A phase picked after the answer was known

The second correction is the cleanest example in the archive of a specific sin: selecting from a menu after seeing the answer, and reporting the selection as if the menu had made the choice. The quantity is a phase in the primordial power spectrum, the value presented was pi over six, and the CMB data prefers pi over six. Those two facts have an ordering, and getting the ordering right is everything.

The prediction that was not one

Paper 10 predicts a wave-like modulation of the primordial spectrum with three parameters: an amplitude, a frequency scale, and a phase. The draft derived the phase from the framework’s modular data, the same algebraic structure that fixes the category’s fusion and congruence properties, and announced pi over six as the predicted value, with the CMB comparison to follow. The structure of the sentence is correct. The history behind it was not.

The modular data does not single out a phase. It admits a family of candidates, different channels and prefactors giving different values, and the route from the algebra to pi over six required choosing one channel among several. The audit traced when the choice was made, and it was made with the best-fit value already on the screen. The channel was selected because it gave pi over six, and pi over six was then reported as predicted. The derivation had the form of a derivation and the provenance of a fit, and no sentence in the original text said which.

This is the most dangerous species in the genus because each step is individually defensible. Choosing a channel is normal theory work. Noticing your favourite candidate matches the data is normal. Writing the match up as a derivation is where the record stops being true, and nothing in the arithmetic flags the moment, because the arithmetic is all correct. Only provenance knows.

The repair, which is procedural

The fix lives in the companion paper, and it is procedural rather than mathematical: the phase must be predicted through one route, named in advance, with the channel fixed by an argument that does not consult cosmological data; fitting the phase freely and calling the result a prediction is forbidden by the document’s own text. The two honest routes on the table are the modular argument with an independently-justified channel, and a holonomy integral with a topologically-fixed cycle. One gets preregistered, the other is discarded, and whichever is chosen must survive without the freedom that produced the original sin.

The epistemic cost of the repair is real and should be stated: pi over six currently has no derivation. The value is demoted from predicted to fitted, and the framework’s spectral feature now has two derived parameters and one open one. That is the correct price for the audit’s finding, and paying it in public is the difference between an archive and a showcase. The next post is about the coefficient that never even had a menu to choose from.