Block sign intervals allow zero later long-cycle profiles in three 2012–2026 BAT records at fixed periods under independent symmetric errors

We apply exact sign intervals to separate block fits of three public Swift/BAT X-ray records from 2012 to 2026. The targets are 4U 1909+07, IGR J16418−4532, and IGR J16479−4514. We use fixed published long periods, two long-cycle harmonics, and 32-, 64-, and 128-day calendar blocks. Each block has its own trend and orbital terms. All nine later coefficient boxes contain zero. All nine early and later pairs intersect, with explicit shared-profile examples. With 64-day blocks, the later RMS intervals are [0, 0.00353], [0, 0.00660], and [0, 0.00497] count cm^-2 s^-1, in source order. They are much wider with 128-day blocks. The method uses established sign intervals and an error allocation across 72 coefficients. Independent, continuous, median-zero block coefficient errors and a correct fixed mean give at least 96.9074 percent simultaneous coverage. Independent symmetric observation-error blocks are sufficient. The assumptions must hold at all tested block lengths. Artificial experiments with valid errors give 96.855 to 97.215 percent coverage in 20,000 trials per model. A deliberately correlated model fails. These experiments do not measure actual sky-data coverage. The broad regions establish neither a lost cycle nor physical stability. The package supplies unchanged source files, provenance, selected rows, code, a proof, exact amplitude bounds, witnesses, figures, checks, and offline instructions. It reports no new planet or period.

Swift BAT · X-ray binaries · superorbital cycles · sign test · Fourier profiles · finite-sample confidence intervals · block regression · simultaneous coverage · public astronomical data · reproducible methods