Carving

In plain terms

Here is the problem with volume explanations of probability, stated as bluntly as a critic would: if you are allowed to draw the regions yourself, you can make any probability come out of any measure. Draw a region of size 0.3, announce that the outcome has probability 0.3, and you have explained nothing. The explanation was smuggled in with the scissors.

CSD calls this move carving, by name, in its own documentation -- because early layers of the formalisation genuinely did it, and the honest label is what kept the debt visible. A carved region realises the Born value. It does not derive it.

The interesting history is the repayment: for the corpus's central results the carving was eliminated. The sizes now come out of the geometry -- forced by symmetry and the moment map -- with no hand on the scissors.

In CSD

Carving is the boundary marker between two kinds of result the programme keeps separate. Realisation: a fibre partition cut by construction so that its volumes match a target -- proved, useful, and honestly labelled as putting the value in. Derivation: the Born weight equal to a volume the geometry fixes independently -- the moment-map identity and the Duistermaat-Heckman law, where nobody chose the sizes.

The corpus's documentation flags every result with which side of the line it sits on, and the volume route to the Born rule now runs entirely on the derived side. The word survives as an audit tool: when a new result lands on a specific number, the first question asked is whether anything was carved.

Mathematically

The carved tier: fibre arcs of prescribed length realising prescribed weights -- genuine disjointness and correct totals, with the target built in. The derived tier: the Born weight as a moment-map coordinate, a forced symplectic invariant; the joint pushforward of the Fubini-Study measure under the moment map equal to the uniform simplex law; and the resulting volume-ratio theorems at every N, unconditional.