Carving

In plain terms

Stated as bluntly as a critic would, the problem with volume explanations of probability is this. If you're allowed to draw the regions yourself, you can make any probability come out of any measure, so if you draw a region covering thirty percent of the space and announce that the outcome has a thirty percent probability, you've explained nothing, as 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, the probability quantum mechanics assigns, and it doesn't derive it.

The interesting history is the repayment. For the corpus's central results the carving was eliminated, so the sizes come out of the geometry, forced by symmetry and by the moment map, a function that reads the outcome weights directly off the quantum state, with no hand on the scissors.

In CSD

Carving is the boundary marker between two kinds of result the programme keeps separate. A realisation is a fibre partition cut by construction so its volumes match a target, which is proved, useful, and honestly labelled as putting the value in. A derivation is the Born weight shown equal to a volume the geometry fixes independently, through the moment-map identity and the Duistermaat-Heckman law, which fixes how the state space's volume is distributed over the possible outcome weights, so nobody chose the sizes.

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

Mathematically

The carved tier is fibre arcs of prescribed length realising prescribed weights, with genuine disjointness and correct totals but the target built in.

The derived tier is the Born weight as a moment-map coordinate, forced by torus generation (CellLawForced.lean, torusGenerated_eq_momentMap) rather than by invariance, 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.

Related entries

• Outcome regionAn outcome is a region, and the apparatus alone draws its boundary, so the preparation decides where the trajectory lands and doesn't get to draw the map.
• Measurement contextA measurement isn't a question put to the quantum state, as it's a piece of apparatus, and the apparatus brings its own way of dividing the world into outcomes.
• Pointer basisA measuring apparatus doesn't record what you ask it to, as it records what it can keep, and what it can keep is decided by its interaction with the surroundings and not by the experimenter.
• FibreThe arena of CSD is larger than the space of quantum states by exactly one compact factor, and from three dimensions upward the natural ways of doing without that factor stop working.
• Record layerA measurement is over when the world itself carries which outcome happened, and the record layer is where that fact lives, on the arena and not in anyone's notebook.