Self-calibration at low signal-to-noise biases flux densities beyond their error bars

Flux densities after radio-interferometric self-calibration carry error bars that treat the fitted gains as exact. In simulations of a 27-antenna array with point sources and known truth, four studies whose tests were fixed in advance (three publicly pre-registered) measure how often nominal 90 per cent intervals contain the truth. At a signal-to-noise ratio per gain solution ρ of 4.6 to 9.6, self-calibration raised the dominant source's flux density by 1.0 to 4.6 per cent, the known noise-fitting bias, and fixed-gain and calibration-aware (Fisher) intervals covered it in 3 to 47 per cent of realisations. A second-order expansion made afterwards gives at leading order (1-1/A)/ρ² for A antennas after phase-only solutions and (A-1)²/[A(A-2)ρ²] with arithmetic-mean-normalised amplitudes (equal antenna noise). In a pre-registered study with fresh seeds (A = 27; ρ = 4 to 20), the paired shift agreed with the reduced-simulation prediction to within 6 per cent (8 at ρ = 4) except after phase-only solutions at ρ = 20, where the predicted sign of the arms' difference also failed: neither prediction was met. Power normalisation per table about doubled the bias, and at ρ = 5.7 the phase-only fractional bias was independent of the number of intervals (6 to 96) to within 5 per cent. A data-only correction is withdrawn: its kill criterion fired for both arms (coverage 83 to 90 per cent, required 86 to 94). Predictions that phase-only solutions halve the bias and that it is a common flux scale failed. For detected faint sources, fixed-gain coverage fell from 89 per cent with the true gains to 79 to 82 per cent (exploratory). Without solution flagging, a lone source's bias in ALMA/VLA pipeline units (not run here) is about 0.54/(S/N)²_self, 6 per cent at the threshold of 3. About this record. A preprint, not peer reviewed: the paper (PDF, CC BY 4.0) with its preprint record (MIT): the scripts that draw Figures 1 to 5 and 7 of the paper, with logs that print every plotted value and its source; the Study 4 points of Figures 2 and 7; Figure 2 as printed in this version, redrawn from the same values with corrected labels; the 48 per-realisation checkpoint files of Study 1; and the support scripts of this version of the paper with their outputs, among them the dated exploratory stratified estimate at ρ = 60 (Appendix G). The scripts read only files of seven published records (doi:10.5281/zenodo.22997348, 10.5281/zenodo.23006306, 10.5281/zenodo.23025765, 10.5281/zenodo.23050205, 10.5281/zenodo.23050199, 10.5281/zenodo.23126516 and 10.5281/zenodo.23127781), which place_inputs.py extracts from their zips and checks by sha256. No script here decides a pre-registered verdict. Clean-copy check: the record was zipped and extracted into an empty folder, its inputs were placed from the published zips, and verify_record.py re-ran the figure scripts and the support scripts that can be re-run from the record; every PNG figure was reproduced byte for byte, every PDF figure byte for byte apart from its creation date, every log and printed output line by line (the run folder's path written '.'), and the arrays behind Figure 5 value by value (verification/clean_copy_check.txt). The code, specifications and results of the four studies are in the twelve records listed under related works. Simulation only; no CASA or production pipeline was run. The paper's Acknowledgements describe how AI was used in this work. Code, checks and reports were developed with the assistance of an AI coding assistant (Anthropic Claude) under the author's direction. No person is recorded as having reviewed the code, the figures, the checkpoint files or the support scripts in this record.