Conclusion and open problems

Scheduler consistency has an exact consequence: legal evaluations of a fixed finite history produce the same records. Acyclic dependency has another: reachability is a partial order. The countermodels show that neither conclusion chooses a light cone.

The matching positive theorem is also exact. An affine realization with a homogeneous, self-dual, irreducible, strictly convex proper influence cone has Lorentz-cone geometry. The standard polyhedral embeddings fail explicit clauses of this hypothesis. The sharper homogeneous strictly convex characterization shows that the pairing need not be assumed if one uses the stronger published selection theorem.

The remaining issue is derivation, not terminology:

Scheduler consistency plus an affine homogeneous strictly convex self-dual influence cone yields a Lorentz cone. Scheduler consistency alone does not produce the affine structure, the automorphism action, or the absence of faces.

The resulting research program has identifiable tasks:

1. construct affine displacement data, or a justified affine completion, from a specified residual theory;

2. prove that operational sensitivity has the required routing and compositional properties;

3. derive homogeneous strictly convex influence geometry, or the explicit axiom $\mathsf{S}$, from the rewrite system rather than assume it;

4. distinguish symmetries of a completed cone from implementable symmetries of records;

5. prove boundary attainability and, where appropriate, Lorentzian manifold realizability;

6. establish transport-aware causal typing for actual programs.

Constructing $V$ from a raw poset is a separate representation problem. Possible approaches through coherent displacement data or simply transitive translation actions remain open here. The present theorem excludes the countermodels as the specified geometric realizations, not as abstract rewrite systems under all conceivable embeddings.

No numerical value of $c$, Einstein equation, preferred spacetime dimension, continuum limit, or quantum measurement rule follows. Even after selecting a cone written as

its numerical slope changes under independent choices of spatial and temporal units. Selecting the Lorentz cone and calibrating physical units are different tasks.

and dependency note. The cone-selection step uses classical symmetric-cone theory and, for its weakening, the precise result of Ito and Lourenço. The causal reconstruction results are invoked only with their Lorentzian hypotheses. No unavailable Enter lemma, residual construction, or companion relay is used as a proof dependency.