Registering an Operator (deposit #1536, 23 August 2026) applies Pearson's factorisation discipline to the Crimson Hexagonal Archive's own principal instrument, the Provenance Erasure Rate, as a worked example of what operator registration costs and buys.
The registration begins by factoring what had been treated as a single operation into a five-stage composition chain — chunking, detachment, reranking, composition and reattribution — and finds that the factoring separates three objects the archive had conflated: the provenance-changing process itself, the measurement functional that maps a provenance change to scores at three levels, and the operative act of measurement by which an unmeasured event acquires quantitative standing. The third is registered separately, and its internal-transform field is null: it changes nothing about the erasure it measures, which is precisely why it is an operative rather than a descriptive act. It operates on standing rather than on the object, making it the archive's clearest instance of an operation whose entire effect lies in coordinates a sign-state calculus projects away.
The factoring pays immediately. The archive's several hundred seated captures become re-readable as profiles rather than scalars, since the same terminal score can arise from different machines — a composition without prior detachment differs from a detachment following chunking, though both may score alike. The recorded blindness of the metric to standing conferred acquires addresses rather than remaining a general caveat.
Reconciliation with the archive's own prior boundary-condition operator, seated the same day after nine months undeposited, finds that five of the thirteen schema fields already existed in the archive's hand and that two coordinates the schema lacked — a declared loss order and an inviolable floor — are exactly the terms that make an operator critical rather than descriptive. They are proposed as fields fourteen and fifteen.
The paper closes with a cost rule, an admitted failure — one field did not earn its place and is retained so the next registration can test whether the schema is one field too long — and a review ledger recording six defects found by external review and corrected, two of which were the document contradicting its own evidence.