Roadmap
Quantum mechanics works extraordinarily well. What it does not yet give us is a clear account of why a single experiment produces one definite outcome, why the observed frequencies follow the Born rule, and how those features might fit into a deeper deterministic picture.
Constraint-Surface Dynamics is a research programme built to tackle those questions in order. It does not try to solve everything at once. It starts with the narrowest question that can be made precise, closes that step, then moves to the next. The roadmap below shows that sequence.
The destination
The long-term goal is a complete geometric framework in which:
physical systems evolve deterministically on an underlying state space ( Sigma )
observed probabilities arise from geometry and symmetry, not primitive randomness
the standard finite-dimensional quantum formalism is recovered as an effective layer
the framework can then be extended, carefully, toward continuum physics and field theory
That is the full ambition. We are not there yet.
Where the programme is now
The statistical foundation is in place.
The first major result of the programme is that stable experimental frequencies can arise from deterministic dynamics, provided repeated trials begin from a preparation ensemble. That result now exists both as a paper result and as a completed Lean4 formalisation. In other words, the programme has already secured the first essential bridge: deterministic dynamics can produce the kind of statistical regularity quantum theory requires.
The next major task is to close the measure bridge. That means showing, in formal terms, how the relevant geometric weights on projective state space take the Born form. After that, the key open problem is to explain why physically relevant Hamiltonians lie in the quantum-effective sector at all. Beyond that lies the harder bridge from finite-dimensional quantum mechanics toward continuum and field-theoretic structure.
The roadmap
1. Establish deterministic statistics
This is the entry point of the whole programme.
Question:
How can a deterministic theory produce stable outcome frequencies?
What this stage does:
It shows that if the ontic dynamics preserve volume, and repeated runs begin from a preparation region, then the long-run frequencies converge to normalised volume weights.
Why it matters:
Without this step, probability would still have to be put in by hand.
Current status:
Completed.
Outputs:
Paper A
LF1, the Lean4 implementation (See: https://github.com/zblore/csd-lean4)
What has been achieved:
The statistical backbone is no longer only conceptual. It is now machine-verified.
2. Fix the probability rule
Once deterministic volume weights exist, the next question is obvious.
Question:
Why should those weights match the Born rule?
What this stage does:
It uses symmetry and operational consistency to identify the relevant projective-space measure and recover the quadratic probability rule in finite dimension.
Why it matters:
This is the step that turns generic geometric weights into the specific probability rule used in quantum mechanics.
Current status:
Substantially developed at the paper level. Formal verification still to come.
Outputs:
Paper B
TN1
planned Lean layer LF2
What remains:
A clean formal Lean implementation of the measure bridge and Born-weight wrapper.
3. Reconstruct finite-dimensional quantum mechanics
Once the probability layer is fixed, the programme can ask a broader question.
Question:
Can the standard finite-dimensional formalism be recovered from deterministic geometry?
What this stage does:
It introduces the projection from the ontic space to projective state space, defines the quantum-effective sector, and reconstructs the operational architecture of finite-dimensional quantum mechanics.
Why it matters:
This is the point at which CSD stops being only a probability proposal and becomes a reconstruction programme.
Current status:
Core architecture established. Several technical parts completed. Some structural gaps remain.
Outputs:
Paper C
TN4
TN6
What remains:
A first-principles account of tensor structure, a general classification of measurement partitions, and stronger closure of the quantum-effective sector.
4. Give a physical account of measurement and outcomes
A formal reconstruction is not enough on its own. It must also say what happens in a single experiment.
Question:
What physically determines the one outcome we actually observe?
What this stage does:
It interprets measurement as deterministic evolution into context-dependent outcome basins. One trajectory leads to one realised outcome. No collapse postulate is added.
Why it matters:
This is the stage that turns the mathematical framework into an ontological proposal.
Current status:
Conceptual structure in place.
Outputs:
Paper D
What remains:
Further refinement as the technical stack below it becomes stronger.
5. Build controlled continuum limits
Finite-dimensional reconstruction is a major milestone, but it is not the end of the story.
Question:
How can continuum-like quantum behaviour emerge from exact finite models?
What this stage does:
It studies nested truncations and asks what converges, in what sense, and under what control.
Why it matters:
This is the first serious bridge from the finite-dimensional programme toward more realistic physics.
Current status:
Initial bridge framework exists.
Outputs:
C3
What remains:
Broader applications and stronger generality.
6. Explain the quantum-effective sector
This is one of the central open problems.
Question:
Why do the physically relevant Hamiltonians project to quantum dynamics?
What this stage is meant to do:
It should replace simple sector selection with a controlled regime statement. Instead of merely assuming that certain Hamiltonians behave quantum mechanically, the goal is to say when and why that approximation holds.
Why it matters:
Without this step, the framework reconstructs quantum mechanics only inside a selected class of admissible dynamics.
Current status:
Open.
Planned output:
(Sigma 1)
7. Extend toward continuum physics and field theory
Only after the earlier bridges are secure does the final research direction become meaningful.
Question:
Can locality, coarse-graining, and effective field structure emerge from the same ontic framework?
What this stage is meant to do:
Develop the path from finite-dimensional reconstruction to many-body structure, continuum limits, and eventually effective field theory.
Why it matters:
This is where CSD either becomes a broader physical framework or remains a finite-dimensional foundation only.
Current status:
Defined as a research direction, not yet solved.
What is done, what is open
Done:
The deterministic statistical foundation is complete.
The finite-dimensional probability rule has a developed paper-level account.
The ontological and measurement picture has been laid out.
Open:
The formal measure bridge in Lean.
A deeper derivation of the quantum-effective sector.
A first-principles account of composite tensor structure.
The bridge to continuum and field-theoretic physics.
Why this roadmap is structured this way
The programme is built from the top down in importance, but from the bottom up in proof.
It begins with the narrowest claims that can be made precise. That is deliberate. If deterministic dynamics cannot recover stable frequencies, nothing else matters. If the resulting weights cannot be shown to take the Born form, the reconstruction fails. If finite-dimensional quantum mechanics cannot be rebuilt cleanly, there is no reason to talk about field theory.
So the roadmap is not a collection of unrelated papers. It is a dependency chain.
The immediate next steps
The next public milestone is LF2, which should formalise the measure bridge and Born-weight layer.
Alongside that, the continuum bridge work will continue, and the A5 problem, explaining the quantum-effective sector, remains one of the most important unresolved parts of the programme.
In one sentence
CSD has already secured the deterministic origin of statistical behaviour and is now working to complete the measure bridge, strengthen the finite-dimensional reconstruction, and open a controlled path toward continuum physics.