The James Webb Space Telescope

The real thingobject

The James Webb Space Telescope holding a guide star in fine guide: the offset of the star's centroid from the lock point on the two axes of the Fine Guidance Sensor's ideal frame, every 64 ms, in quiet stretches.

The passing grade, fixed firstpass_line

Fixed before any held-back file was downloaded (pre-registration SHA-256 9e160724092e182f847eb0103e6ca7a54aba0f75c5d1ca14dcd275c9a554c8f5), on the quiet frames of the held-back files, for each axis: the error of the prediction one frame ahead at most 0.85 of the error of taking the last centroid and at most 0.85 of the error of taking the lock point; the mean of the squared error over the variance the card states between 0.67 and 1.50; the correlation of that normalised error from one frame to the next at most 0.15 in size; and that mean between 0.5 and 2.0 in at least 80 percent of the files with 500 quiet frames or more.

The resultresult

Compared with the held-back visits on 2026-10-09, and by the rule fixed beforehand the comparison passed: all five marks were met on both axes. The marks are on quiet frames. The card as it was scored answered every frame of a file, and on a whole file the outcome was the other way. Over all 973,388 measured held-back frames, quiet and disturbed together, the card's error one frame ahead was 1.35 on x and 1.26 on y of the error of taking the last centroid, and the squared error over the variance it states was 3.9 and 3.0. Disturbances are in 121 of the 134 files and make up 18.3 percent of the measured frames. The card's own whole-file figure on x, nis_sum_x over measured_frames in the final state, lies in 0.5 to 2.0 in only 39 of the 134 files. The card as scored marked the 5.8 percent of frames above 5 mas with a flag and answered them, and answered the 30 s after them with no mark. It now refuses those frames; what that gives on the same files is at the end of this record. On the 795,021 quiet frames of the 134 held-back files, one frame ahead, the card's error was 0.510 mas on x and 0.472 mas on y, root mean square, against 0.644 and 0.584 for taking the last centroid (0.790 and 0.807 of it) and 0.660 and 0.748 for taking the lock point (0.772 and 0.631 of it). The mean of the squared error over the variance the card states was 1.004 and 0.986, the correlation from one frame to the next 0.074 and 0.074, and in every one of the 134 files that mean was between 0.5 and 2.0: from 0.68 to 1.27 on x and from 0.70 to 1.75 on y. All 134 runs completed and none was outside the card. Inside the disturbances, 178,367 frames within 2 s before and 30 s after a centroid more than 5 mas from the lock point, the card was worse than taking the last centroid: 2.03 mas against 1.00 on x and 1.57 against 0.78 on y, and the variance it stated was too small by a factor of 17 on x and 12 on y. No mark was set on those frames. A random walk with the same power-law sensor noise, three constants an axis fitted on the same April data, meets all five marks, at 0.808 and 0.837 of the last centroid's error. The card's two modes and twelve further constants lower the error by 2 and 4 percent: 0.510 and 0.472 mas against 0.521 and 0.489. The marks do not test the mode frequencies: with both moved 20 percent up or down every mark is still met. The error is near the floor the sensor's noise sets. The sensor-noise law is what carries the variance marks: a second-order autoregression with one variance misses the per-file mark. The y noise exponent was not reproduced on the held-back guide stars: 1.045 fitted there against the card's 1.273, where x gave 1.134 against 1.151. Inside the tested count rates the two y laws differ by +27 to -21 percent in variance, which the variance mark cannot resolve. With a lock point that uses no future, the median of the first 10 s or a running median of past frames, the last-centroid, variance, correlation and per-file marks still hold, each number within 0.04 of the scored one, and the lock-point mark is no longer a test. Held-back files longer than 10,000 frames were cut at the gateway's limit: 43 files, which lose 12 percent of the set's frames. The second scorer's own filter on whole files still meets the marks. A second scoring of 2026-10-09, on the same machine and with the scorer's own FITS reader, found the same numbers: evidence/checks/second_party/V-35/. All of that is the registered result, of the card as it then was. What follows was done after the scoring and is not a blind test (amendment 1 of the research record, SHA-256 e0e4b86fcc18c2cd868f587627a0ac2ed0d5dd692292b1febbcc6358976dd849). The card was changed to refuse where it is wrong: a centroid more than 5 mas from the lock point, a centroid more than four stated standard deviations from where it was expected, and a start less than 30 s after either. The three numbers are the protocol's own and none was fitted to a held-back file. The second rule was decided on the fitted files of April 2022: there, in the 30 s after a centroid beyond four standard deviations, the x axis missed four of the five marks (0.921, a squared error over stated variance of 1.641, a correlation of 0.272, 74 percent of files), and on the held-back files three (0.933, 1.513, 0.316); such a centroid came 31 times as often on x as a right variance gives on the fitted files and 21 times on the held-back files. The 134 held-back files run again as the card now runs them, each file as a chain of runs that end at a refused centroid and start again 30 s later with nothing known, with the registered lock point: of 973,388 measured frames the card answered 721,727, 74.1 percent, in 428 runs, and refused 251,661: 56,910 centroids above 5 mas, 305 beyond four standard deviations, where a right variance gives about 91 by chance, and 194,446 in the 30 s after one. 130 of the 134 files hold a refused frame. Over the answered frames the five marks, x and y: 0.787 and 0.805 of the last centroid's error, 0.779 and 0.640 of the lock point's, a squared error over stated variance of 0.987 and 0.970, a frame-to-frame correlation of 0.064 and 0.072, and that mean between 0.5 and 2.0 in 100 and 100 percent of the files with 500 answered frames or more. Beside the registered 0.790 and 0.807, 0.772 and 0.631, 1.004 and 0.986, 0.074 and 0.074, 100 and 100 percent on the 795,021 quiet frames, which were chosen with 2 s of look-ahead that the card does not have. The card's own figure, nis_sum_x and nis_sum_y over measured_frames in the final state of a run, lies in 0.5 to 2.0 on both axes in every one of the 312 runs that landed 500 frames or more, where on x it did in 39 of the 134 whole files. The run through the engine and the same chain in plain Python answer the same frames, and their numbers agree to 2.4e-7 mas (evidence/research/pointing_jwst_fine_guidance/analysis/out/11_enforced/).

