Scope and Current Limits

Constraint-Surface Dynamics is a staged research programme. Its reconstruction of finite-dimensional quantum mechanics is now established within a posited quantum-effective sector and machine-checked in Lean 4. The remaining limits concern the physical derivation of that sector and the extension of the framework beyond finite-dimensional, nonrelativistic quantum mechanics.

What is not being claimed at this stage

The current work does not attempt to derive every part of the framework from first principles. In particular, CSD does not yet claim a derivation of:

  • the underlying ontic manifold (Sigma)

  • the projection map

  • the full structure of composite systems from ontic principles

  • a general classification of all physically realised measurement partitions

These structures are part of the working framework. Some are motivated, some are constrained by consistency, but they are not yet derived uniquely from deeper principles.

The quantum-effective sector is posited

A central question is why physical systems follow quantum dynamics at all. In the current framework, this is handled by identifying a class of admissible dynamics, the quantum-effective sector. Within that sector, the projected dynamics reproduces standard quantum evolution.

The sector is posited, not derived. That is a scope decision rather than unfinished work, and it is not expected to change. A machine-checked no-go in the formalisation shows that deriving the sector from a single flow is not available, so the posit is not a gap waiting to be filled.

Everything the programme claims rests on it. The reconstruction is conditional, and this is the condition.

The reconstruction is finite-dimensional

The present results are stated at the level of finite-dimensional systems. They show how:

  • deterministic dynamics can produce stable frequencies

  • geometric structure can fix the probability rule

  • the operational structure of quantum mechanics can be reconstructed

  • deterministic, context-indexed outcomes can reproduce the complete singlet probability table and maximal CHSH violation while preserving operational no-signalling

The finite-dimensional reconstruction is complete within its stated assumptions. What remains open is the bridge from this controlled sector to continuum, field-theoretic and relativistic physics.

Extension to field theory and unification

In particular, CSD does not claim:

  • a reconstruction of quantum field theory

  • a derivation of relativistic field structure

  • a complete account of interacting many-body or continuum systems

  • a unified framework covering all fundamental interactions

The current approach is to first establish a controlled bridge from finite models to continuum behaviour. At present, the relevant components are:

  • continuous-variable modules covering the harmonic oscillator, its spectrum, position, dispersion, approximate canonical commutation relations, field modes and mode locality

  • planned development of locality, coarse-graining, and many-body structure

  • future investigation of how field-like behaviour could emerge from the same underlying framework

No claim is made that these extensions are complete, or that a full unified theory has been achieved.

Not all structural gaps are closed

Several important structural questions remain open, including:

  • a derivation of composite tensor structure from ontic rather than operational principles

  • a complete classification of measurement partitions

  • tighter control of approximation regimes in the quantum-effective sector

These are active parts of the research programme, not resolved results.

What this means for the current work

CSD now claims a deterministic reconstruction of finite-dimensional quantum mechanics within its posited quantum-effective sector. This includes:

  • deterministic statistical typicality and Born-form probabilities

  • Schrödinger evolution, composite systems and general measurements

  • deterministic measurement, persistent records and post-measurement update

  • Bell-singlet correlations, maximal CHSH violation and operational no-signalling

  • machine verification of the central reconstruction in Lean 4

The underlying ontic manifold, projection and quantum-effective sector remain posited rather than uniquely derived. Continuum, quantum-field-theoretic and relativistic extensions also remain outside the completed reconstruction.

These are the boundaries of the present theory, not unfinished components of its finite-dimensional quantum-mechanical reconstruction.