Half a Grain of Anticipation: The Residue Priced, and the Dress Table at the Bounce Time
AF-6's symmetric grain dress killed the Abraham–Lorentz runaway and rented the cure with pre-acceleration compressed to τ_cell/2 = 1.108394×10⁻²⁴ s — half a grain. This paper evaluates that residue as a frame object. It is not one: the anticipation window of the symmetric dress is exactly g/2 for any grain g, an invariant ratio, so the residue carries no scale of its own — it is denominated in whichever grain is chosen, and it equals no owned time of the frame (τ_b, τ_cell, Δt_sep, τ₀) nor any simple multiple of one. Nor is it a smaller grain: a smaller grain would move the spectrum, and §2 shows what actually happens when the grain is moved to the frame's second owned time, τ_b = 2.8630×10⁻²⁵ s — the one-sided dresses still run away, the symmetric dress still kills the runaway, the neutral pair tightens to a period of 1.04583 grains, and the anticipation shrinks in absolute terms to τ_b/2 while remaining exactly half a grain. The residue is therefore graded a standing cost: half a grain of anticipation is the value of a runaway-free grained electron, at any grain the frame owns, and it does not go away by refining the grain — it scales with it.
Authors
- William Alexander Aldred
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-06
- DOI
- https://doi.org/10.5281/zenodo.24013721
- Primary Topic
- Quantum and Classical Electrodynamics
- Type
- preprint