Protiform's Variational Principle --- Foundational Derivation of the Fractasis Action and MGDC Convergence Geometry Article Swipe

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Chino, Hideyuki ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5281/zenodo.17591918

Overview. This preprint presents PVP (Protiform's Variational Principle), specifying the pair-potential/force laws under Protiform’s fluctuation kernel Kℓ(r)=e−r/ℓ/rK_\ell(r)=e^{-r/\ell}/rKℓ(r)=e−r/ℓ/r and the sign/proportional-constant dictionary. We derive two-body and field-level formulations, establish stability/irreversibility correspondences, and provide reproducible figures (log-log CCDF, κ-sweeps, winner-maps).Contributions. (i) A unified variational principle deriving stability flows from fluctuation structure; (ii) a general framework linking monotone information dynamics, convergence geometry, and Sₙ-type stability; (iii) a geometric formulation of irreversibility based on stability-preserving flows and the Protiform action.Artifacts. PDF; TeX/figures.Licensing. Text: CC BY 4.0; Code: MIT.This record is part of the Protiform / Fractasis series aiming at a fluctuation-based unification of stability geometry from quantum to cosmological scales. Feedback and independent checks are welcome; a short “repro kit” is provided in the source/code archives.

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Mathematics Preprint Variational principle Convergence (economics) Stability (learning theory) Monotone polygon Series (stratigraphy) Unification Action (physics) Kernel (algebra) Applied mathematics Principle of least action Variational analysis Information geometry Term (time) Mathematical analysis Monotonic function Calculus of variations Differential geometry Geometry Domain (mathematical analysis) Variational inequality Calculus (dental) Hamilton's principle

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Title: Protiform's Variational Principle --- Foundational Derivation of the Fractasis Action and MGDC Convergence Geometry

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Publication year: 2025

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Authors: Chino, Hideyuki

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Concepts: Mathematics, Preprint, Variational principle, Convergence (economics), Stability (learning theory), Monotone polygon, Series (stratigraphy), Unification, Action (physics), Kernel (algebra), Applied mathematics, Principle of least action, Variational analysis, Information geometry, Term (time), Mathematical analysis, Monotonic function, Calculus of variations, Differential geometry, Geometry, Domain (mathematical analysis), Variational inequality, Calculus (dental), Hamilton's principle

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