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  "slug": "continuum-critique-trilogy",
  "title": "The Continuum Critique Trilogy",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Three papers, one thesis: the real-number continuum is a map, not the territory — and many \"unsolved problems\" in mathematics and physics are artifacts of representational choices rather than genuine ignorance. This monograph unifies three companion papers into a single narrative. Paper I (The Notation Problem) proposes the scaffold-stripping hypothesis: six marginalised formal systems — Laws of Form, Existential Graphs, the Viable System Model, Catastrophe Theory, Pattern Language, and Polycontextural Logic — contain valid category-theoretic invariants imprisoned in inaccessible notation. Paper II (Alpha as Bifurcation Parameter) poses the helical electron stability problem: the fine-structure constant α ≈ 1/137 is hypothesised to be a critical eigenvalue of a null-curve variational principle, the pitch angle separating three qualitatively distinct geometric regimes. Paper III (Poisson Summation as the Adelic Bridge) provides the analytic undergirding for the adelic physics programme: the Poisson summation formula bridges discrete (Q) and continuous (R) via the Gaussian, the unique invariant kernel at every place, within Tate's adelic Fourier transform framework. [...]",
  "abstract_markdown": "Three papers, one thesis: **the real-number continuum is a map, not the territory — and many \"unsolved problems\" in mathematics and physics are artifacts of representational choices rather than genuine ignorance.** This monograph unifies three companion papers into a single narrative. Paper I (The Notation Problem) proposes the scaffold-stripping hypothesis: six marginalised formal systems — Laws of Form, Existential Graphs, the Viable System Model, Catastrophe Theory, Pattern Language, and Polycontextural Logic — contain valid category-theoretic invariants imprisoned in inaccessible notation. Paper II (Alpha as Bifurcation Parameter) poses the helical electron stability problem: the fine-structure constant α ≈ 1/137 is hypothesised to be a critical eigenvalue of a null-curve variational principle, the pitch angle separating three qualitatively distinct geometric regimes. Paper III (Poisson Summation as the Adelic Bridge) provides the analytic undergirding for the adelic physics programme: the Poisson summation formula bridges discrete (Q) and continuous (R) via the Gaussian, the unique invariant kernel at every place, within Tate's adelic Fourier transform framework. [...]",
  "date": "2026-07-29",
  "first_published": "2026-07-29",
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        "description": "Three papers, one thesis: the real-number continuum is a map, not the territory — and many \"unsolved problems\" in mathematics and physics are artifacts of representational choices rather than genuine ignorance. This monograph unifies three companion papers into a single narrative. Paper I (The Notation Problem) proposes the scaffold-stripping hypothesis: six marginalised formal systems — Laws of Form, Existential Graphs, the Viable System Model, Catastrophe Theory, Pattern Language, and Polycontextural Logic — contain valid category-theoretic invariants imprisoned in inaccessible notation. Paper II (Alpha as Bifurcation Parameter) poses the helical electron stability problem: the fine-structure constant α ≈ 1/137 is hypothesised to be a critical eigenvalue of a null-curve variational principle, the pitch angle separating three qualitatively distinct geometric regimes. Paper III (Poisson Summation as the Adelic Bridge) provides the analytic undergirding for the adelic physics programme: the Poisson summation formula bridges discrete (Q) and continuous (R) via the Gaussian, the unique invariant kernel at every place, within Tate's adelic Fourier transform framework. [...]",
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