Rank discretization destroys continuum spacing information

Filed as the mechanism behind a negative result, not as a positive result. The negative result on its own — per-colour GUE statistics do not imply joint GUE rigidity — reads as a contradiction of the adjacent positive result. With the mechanism attached it reads as a consequence of it. That is the whole reason this note exists; see OPS.md, a negative result without its mechanism reads as a contradiction.

The mechanism. Replacing values by their ranks discards the metric on which spacing statistics are defined. GUE rigidity is a statement about the spacing distribution of a continuum spectrum; ranks retain only the order. So any statistic computed after rank discretization cannot see the quantity the rigidity statement is about, and per-colour GUE behaviour is not preserved into the joint object — not because the joint object fails to be GUE-like, but because the step that produced it is not spacing-preserving.

What it makes coherent. The adjacent positive result (per-colour GUE) and the joint-rigidity failure stop being in tension: they are measurements of two different things, separated by a lossy step that was not previously named as lossy.

Scope, honestly. The mechanism was stated in the source chat and is recorded here as stated. It has not been re-derived in this repo, and no run tests it. The claim it licenses is narrow: it explains why the failure is expected, and it does not establish that the joint object would be GUE under a spacing-preserving map. Treating it as evidence for the latter would be the inflation this note is filed to prevent.

What would falsify it. A rank-based statistic that provably recovers the spacing distribution, or a joint-rigidity failure in a construction with no rank-discretization step — either would mean the mechanism is not what is doing the work.

Matched pair. [[N-024]] is the same shape from the other side: a failed predictor whose mechanism explains why its successor works. The pair is the reason the OPS entry is written as a class rather than as two instances.