Projectability

In plain terms

Here is the problem. If the world is a big deterministic space and quantum mechanics is written on a much smaller curved one, something must connect them. You cannot get the small picture out of the big one for free; the connection is structure, and structure has to be paid for.

Projectability is the payment, made openly. It says: the arena admits a many-to-one projection onto the quantum state space, compatible with the dynamics and the symmetry. One postulate, stated once, carried honestly as a hypothesis everywhere it is used.

The discipline is in what is NOT postulated. Not the measure -- forced by symmetry. Not the Born rule -- computed as volume. Not the dynamics on the projected space -- derived from record statistics. The programme keeps its postulate count where you can audit it.

In CSD

This is Paper C's sector postulate: the assumption that Sigma projects onto a projective sector on which the reconstruction runs. It is projectability -- never "the origin of Sigma". The projection points the wrong way for that reading: Sigma is the floor, and the sector is a view of it, not its source.

In the Lean corpus the postulate is a structure field, not an axiom: theorems that need it take it as a hypothesis, so the kernel's axiom report stays clean and the cost is visible at every use site.

Mathematically

SectorData packages the postulate: a measurable projection from the ontic space to an abstract projective target, a group acting on both sides, invariance of the Liouville measure, and equivariance of the projection. A guard script enforces that the descent equation is genuinely consumed downstream -- the corpus has been burned once by a substrate that was carried but unused, and the linkage is now checked mechanically.