Constraint surface

In plain terms

Here is the problem. Quantum mechanics is spectacularly good at predicting what detectors do, and spectacularly silent about what the world is. The textbook hands you a recipe for outcomes and no picture of what exists between them.

CSD starts by paying the cost most approaches defer: it posits the world. One total space of everything that exists -- called Sigma, the constraint surface -- with a single deterministic trajectory running on it. No branching, no dice, no observer in the basement. What you cannot do is ask what Sigma is made of. It is the floor. Every theory has a floor; this programme just says where its floor is out loud.

The surprise is how little freedom the floor turns out to have. Ask what Sigma must look like for quantum statistics to come out, and symmetry pins down its measure uniquely, its geometry tightly. Posited, then constrained until almost nothing about it is a choice.

In CSD

Sigma is the floor and Sigma is everything: the total, fixed, local ontic space. Deriving it is a non-question -- there is nothing beneath a floor to derive it from. What is legitimate, and actively pursued, is constraining it from above: the measure on the projected state space is forced by unitary symmetry, and the concrete working arena is a compact Kahler space.

Everything quantum then happens at two levels. Contexts partition the projected view of Sigma into outcome regions -- that partition is epistemic. The weight of each region is an honest volume on Sigma -- that measure is ontic. The Born rule is the meeting point of the two.

Mathematically

The corpus carries Sigma as the OnticSetup structure: a measurable space with a FINITE measure (the Liouville measure -- finite, not normalised; weights are ratios, and the preparation region is required to have nonzero measure so the normalisation is well-defined), a deterministic flow with a measure-preservation field, and a preparation region. Outcome frequencies converge almost surely to volume ratios by the strong law -- the LF1 main theorem, with no probabilistic input beyond repeated-preparation sampling.

One disclosure the module makes and this page should repeat: through LF1 to LF3 only MEASURABILITY of the flow is consumed. The measure-preservation content is carried as structural payload for physical admissibility and becomes load-bearing only when LF4 derives the measure from a concrete volume form.

The concrete instance is Sigma = CP^(N-1) x T^2 with the Fubini-Study measure on the base times normalised Haar on the torus fibre. Compactness does real work: it is what forces the invariant measure to be unique.