A Quantitative Correspondence between the Lattice Volume Deficit and the Tangherlini Bekenstein–Hawking Entropy (Paper 4)

v2 (April 2026): Reference list refined per paper. External references corrected and finalized; no self-citations. v1 (DOI 10.5281/zenodo.19837594) remains the original publication.

English: We compare the volume deficit $\Delta(R)$ from the cube packing problem with the Bekenstein–Hawking entropy of a four-plus-one-dimensional Schwarzschild–Tangherlini black hole. Both quantities scale as $R^3$, and the asymptotic ratio is $\Delta/S_{BH} \to 32/(3\pi) \approx 3.40$, independent of any free parameter. The correspondence is structural and quantitative; the physical interpretation of the constant ratio is left open.

日本語: 立方体充填問題からの体積不足 $\Delta(R)$ と4+1次元 Schwarzschild–Tangherlini ブラックホールの Bekenstein–Hawking エントロピーを比較する。両量は $R^3$ にスケールし、漸近比 $\Delta/S_{BH} \to 32/(3\pi) \approx 3.40$(自由パラメータ非依存)。対応は構造的・定量的;定数比の物理的解釈は未解決。