Quantum Speed Limit as a Sensitive Probe of Planck-Scale Effect

This repository introduces the Thickness‑Structure Hypothesis, a theoretical framework extending special relativity. In special relativity, the spacetime interval is defined as ds2=c2dτ2=c2dt2−dx2−dy2−dz2ds^2 = c^2 dτ^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 For lightlike particles, dτ=0dτ = 0, meaning the proper time is always null. We regard this boundary condition as the ground state and define the thickness degree of freedom as δT≡dτc,δT=0 at the lightlike boundary.δ T ≡ dτ/c, δ T = 0 \;\; at the lightlike boundary. A finite extension δT=εδ T = ε (finite but infinitesimal) represents a microscopic fluctuation relative to the null‑proper‑time system, providing a unifying degree of freedom for both lightlike and non‑lightlike systems. Intuitive foundation: According to special relativity, a particle moving at the speed of light experiences no proper time—its creation and annihilation coincide as a single event. Extending this intuition to the early universe, matter at that epoch can be interpreted as governed by near‑lightlike motion, with the universe itself existing as a structure where beginning and end overlap. This study builds on that perspective, proposing the Thickness‑Structure Hypothesis as an attempt to unify the largest cosmic scales with the smallest quantum scales. Model (classical + quantum correction): εeff(q)=εexp⁡(αTT),τscale(q)=τclexp⁡(γTT)εeff(q) = ε exp(α_T T), τscale(q) = τcl exp(γ_T T) This framework connects gravitational waves, cosmology, solar‑system tests, and high‑energy physics under a reproducible methodology. This record also includes a Japanese version of the manuscript and a reproducibility package (thickness_structure_repro.zip).