{
  "id": "oai:papers.qnfo.org:radix-agnostic-dsi-detection",
  "slug": "radix-agnostic-dsi-detection",
  "title": "Radix-Agnostic Detection of Discrete Scale Invariance: A Certified Three-Stage Protocol and a Null Result from Planck 2018",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Discrete scale invariance (DSI) — invariance under a discrete set of rescalings x → λ^n x — predicts log-periodic oscillations whose angular frequency in the logarithmic coordinate u = ln x is ω₀ = 2π/lnλ. When the scaling radix λ is unknown, a radix-locked search at assumed radices risks both false negatives (the true radix was never probed) and multiplicity inflation (a continuum of probed frequencies is scanned without correction). This work develops and certifies a radix-agnostic detection protocol in three stages: (1) detrend in log-space and locate the spectral peak by FFT or Lomb–Scargle periodogram; (2) refine the peak with a bounded sinusoid fit on the detrended residuals, yielding hatλ ± σ_λ; (3) test candidate radices against the measured value. Certification is mandatory: a max-statistic bootstrap null (already multiplicity-corrected), a likelihood-ratio test (DeltaBIC > 10), and three integrity gates — resolvability (ω ≥ 2π/u_rm span), amplitude (SNR ≥ 1), and radix precision (σ_λ/λ < 10\\%). [...]",
  "abstract_markdown": "Discrete scale invariance (DSI) — invariance under a discrete set of rescalings $x \\to \\lambda^n x$ — predicts log-periodic oscillations whose angular frequency in the logarithmic coordinate $u = \\ln x$ is $\\omega_0 = 2\\pi/\\ln\\lambda$. When the scaling radix $\\lambda$ is unknown, a radix-locked search at assumed radices risks both false negatives (the true radix was never probed) and multiplicity inflation (a continuum of probed frequencies is scanned without correction). This work develops and certifies a radix-agnostic detection protocol in three stages: (1) detrend in log-space and locate the spectral peak by FFT or Lomb–Scargle periodogram; (2) refine the peak with a bounded sinusoid fit on the detrended residuals, yielding $\\hat\\lambda \\pm \\sigma_\\lambda$; (3) test candidate radices against the measured value. Certification is mandatory: a max-statistic bootstrap null (already multiplicity-corrected), a likelihood-ratio test ($\\Delta\\mathrm{BIC} > 10$), and three integrity gates — resolvability ($\\omega \\ge 2\\pi/u_{\\rm span}$), amplitude ($\\mathrm{SNR} \\ge 1$), and radix precision ($\\sigma_\\lambda/\\lambda < 10\\%$). [...]",
  "date": "2026-08-01",
  "first_published": "2026-08-01",
  "last_revised": "2026-10-26T07:11:00Z",
  "modified": "2026-10-26T07:11:00Z",
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  "peer_review_status": "Not independently peer-reviewed",
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  "url": "https://papers.qnfo.org/papers/radix-agnostic-dsi-detection",
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  "sha256": "8008bdcb24beec5a4e8ba6a7ac6766970f6fe67174a7829cd8d8226f27f47d8f",
  "version_url": "https://papers.qnfo.org/papers/radix-agnostic-dsi-detection/v/0.1.0",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Radix-Agnostic Detection of Discrete Scale Invariance: A Certified Three-Stage Protocol and a Null Result from Planck 2018"
      }
    ],
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    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-08-01",
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        "date": "2026-10-26",
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        "description": "Discrete scale invariance (DSI) — invariance under a discrete set of rescalings x → λ^n x — predicts log-periodic oscillations whose angular frequency in the logarithmic coordinate u = ln x is ω₀ = 2π/lnλ. When the scaling radix λ is unknown, a radix-locked search at assumed radices risks both false negatives (the true radix was never probed) and multiplicity inflation (a continuum of probed frequencies is scanned without correction). This work develops and certifies a radix-agnostic detection protocol in three stages: (1) detrend in log-space and locate the spectral peak by FFT or Lomb–Scargle periodogram; (2) refine the peak with a bounded sinusoid fit on the detrended residuals, yielding hatλ ± σ_λ; (3) test candidate radices against the measured value. Certification is mandatory: a max-statistic bootstrap null (already multiplicity-corrected), a likelihood-ratio test (DeltaBIC > 10), and three integrity gates — resolvability (ω ≥ 2π/u_rm span), amplitude (SNR ≥ 1), and radix precision (σ_λ/λ < 10\\%). [...]",
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