Can Rotation Make Spacetime Grains Last? Internal Angular Momentum and Longevity of Source-Free Enchan Grains

Abstract

This work studies whether internal rotation changes the longevity of source-free localized excitations in the reduced Enchan local time-rate field. The frozen scalar dynamics are S_tt = div[mu(D) grad S] - S with D = |grad S| and mu(D) = 1/(1 + D^(3/2)); no continuing external torque, centrifugal force, primitive matter source, or added rotational potential is used during the reported evolutions. Stage A supplies the non-rotating source-free baseline. Stage B1 initializes rotating phase-space states at omega = 4, 8, and 12 and evolves the extended runs to dimensionless time t = 100. Over 80 <= t <= 100, the mean localized-energy fractions are approximately 0.002207 for the non-rotating baseline and 0.006006, 0.149470, and 0.368846 for omega = 4, 8, and 12. The result is a graded rotation-associated longevity hierarchy: weak rotation gives little practical rescue, intermediate rotation substantially extends localization, and the strongest tested branch remains transient-localized through t = 100. Matched-energy near-zero-J_z controls provide a separate causality check and show that net canonical angular momentum alone is not a monotonic explanation of every late-time difference. Stage B2 separately tests spontaneous self-spin from exactly zero initial total angular momentum and finds no validated convergent counter-rotating branch in the tested scalar-only initial-data families. The ordered scan supports a physical formation picture in which a localized grain can move from weak rotational asymmetry through progressive spin-up into a strong-rotation long-lived branch. Time, space, and omega are dimensionless reduced-branch quantities; t = 100 is not assigned an SI duration in this work. The deposit contains the Version 1.0 manuscript PDF, a reproducibility ZIP with the publication source, code, selected archived numerical outputs, README, LICENSE, and SHA-256 integrity manifest. The final main.pdf is the default preview. License: Enchan Research & Verification License v1.0. Copyright (c) 2026 Mitsuhiro Kobayashi.