PREPRINT · VERSION 0.5 · 31 OCTOBER 2026

A First-Repair Mass Zero Without Angular-Moment Cancellation

Yun Kwansub · 11 pages · CC BY 4.0

Abstract

We study two weighted histories in a specified outgoing-profile construction. For each fixed source Profile, we prove that every sufficiently small positive angular parameter admits a point strictly inside the first repair window where the mass history vanishes and the angular-weighted history is strictly positive at the same point. The positive parameter threshold may depend on the Profile. The decisive argument compares future moments of two separated repair bumps. At a mass zero, positivity of the second repair coefficient forces the first coefficient to be negative; the decreasing relative weight between the two histories then makes the angular tail negative and the accumulated angular history positive. We give the coefficient, boundary-sign, continuity and coordinate arguments needed to turn this conditional statement into an existence theorem. We further extract a strictly positive angular-history lower bound independent of the selected mass zero, and normalize its bump moment to obtain an explicit cutoff-plateau bound. The corresponding source-bound propositions are formalized in Lean 4 and have a recorded fixed-checkpoint compilation. The result identifies a denominator obstruction for a prospective normalized ratio without requiring that ratio to be introduced into the source construction.

@misc{yun_2026_23835054,
  author       = {Yun, Kwansub},
  title        = {A First-Repair Mass Zero Without Angular-Moment
                   Cancellation
                  },
  month        = oct,
  year         = 2026,
  publisher    = {Zenodo},
  version      = {0.5},
  doi          = {10.5281/zenodo.23835054},
  url          = {https://doi.org/10.5281/zenodo.23835054},
}