Casimir Energy of a Hardened Dispersion and the Equilibrium Conditions of a Compact Radius(硬化分散のカシミール項とコンパクト半径の平衡条件)
Year: 2026
Type: preprint
Abstract: EnglishA correction to and follow-up of “The Address of the Fine Structure Constant” (Healing-Length Theory). This unreviewed preprint re-examines compact-radius stabilization on R³ × S¹ for periodic free bosons with quartically hardened dispersion, ω² = q² + q⁴/M². The unexpanded, noncompact-subtracted Casimir potential is negative and monotonically increasing for every R > 0: the minimum inferred from a two-term asymptotic truncation is absent. Earlier coefficients and the radion-mass estimate are therefore not retained as results of a controlled stabilization mechanism.The paper gives necessary conditions for additional restoring forces and for simultaneous vacuum self-neutralization and radius equilibrium. Mixed periodic/antiperiodic sectors can produce a radius valley for specified composition and an input scale M. A DBI test action admits formal zero-vacuum local minima, but the specified first interaction correction is larger than the Gaussian one-loop term; the construction does not establish controlled stabilization. A restricted identification of winding with the electromagnetic KK fiber generates a Stückelberg mass. The paper derives neither the numerical value of α (or 137) nor a vacuum self-adjustment mechanism.Files: English and Japanese PDF and Markdown manuscripts (v1.0, 15 October 2026) and Supplementary_Materials.zip. The archive includes eight original Japanese research notes, portable publication copies of ten computational scripts, saved JSON/CSV results, pre-run records, a bilingual README with manuscript-to-file mappings and reproduction commands, pinned recheck dependencies, provenance hashes, and a publication recheck report. Numerical values and scientific judgments agreed within the stated comparison tolerance when all ten scripts were rerun in a separate working copy, including reproduction of the historical failed DBI frame-curvature check. Private local-path dependencies were removed from publication copies; the original research files were not modified. A pre-publication editorial update (16 October 2026) adds reference links and publication-material guidance to the submission manuscripts and regenerates both PDFs; scientific equations, numbers, and conclusions are unchanged. The earlier healing-length paper remains unrevised. Implementation verification does not establish controlled physical stabilization. 日本語「硬化分散のカシミール項とコンパクト半径の平衡条件――治癒長論への訂正と続報(短報)」。四次硬化分散を持つ周期自由ボソンの非展開カシミール項を再検査した未査読原稿です。全ての正の半径でポテンシャルは負かつ単調増加し、二項の漸近展開から得た極小は存在しません。旧提案の係数とラディオン質量を、制御された安定化機構の結果としては維持しません。復元力、周期・反周期セクターの混合、真空の自己中和と半径平衡の必要条件を整理します。DBI試験模型の形式的なゼロ真空局所極小は相互作用補正が大きく、制御された安定化には至りません。限定した電磁KKファイバーへの同定ではStückelberg質量が生じます。αや137の数値、真空値の自己調整を導出したものではありません。日英PDF・Markdown原稿と補足ZIPを収録しています。補足ZIPには研究ノート8本に加え、計算コード10本の公開用コピー、保存JSON/CSV、事前記録、本文との対応・実行方法を記した日英README、依存環境、出典ハッシュ、再実行照合記録を追加しました。別の作業コピーで10本を再実行し、記載した許容差内での科学的な数値・判定の一致と初回DBI失敗の再現を確認しています。私的な絶対パスへの依存を公開用コピーから除き、元の研究資料は変更していません。2026-10-16 の公開前編集で提出用原稿の参照リンク・資料案内・公開状況を整え、日英PDFを更新しました。数式・数値・科学的結論は変更していません。旧・治癒長論そのものは未改訂です。実装検証の合格を、物理的安定化の成功とは扱いません。
Author: Sato, Motohiko
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222102095
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