantum harmonic oscillator (HO) has been examined only over the Archimedean absolute value on ℚ. This work asks whether the attractor status survives under the non‑Archimedean $p$‑adic and adelic norms. We construct a place‑resolved renormalization‑group (RG) framework, define a dimensionless distance $\\alpha_v$ from a flowing bosonic system to the HO fixed point for each place $v$, and adopt a geometric $p$‑adic spectrum $E^{(p)}_n=E_0\\,p^{-n}$ organized on Bruhat–Tits tree levels. Explicit derivations include (i) verification of the adelic product formula for three rationals, (ii) counting of Bruhat–Tits tree vertices up to depth 5, (iii) comparison of constant Archimedean gaps with geometric $p$‑adic gaps for $p=2,3,5$, (iv) exponential RG decay $\\alpha_v(\\ell)=e^{-\\gamma_v\\ell}$ with illustrative $\\gamma_v=0.1$, (v) testing a product‑of‑distances linkage hypothesis, and (vi) a cross‑place gap‑ratio divergence. The principal result is that attraction can occur in every place but with spectrally distinct fixed points; the adelic product formula constrains amplitudes, not spectra, so no strong spectral linkage exists. Consequently, the Harmonic Paradigm’s attractor thesis is not an Archimedean artifact but also not place‑invariant in a strong sense.",
  "date": "2026-10-10",
  "first_published": "2026-10-10",
  "last_revised": "2026-10-24T04:11:10Z",
  "modified": "2026-10-24T04:11:10Z",
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  "doi": null,
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  "url": "https://papers.qnfo.org/papers/is-the-harmonic-oscillator-an-infrared-attractor-in-all-places-a-place-resolved-",
  "license_url": "https://legal.qnfo.org/",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Is the Harmonic Oscillator an Infrared Attractor in All Places? A Place‑Resolved Analysis of the Harmonic Paradigm"
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    ],
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    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-10",
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        "description": "The universal infrared (IR) attractor claim for the quantum harmonic oscillator (HO) has been examined only over the Archimedean absolute value on ℚ. This work asks whether the attractor status survives under the non‑Archimedean p‑adic and adelic norms. We construct a place‑resolved renormalization‑group (RG) framework, define a dimensionless distance α_v from a flowing bosonic system to the HO fixed point for each place v, and adopt a geometric p‑adic spectrum E^(p)_n=E₀ p^-n organized on Bruhat–Tits tree levels. Explicit derivations include (i) verification of the adelic product formula for three rationals, (ii) counting of Bruhat–Tits tree vertices up to depth 5, (iii) comparison of constant Archimedean gaps with geometric p‑adic gaps for p=2,3,5, (iv) exponential RG decay α_v(ℓ)=e^-γ_vℓ with illustrative γ_v=0.1, (v) testing a product‑of‑distances linkage hypothesis, and (vi) a cross‑place gap‑ratio divergence. The principal result is that attraction can occur in every place but with spectrally distinct fixed points; the adelic product formula constrains amplitudes, not spectra, so no strong spectral linkage exists. Consequently, the Harmonic Paradigm’s attractor thesis is not an Archimedean artifact but also not place‑invariant in a strong sense.",
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