What CSD currently claims
Constraint-Surface Dynamics is not presented as a finished theory of everything. It makes a narrower set of claims, in a specific order. At present, CSD claims that the finite-dimensional statistical and operational structure of quantum mechanics can be reconstructed from deterministic Hamiltonian dynamics on an underlying ontic manifold, together with geometric projection, invariant measure, and context-dependent outcome regions. It does not claim a complete derivation of continuum quantum field theory, relativity, or the Standard Model.The most important point for a new reader is this: CSD currently claims to have established a finite-dimensional reconstruction programme, not a universal final theory.
The central current claim
The core current claim is that observed quantum statistics do not require primitive randomness at the fundamental level. In CSD, a physical system follows deterministic, measure-preserving dynamics on an ontic space, while observed frequencies arise from volume typicality under repeated preparation. That is the role of Paper A and, in formal terms, LF1.This is not yet the full Born rule by itself. The programme's present claim is more structured than that:Deterministic repeated trials produce stable frequencies under a preparation model.Symmetry and operational consistency fix the admissible probability rule in finite dimension, yielding the Born form on projective space.Measurement outcomes are represented by context-dependent measurable regions, not by collapse postulates.Mixed states, POVMs, reduced states, and sequential update can be represented within the same finite-dimensional framework.Deterministic, context-indexed outcomes reproduce the complete singlet probability table and maximal CHSH violation while preserving operational no-signalling. Taken together, that is the current finite-dimensional claim.
What CSD says is already established
1. Deterministic typicality can replace primitive randomness
CSD claims that long-run experimental frequencies can arise from deterministic, volume-preserving dynamics plus repeated preparation sampling. This is the statistical backbone of the programme, and it is machine-verified in the Lean4 formalisation (See: ).
2. The finite-dimensional probability rule can be fixed without adding stochastic axioms
Paper B claims that, in finite dimension, the relevant projective-space measure is fixed by symmetry, and the Born-form rule follows from operational consistency conditions together with Gleason-class machinery for (N > 3), plus a standard strengthening for the qubit case.The formalisation reaches the same rule by a second and independent route. Born weights are derived as Fubini-Study volume ratios, for general dimension and for general POVM measurements. That route does not use Gleason-class machinery at all. The two arguments agree, and the geometric one is the primary derivation.
3. Finite-dimensional quantum mechanics can be reconstructed as an effective operational layer
Paper C presents the current architecture of the programme: deterministic ontic dynamics on (Sigma), a projection, a quantum-effective sector for projected dynamics, and context-dependent measurement regions on projective space. It is explicitly presented as a finite-dimensional reconstruction architecture rather than a completed universal theory.Composite systems are now part of this layer. The tensor product is derived from locality and local tomography rather than assumed. Local tomography itself is not derived, and is stated as an assumption.
4. Measurement is treated as deterministic dynamics plus context-defined outcome structure
Paper D presents the ontological claim that one ontic trajectory leads to one realised outcome, with observed probabilities arising from invariant geometric structure rather than collapse or many-world branching.This is no longer only a conceptual claim. The measurement layer is machine-verified. An explicit volume-preserving interaction creates a record from an apparatus-ready state, the record persists, distinct outcomes exclude one another, and the resulting statistics are Born. The rank-one Lüders update, that is wavefunction collapse, is a theorem rather than a postulate. No-signalling holds dynamically, in every basis.A trade-off theorem constrains what any such account can be. Continuity and records that are exact everywhere cannot both hold. Three witness families exist and each pays one price. No horn is canonical, and whether a fourth is impossible is an open question rather than a claim.
5. Bell-violating correlations are compatible with deterministic outcomes and local measurement dynamics
C1 provides a machine-checked construction in which deterministic, context-indexed outcome maps on a shared ontic probability space reproduce the complete two-qubit singlet probability table, the correlation E(a,b) = −a · b, and the maximal CHSH value 2√2.
The formalisation proves that no compatible global assignment across the four CHSH settings can reproduce these correlations. It also verifies uniform local marginals and operational no-signalling, while showing that locally factorised measurement dynamics can coexist with Bell-violating outcome statistics.
The Bell obstruction therefore falls on compatible global assignments and Bell-local product outcomes, not on deterministic realised outcomes.
6. Several finite-dimensional closure layers are claimed within the current programme stack
TN4 claims a finite-dimensional account of mixed states, generalised measurements, and subsystem reduction. TN6 claims finite-dimensional post-measurement update and sequential consistency. These are part of the current operational closure package, not future speculation, and both are now supported by the formalisation.
The present status in one line
CSD currently claims a deterministic finite-dimensional reconstruction of quantum statistics and operational structure, machine-verified through the Born rule, Schrödinger evolution, measurement, post-measurement update, Bell-singlet correlations, maximal CHSH violation and operational no-signalling, on a posited sector. It does not claim that the deeper bridge to continuum physics and field theory is complete.
Why the claims are staged this way
The programme is deliberately narrow before it becomes broad. It starts by asking whether deterministic dynamics can recover stable frequencies at all. Then it asks whether those weights can be shown to take the Born form. Then it asks whether finite-dimensional quantum mechanics can be reconstructed from that structure. Only after those steps does it attempt continuum limits and field-theoretic extensions. The dependency map makes this layering explicit.So CSD should not be read as claiming to have solved every foundational and physical problem at once. It should be read as claiming that a specific finite-dimensional reconstruction stack now exists, with clearly identified completed parts and clearly identified open gaps.