Required Internal Field Strengths from Flare Energies: A Reservoir Inversion for Giant Flares, Storms and Single Bursts

Flare energies are usually compared with a field assumed in advance. This study runs the comparison backwards: given an observed energy and a stated fraction of the reservoir that an event may draw, the algebra returns the internal field the star must possess. Applied from giant flares down to single short bursts, the inversion yields a ladder of minimum internal strengths. Working from published values for the sources concerned, this paper computes the relevant quantities under one stated set of conventions and compares them source by source. Headline results: largest required B case SGR 1806-20 giant flare; largest required B G 1.10e+15; required B for typical burst G 2.45e+12; giant flare required over BQ 25. The comparisons are budget statements: they establish whether the energies, stresses, powers and timescales involved are mutually consistent, and by what margin. Every number quoted is produced by the deposited compute.py script from the stated inputs, and the full per-source record is deposited as results.json alongside the text.