There's one arena, it's deterministic, and it doesn't grow, and everything else in the programme is bookkeeping about how much of it a measurement context lets you see.
Quantum mechanics is spectacularly good at predicting what detectors do and spectacularly silent about what the world is, as 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, as it posits the world. There's one total space of everything that exists, called the constraint surface (the programme names it Sigma), and a single deterministic trajectory runs on it, a path in which each state fixes the next by law, with no branching, no dice, and no observer in the basement. What you can't do is ask what the surface is made of, as it's the floor, and every theory has a floor, so this programme says out loud where its floor is.
The surprise is how little freedom the floor turns out to have. Ask what the surface must look like for quantum statistics to come out, and symmetry pins down its measure uniquely, where the measure is the rule that assigns a size to each region of the surface and so, eventually, a probability to each outcome, and symmetry also constrains its geometry tightly. The surface is posited, then constrained until almost nothing about it is a choice.
The constraint surface is the floor and it's everything, the total, fixed, local ontic space, where ontic means existing independently of anyone's knowledge. Deriving it is a non-question, since there's nothing beneath a floor to derive it from, and what's legitimate, and actively pursued, is constraining it from above. The measure on the projected state space, the space of quantum states seen as a shadow of the surface, is forced by unitary symmetry, the group of transformations that preserve every quantum probability, and the concrete working arena is a compact Kahler space, a space of finite extent whose curved geometry is of the kind complex projective space carries.
Everything quantum then happens at two levels. A measurement context, the choice of what to measure, partitions the projected view of the surface into outcome regions, and that partition is epistemic, a matter of description, while the weight of each region is an honest volume on the surface, and that measure is ontic. The Born rule, the quantum rule for assigning probabilities to outcomes, is the meeting point of the two.
The corpus carries Sigma as the OnticSetup structure, a measurable space with a finite measure (the Liouville measure, finite but not normalised, as 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, which is the LF1 main theorem, with no probabilistic input beyond repeated-preparation sampling.
The module makes one disclosure this page repeats, which is that 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, as it's what forces the invariant measure to be unique.
CsdLean4/LF1/Setup.leanSource links are pinned to a commit, so they do not drift. The anchors above are checked mechanically against the Lean tree on every build. The mathematics is not, and cannot be: that is a human responsibility and it rests with the author.
Part of Constraint-Surface Dynamics · Formalised in csd-lean4.
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