Its limitslimits

A forecast is not a result. The forecast, made outside the engine with constants fitted on the first nine April visits and scored on the other ten: 0.774 and 0.785 against the last centroid on x and y, 0.779 and 0.636 against the lock point, a mean normalised squared error of 0.680 and 0.938, a frame-to-frame correlation of 0.113 and 0.067, and 84 and 100 percent of files. The constants are fitted to this observatory's own centroids, so the held-back visits test extrapolation in time and to other guide stars and nothing else: one observatory, one season, one guiding mode. In brightness they are interpolation: their count rates, 62,000 to 816,000 counts per second, lie inside the fitted 22,900 to 2,820,000, so the noise law was not tested at either end of the card's range. One party wrote the card and ran it. It was scored twice, the second time by a second scorer, on one machine. The prediction is one frame, 64 ms, ahead. The estimate of the line of sight with the noise taken out is a model output that no measurement here checks. The lock point is not in the file and is the caller's; the validation took the median of the run's good centroids, which uses the whole run. The lock points of the files the comparison answered span -61.1512947 to 60.4564934 arcsec on x and -64.2767 to 50.1812668 arcsec on y, fitted and held-back files together, and the card refuses a lock point outside that span as LockOutsideCard; no lock point nearer the edge of the sensor's field was compared. The longest run of frames with no measurement that a run of the comparison crossed was 10 frames on the fitted files and 2 on the held-back files, and the card refuses an eleventh such frame in a row as MeasurementGapOutsideCard. Nothing above 7.8 Hz is resolved by a 64 ms frame: the Nyquist frequency is 7.81 Hz, and the card cannot see or state jitter above it, nor tell a folded line from a true one. The card describes quiet fine guide: inside a disturbance, a centroid more than 5 mas from the lock point and the 30 s after it, the filter follows slowly, and on the fitted visits as on the held-back ones its error was larger than that of taking the last centroid. The card refuses there. It holds a new run to 30 s after the last disturbance only by the caller's statement, which it cannot check; and a caller's lock point that is off by a few mas makes quiet frames read as disturbed, so the card then refuses frames it could have answered. It says nothing of the line of sight during a disturbance: the visits of March 2022 are unopened and kept for a card that follows one. The y axis shows lines near 0.51, 1.02 and 1.53 Hz that the model has no part for. In the held-back spectra the y feature is a narrow line at 0.290 to 0.294 Hz with a shoulder at 0.32 to 0.34 Hz; the card's 0.3025 Hz is one damped mode laid across both. The commissioning report of the telescope (Rigby et al., arXiv:2207.05632, section 3) names a 0.3 Hz oscillation of a vibration damper between the telescope and the spacecraft bus and a 0.045 Hz oscillation attributed to fuel slosh; the card has no part for the 0.045 Hz one. The x feature is a broad hump at 0.50 to 0.60 Hz, for which no published attribution was found. The ledger is an account of variance that follows from the model; it is not a conservation law, and it cannot detect a wrong constant. It checks that each update is a Kalman update with the optimal gain: it passes with a wrong mode frequency, wrong noise or the two axes swapped, and it says nothing about the telescope.